2,857 results
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2. Some remarks on a paper by R. R. Yager
- Author
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Erich Peter Klement
- Subjects
Pure mathematics ,Information Systems and Management ,Artificial Intelligence ,Control and Systems Engineering ,Additive function ,Point (geometry) ,Monotonic function ,Fuzzy logic ,Software ,Computer Science Applications ,Theoretical Computer Science ,Mathematics - Abstract
We show that slight technical changes in the definition transform the probability of fuzzy events introduced by R. R. Yager [16] into a new concept of such probabilities having nice properties, both from an intuitive and from a mathematical point of view: monotonicity, additivity, and continuity.
- Published
- 1982
3. Survival functions versus conditional aggregation-based survival functions on discrete space
- Author
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Borzová Jana, Halčinová Lenka, and Basarik Stanislav
- Subjects
Mathematical theory ,Information Systems and Management ,Survival function ,Artificial Intelligence ,Control and Systems Engineering ,Discrete space ,Applied mathematics ,State (functional analysis) ,Characterization (mathematics) ,Software ,Computer Science Applications ,Theoretical Computer Science ,Mathematics - Abstract
In this paper we deal with conditional aggregation-based survival functions recently introduced by Boczek et al. (2020). The concept is worth to study because of its possible implementation in real-life situations and mathematical theory as well. The aim of this paper is the comparison of this new notion with the standard survival function. We state sufficient and necessary conditions under which the generalized and the standard survival function equal. The main result is the characterization of the family of conditional aggregation operators (on discrete space) for which these functions coincide.
- Published
- 2022
4. The strategy of modeling and solving the problems described by Laplace’s equation with uncertainly defined boundary shape and boundary conditions
- Author
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Eugeniusz Zieniuk and Marta Czupryna
- Subjects
Laplace's equation ,Information Systems and Management ,Laplace transform ,Boundary (topology) ,Interval (mathematics) ,Integral equation ,Computer Science Applications ,Theoretical Computer Science ,Interval arithmetic ,Artificial Intelligence ,Control and Systems Engineering ,Applied mathematics ,Measurement uncertainty ,Boundary value problem ,Software ,Mathematics - Abstract
This paper presents a new method for simultaneous modeling the uncertainty of measurement data (necessary to define the boundary shape and boundary conditions) in boundary problems. The interval parametric integral equation system (interval PIES) was developed for solving boundary problems with input data defined in this way. The motivation for conducting this research was that this topic (simultaneous consideration of uncertainties of all input data) has appeared sporadically in the literature (mainly with uncertainly defined boundary conditions or other parameters). In this paper, the uncertainty was defined using interval numbers and modeled using interval arithmetic. The direct application of both classical and directed interval arithmetic caused the overestimation and obtained solutions were useless in practice. Therefore, modification of the directed interval arithmetic was developed. The reliability of the interval PIES solutions obtained using such arithmetic was verified on 2D problems described by Laplace’s equation. The solutions were compared with the interval analytical solutions (differently obtained), as well as with the solutions of exactly defined (without the uncertainty) numerical methods. All performed tests indicated the high potential of the method. Obtained interval solutions occurred to be less overestimated and not as time-consuming as presented alternative methods.
- Published
- 2022
5. Remarks on the cryptanalysis of common prime RSA for IoT constrained low power devices.
- Author
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Mumtaz, Majid and Ping, Luo
- Subjects
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INTERNET of things , *CRYPTOGRAPHY , *MATHEMATICS , *COMMONS , *EXPLANATION - Abstract
• Introduction of the Common Prime RSA and a brief description of its background mathematics. • An overview and explanation of previous CP-RSA cryptanalytic attacks. • Formulation of new cryptanalytic attack on CP-RSA using Lattice Basis Reduction method. • Explanation and detail description of new Cryptanalytic attack solution on CP-RSA. • CP-RSA Speed and efficiency measures w.r.t practical and asymptotic aspects. • Detail explanation and comparison results with the previous CP-RSA cryptanalytic attacks. Standard RSA cryptosystem becomes vulnerable, when private key d < N 0.292 is used inside CryptoChips of constrained devices, thus an alternate scheme is the Common Prime RSA (CP-RSA) variant, which provides cryptographic (decryption/signing) operations. In this paper, we perform a cryptanalytic attack on CP-RSA using lattice basis reduction method that is used to exploit possible vulnerabilities of RSA small private key attacks. In addition, we performed detail experiments on CP-RSA weak or overestimated bounds and compare results to the past studies. Our implemented cryptanalytic attack implicates more precise and direct method to exploit the CP-RSA existing theoretical and experimental bounds. Also, our results prove that CP-RSA is an effective approach that provides resistance against standard RSA small private key attacks. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
6. Dynamic output-feedback control for singular interval-valued fuzzy systems: Linear matrix inequality approach
- Author
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In Seok Park, Nam Kyu Kwon, Chan-eun Park, and PooGyeon Park
- Subjects
Lemma (mathematics) ,Information Systems and Management ,MathematicsofComputing_NUMERICALANALYSIS ,Linear matrix inequality ,Parameterized complexity ,Relaxation (iterative method) ,Fuzzy control system ,Computer Science Applications ,Theoretical Computer Science ,Matrix (mathematics) ,Transformation matrix ,Artificial Intelligence ,Control and Systems Engineering ,Control theory ,Applied mathematics ,Software ,Mathematics - Abstract
This paper introduces an admissibilization condition for singular interval-valued fuzzy systems with a dynamic output-feedback controller using a linear matrix inequality approach. The derivation of the admissibility criterion (satisfying regularity, non-impulsiveness and stability) for the closed-loop system of the singular interval-valued fuzzy systems using the dynamic output-feedback controller is concerned. Here, the derived criterion is represented as the parameterized matrix inequalities depending on the membership functions of the system and the controller. To relax the derived parameterized matrix inequalities, this paper proposes a relaxation lemma based on the properties of the membership functions and their relations. By using this lemma, the parameterized matrix inequalities are converted into the matrix inequalities independent of the membership functions but not convex. Therefore, by introducing the structures of the variables and the congruent transformation matrix , a sufficient condition for the admissibility criterion is successfully given in terms of strict linear matrix inequalities. Two numerical examples are given to show the effectiveness of the proposed control.
- Published
- 2021
7. Cartesian product of sets without repeated elements
- Author
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Carlos Alberto Cobos-Lozada, Jose Torres-Jimenez, Carlos Lara-Alvarez, Alfredo Cardenas-Castillo, and Roberto Blanco-Rocha
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Information Systems and Management ,Stirling numbers of the first kind ,05 social sciences ,050301 education ,Value (computer science) ,Stirling numbers of the second kind ,02 engineering and technology ,Cartesian product ,Computer Science Applications ,Theoretical Computer Science ,Combinatorics ,symbols.namesake ,Cardinality ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,020201 artificial intelligence & image processing ,Multiplication ,0503 education ,Software ,Mathematics ,Integer (computer science) ,Bell number - Abstract
In many applications, like database management systems , is very useful to have an expression to compute the cardinality of cartesian product of k sets without repeated elements; we designate this problem as T ( k ) . The value of | T ( k ) | is upper-bounded by the multiplication of cardinalities of the sets. As long as we have searched, it has not been reported a general expression to compute T ( k ) using cardinalities of the intersections of sets, this is the main topic of this paper. Given three sets with indices { 0 , 1 , 2 } , C i is the cardinality of one set, C i , j ( i j ) and C i , j , l ( i j l ) are respectively the cardinalities of the intersections of 2 and 3 sets, then the searched formulas for T ( k ) are: T ( 1 ) = C 0 ; T ( 2 ) = C 0 C 1 - C 0 , 1 ; T ( 3 ) = C 0 C 1 C 2 - ( C 0 , 1 C 2 + C 0 , 2 C 1 + C 1 , 2 C 0 ) + 2 C 0 , 1 , 2 . In this paper, we prove formulas for computing T ( k ) and its specialization when a set is contained in the next sets. For this purpose, we will use concepts like partitions of the integer k in v parts, Bell numbers, Stirling numbers of the first kind and Stirling numbers of the second kind. Additionally, we present a complexity analysis for the computation of T ( k ) .
- Published
- 2021
8. On the minimality of some generating sets of the aggregation clone on a finite chain
- Author
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Jozef Pócs, Zbyněk Kurač, and Radomír Halaš
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Information Systems and Management ,05 social sciences ,050301 education ,02 engineering and technology ,Computer Science Applications ,Theoretical Computer Science ,Combinatorics ,Set (abstract data type) ,Chain (algebraic topology) ,Artificial Intelligence ,Control and Systems Engineering ,Clone (algebra) ,Bounded function ,Lattice (order) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Bounded lattice ,Finitely-generated abelian group ,0503 education ,Software ,Mathematics - Abstract
Clone theory plays an important role in studying aggregation functions on bounded posets or bounded lattices. Several important classes of aggregation functions on a bounded lattice L form a clone, particularly the set of all aggregation functions on L, the so-called full aggregation clone on L. For any finite lattice L, this clone is known to be finitely generated and various generating sets and their constructions have been presented in recent papers. The aim of this paper is to extend previous results concerning generating sets of aggregation clones on finite chains. Namely, the objective is to discuss the minimality of certain generating bases, the so-called ( χ , ⊕ ) -generating sets.
- Published
- 2021
9. Multi-factor one-order cross-association fuzzy logical relationships based forecasting models of time series.
- Author
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Li, Fang and Yu, Fusheng
- Subjects
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TIME series analysis , *FUZZY sets , *SET theory , *REAL numbers , *MATHEMATICS - Abstract
In the existing multi-factor one-order (MFOO) forecasting models, each fuzzy logical relation (FLR) has one consequent and more than one premise reflecting the association between the fuzzy values at two consecutive moments, and its premises are related to all the factors involved in forecasting. When using such FLRs to realize prediction, no matched FLR cases happened often and thus no logical prediction can be made. Two shortcomings are found for that: one is that more premises make FLRs matching more difficult; the other is that there are no enough FLRs. To overcome these shortcomings, this paper proposes two kinds of FLRs: short cross-association FLRs and long cross-association FLRs, which mean the influence on the consequent is from a part of the factors instead of all the factors. Specifically, the long cross-association FLRs aim at finding the association between fuzzy values at two non-consecutive moments. Such cross-associations exist in reality, the construction of them allows more FLRs to be mined from history observations. They can raise the possibility of finding available FLRs for forecasting. Based on the proposed FLRs, two MFOO forecasting models are proposed. Experiments show the advantage of the new FLRs and the good performance of the proposed models. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
10. Multicriteria decision making based on bi-direction Choquet integrals
- Author
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Fanyong Meng, Shyi-Ming Chen, and Jie Tang
- Subjects
Multicriteria decision ,Information Systems and Management ,05 social sciences ,050301 education ,02 engineering and technology ,Expression (computer science) ,Multiple-criteria decision analysis ,Computer Science Applications ,Theoretical Computer Science ,Algebra ,Choquet integral ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Exponent ,020201 artificial intelligence & image processing ,Convex combination ,Representation (mathematics) ,0503 education ,Software ,Mathematics - Abstract
To deal with multicriteria decision making (MCDM) problems with interaction criteria, the Choquet integral (CI) is one of effective tools. This paper first proposes the reverse Choquet integral (RCI), which defines the importance of the ordered elements in an opposite principle to the CI. To show the principle of the RCI, we offer its concrete expression in view of the Mobius representation by which one can clearly see the difference and the relationship between the CI and the RCI. Then, we propose the “bi-direction Choquet integral” (BDCI), which is a convex combination of the CI and the RCI. To get the interactions of ordered coalitions comprehensively, this paper further proposes the generalized Shapley bi-direction Choquet integral (GSBDCI). Furthermore, the hybrid generalized Shapley bi-direction Choquet integral (HGSBDCI) is proposed, which defines the importance of ordered positions and the criteria with interactions simultaneously. With respect to these types of CIs, their exponent forms are also discussed. Finally, we use an application case to show the utilization of the proposed new CIs for MCDM. The proposed new Choquet integrals provide us a very useful way to deal with MCDM problems.
- Published
- 2021
11. On the existence of solutions to boundary value problems for interval-valued differential equations under gH-differentiability
- Author
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Rosana Rodríguez-López and Hongzhou Wang
- Subjects
Information Systems and Management ,Differential equation ,05 social sciences ,050301 education ,02 engineering and technology ,First order ,Boundary values ,Interval valued ,Computer Science Applications ,Theoretical Computer Science ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,Differentiable function ,Boundary value problem ,0503 education ,Software ,Mathematics - Abstract
In this paper, we study first order interval-valued differential equations with the boundary value condition x(0)=αx(T). By constructing proper operators, some sufficient conditions for the existence of solutions are provided for α∈R⧹{0,1}, corresponding to non-periodic boundary value problems. At the end of this paper, some examples are shown to illustrate the theorems proved.
- Published
- 2021
12. Weights for short quartic Boolean functions
- Author
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Thomas W. Cusick and Younhwan Cheon
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Monomial ,Information Systems and Management ,Rotation symmetry ,05 social sciences ,050301 education ,02 engineering and technology ,Notation ,Computer Science Applications ,Theoretical Computer Science ,Combinatorics ,Artificial Intelligence ,Control and Systems Engineering ,Quartic function ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Invariant (mathematics) ,Boolean function ,0503 education ,Hamming code ,Software ,Mathematics - Abstract
A Boolean function in n variables is 2-rotation symmetric if it is invariant under even powers of ρ ( x 1 , … , x n ) = ( x 2 , … , x n , x 1 ) , but not under the first power (ordinary rotation symmetry); we call such a function a 2-function. A 2-function is called monomial rotation symmetric (MRS) if it is generated by applying powers of ρ 2 to a single monomial. If the quartic MRS 2-function in 2 n variables has a monomial x 1 x q x r x s , then we use the notation 2 - ( 1 , q , r , s ) 2 n for the function. A detailed theory of equivalence of quartic MRS 2-functions in 2 n variables was given in a 2020 paper by Cusick, Cheon and Dougan. This theory divides naturally into two classes, called mf 1 and mf 2 in the paper. Next to describing the equivalence classes, the second major problem is giving details of the linear recursions that the Hamming weights for any sequence of functions 2 - ( 1 , q , r , s ) 2 n (with q r s , say), n = s , s + 1 , … can be shown to satisfy. This problem was solved for the mf 1 case only in the 2020 paper. In this paper the problem for the mf 2 case is solved, using new ideas about short functions, as defined in this paper. These short functions are also of independent interest, and further results about them are in the paper.
- Published
- 2021
13. Exponential stabilization and non-fragile sampled-date dissipative control for uncertain time-varying delay T-S fuzzy systems with state quantization
- Author
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Pengyi Tang and Yuechao Ma
- Subjects
Information Systems and Management ,Quantization (signal processing) ,05 social sciences ,050301 education ,02 engineering and technology ,Fuzzy control system ,Dissipation ,Leibniz formula for π ,Computer Science Applications ,Theoretical Computer Science ,Exponential function ,Exponential stabilization ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Dissipative system ,Applied mathematics ,020201 artificial intelligence & image processing ,0503 education ,Software ,Mathematics - Abstract
In this paper, the problem of exponential dissipation stability of T-S fuzzy system with state quantization is studied by using non-fragile sampled-data control. First, A Lyapunov-Krasovskii function containing all sampled-data and quantization information is constructed. Second, the better results can be obtained by using the integral inequality and the Newton Leibniz formula. In addition, a dissipative controller for non-fragile sampled-data is designed. Finally, The reasonable examples illustrate the significant improvement and value of this paper.
- Published
- 2021
14. And-like-uninorm-based transitivity and analytic hierarchy process with interval-valued fuzzy preference relations
- Author
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Xuan Yang, Xiao-Tong Jin, and Zhou-Jing Wang
- Subjects
Transitive relation ,Mathematical optimization ,Information Systems and Management ,05 social sciences ,Multiplicative function ,050301 education ,Analytic hierarchy process ,02 engineering and technology ,Interval (mathematics) ,Maximization ,Fuzzy logic ,Computer Science Applications ,Theoretical Computer Science ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Quadratic programming ,0503 education ,Decision model ,Software ,Mathematics - Abstract
The framework of interval-valued fuzzy preference relations (IVFPRs) is adequate and effective to model human preference evaluations under indeterminacy. This paper analyzes three recently presented multiplicative transitivity models of IVFPRs and exposes their drawbacks. An and-like-uninorm-based functional transitivity equation is developed to introduce a multiplicative consistency notion for IVFPRs. Based on the transitivity logarithmic equation, a geometric-consistency index is further proposed to compute the inconsistency level of an IVFPR. The paper builds a logarithmic least squares model with row indeterminacy constraints and equivalently transforms it into a quadratic programming model for finding a closed-form solution of the normalized interval-valued fuzzy weights of IVFPRs. A novel method is subsequently presented to check the acceptability of an IVFPR by examining its acceptable consistency and acceptable indeterminacy. An approach including an and-like-uninorm-based maximization model is introduced to aggregate local interval-valued fuzzy weights and an interval fuzzy analytic hierarchy process is designed step-by-step. An illustrative example and a comparison study are utilized to demonstrate the performance and merits of the presented models. Meanwhile, an outstanding undergraduate student selection problem in international exchange is provided to show the application of the proposed decision method.
- Published
- 2020
15. On fuzzy implications determined by aggregation operators
- Author
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Ouyang, Yao
- Subjects
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AGGREGATION operators , *FUZZY sets , *MATHEMATICAL analysis , *SET theory , *OPERATOR theory , *ALGEBRA , *MATHEMATICS , *NUMERICAL analysis - Abstract
Abstract: Fuzzy implication operators play important roles in both theoretical and applied aspects of fuzzy sets theory. Many papers investigated various properties of different types of implications and the interrelationships among these properties. In this paper, we exploit the minimal conditions which must be satisfied for a binary operation A to generate a residual implication with additional properties. It includes several examples to clarify the situation. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
16. Transfer-stable aggregation functions on finite lattices
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Lenka Rýparová, Zbyněk Kurač, and Tomáš Riemel
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Pure mathematics ,Information Systems and Management ,05 social sciences ,050301 education ,02 engineering and technology ,Computer Science Applications ,Theoretical Computer Science ,Artificial Intelligence ,Control and Systems Engineering ,Lattice (order) ,Idempotence ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0503 education ,Software ,Mathematics ,Arithmetic mean - Abstract
The paper by Z. Kurac, 2019 deals with a new property, the so-called transfer-stability, characterizing the arithmetic mean. With this property, it is possible to define special forms of arithmetic mean on finite chains. The idempotence property was required for this definition. In this paper, we neglect this necessity and deal only with transfer-stable aggregation functions. Thanks to this fact, it is possible to define these aggregation functions on any finite lattice (hereinafter “lattice”) and not only on finite chains. Transfer-stable aggregation functions can be defined on any finite lattice. Nevertheless, there is a subclass of finite lattices, the so-called transfer-stable lattices, where the behavior of the transfer-stable aggregation functions is simply described because the transfer-stability classes are linearly ordered. Therefore, the main goal of this paper is characterization of these transfer-stable lattices. The second half of the paper deals with some useful properties associated with the lattice of all k-ary transfer-stable aggregation functions.
- Published
- 2020
17. Comments on “Distinguishability quantification of fuzzy sets”
- Author
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Hefny, Hesham A.
- Subjects
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FUZZY sets , *SET theory , *GAUSSIAN processes , *MATHEMATICS - Abstract
Abstract: This paper presents some comments on the above paper regarding the manipulation of Gaussian fuzzy sets and provides two useful generalized formulas for both of similarity and similarity/possibility relationships of Gaussian fuzzy sets with different widths. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
18. T-sum of sigmoid-shaped fuzzy intervals
- Author
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Hong, Dug Hun, Hwang, Changha, and Kim, Kyung Tae
- Subjects
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MATHEMATICS , *SCIENCE , *CYBERNETICS , *MATHEMATICAL economics - Abstract
Abstract: The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh’s extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation, if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with particular types of fuzzy intervals. Recently, Dombi and Győrbíró [J. Dombi, N. Győrbíró, Additions of sigmoid-shaped fuzzy intervals using the Dombi operator and infinite sum theorems, Fuzzy Sets and Systems 157 (2006) 952–963] proved that addition is closed if the Dombi t-norm is used with sigmoid-shaped fuzzy intervals. In this paper, we define a broader class of sigmoid-shaped fuzzy intervals. Then, we study t-norms that are consistent with these particular types of fuzzy intervals. Dombi and Győrbíró’s results are special cases of the results described in this paper. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
19. Interactive balance space approach for solving multi-level multi-objective programming problems
- Author
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Abo-Sinna, Mahmoud A. and Baky, Ibrahim A.
- Subjects
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MATHEMATICAL programming , *DECISION making , *PROBLEM solving , *MATHEMATICS - Abstract
Abstract: This paper studies a multi-level multi-objective decision-making (ML-MODM) problems with linear or non-linear constraints. The objective functions at each level are non-linear functions, which are to be maximized or minimized. This paper presents a three-level multi-objective decision-making (TL-MODM) model and an interactive algorithm for solving such a model. The algorithm simplifies three-level multi-objective decision-making problems by transforming them into separate multi-objective decision making problems at each level, thereby avoiding the difficulty associated with non-convex mathematical programming. Our algorithm is an extension of the work of Shi and Xia [X. Shi, H. Xia, Interactive bi-level multi-objective decision making, Journal of the Operational Research Society 48 (1997) 943–949], which dealt with interactive bi-level multi-objective decision-making problems, with some modifications in assigning satisfactoriness to each objective function in all the levels of the TL-MODM problem. Also, we solve each separate multi-objective decision making problem of the TL-MODM problem by the balance space approach. A new formula is introduced to interconnect the satisfactoriness and the proportions of deviation needed to reflect the relative importance of each objective function. Thus, we have the proportions of deviation including satisfactoriness. In addition, we present new definitions for the satisfactoriness and the preferred solution in view of singular-level multi-objective decision making problems that corresponds to the η-optimal solution of the balance space approach. Also, new definitions for the feasible solution and the preferred solution (η-optimal point) of the TL-MODM problem are presented. An illustrative numerical example is given to demonstrate the algorithm. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
20. Cognitive high level information fusion
- Author
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Perlovsky, Leonid I.
- Subjects
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SEMANTICS , *MATHEMATICS , *INFORMATION services , *SEARCH engines - Abstract
Abstract: Fusion of sensor and communication data currently can only be performed at a late processing stage after sensor and textual information are formulated as logical statements at appropriately high level of abstraction. Contrary to this it seems, the human mind integrates sensor and language signals seamlessly, before signals are understood, at pre-conceptual level. Learning of conceptual contents of the surrounding world depends on language and vice versa. The paper describes a mathematical technique for such integration. It combines fuzzy dynamic logic with dual cognitive-language models. The paper briefly discusses relationships between the proposed mathematical technique, working of the mind and applications to understanding-based search engines. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
21. An introduction to vague complemented ordered sets
- Author
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Demirci, Mustafa and Eken, Zeynep
- Subjects
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FUZZY sets , *MATHEMATICAL logic , *SET theory , *MATHEMATICS - Abstract
Abstract: The purpose of this paper is to introduce a theory of fuzzily defined complement operations on nonempty sets equipped with fuzzily defined ordering relations. Many-valued equivalence relation-based fuzzy ordering relations (also called vague ordering relations) provide a powerful and a comprehensive mathematical modelling of fuzzily defined partial ordering relations. For this reason, starting with a nonempty set X equipped with a many-valued equivalence relation and a vague ordering relation, a fuzzily defined complement operation (called a vague complement operation) on X will be formulated by means of the underling many-valued equivalence relation and vague ordering relation. Because of the fact that the practical implementations of vague complement operations basically depend on their representation properties, a considerable part of this paper is devoted to the representations of vague complement operations. In addition to this, the present paper provides various nontrivial examples for vague complements, and introduces a many-valued logical interpretation of quantum logic as a real application of vague complements. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
22. Roughness in rings.
- Author
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Davvaz, B.
- Subjects
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ROUGH sets , *SET theory , *RING theory , *ALGEBRA , *APPROXIMATION theory , *MATHEMATICS - Abstract
In this paper basic notions of the rough set theory will be given. In fact, the paper concerns a relationship between rough sets and ring theory. We shall introduce the notion of rough subring (resp. ideal) with respect to an ideal of a ring which is an extended notion of a subring (resp. ideal) in a ring, and we shall give some properties of the lower and the upper approximations in a ring. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
23. On matching of intuitionistic fuzzy sets
- Author
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Grażyna Szkatuła and Maciej Krawczak
- Subjects
Information Systems and Management ,Mathematics::General Mathematics ,05 social sciences ,Mathematical properties ,050301 education ,Intuitionistic fuzzy ,02 engineering and technology ,Computer Science Applications ,Theoretical Computer Science ,Algebra ,Mathematics::Logic ,Artificial Intelligence ,Control and Systems Engineering ,Computer Science::Logic in Computer Science ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0503 education ,Software ,Mathematics - Abstract
In the paper, we describe the new measure of matching two intuitionistic fuzzy sets. The operations known in the intuitionistic fuzzy set theory are used, and the perturbation of one intuitionistic fuzzy set by another intuitionistic fuzzy set is understood as an impact of one intuitionistic fuzzy set on another intuitionistic fuzzy set. The opposite case can also be considered wherein the second intuitionistic fuzzy set is perturbed by the first one. The introduced measure of the perturbation of one intuitionistic fuzzy set by another intuitionistic fuzzy set is considered instead of commonly used distance between two intuitionistic fuzzy sets. In general, the new measure can be asymmetric and therefore can provide more information compare to a distance between intuitionistic fuzzy sets. The values of such measures of intuitionistic fuzzy sets’ perturbation are ranged between 0 and 1. In this paper specific mathematical properties of the measure of intuitionistic fuzzy sets’ perturbation are studied. The presented methodology is explained by several illustrative examples.
- Published
- 2020
24. Pareto optimal strategy for linear stochastic systems with H∞ constraint in finite horizon
- Author
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Xiushan Jiang, Senping Tian, Weihai Zhang, and Tianliang Zhang
- Subjects
Mathematical optimization ,Information Systems and Management ,05 social sciences ,Pareto principle ,050301 education ,02 engineering and technology ,State (functional analysis) ,Computer Science Applications ,Theoretical Computer Science ,Constraint (information theory) ,Noise ,Artificial Intelligence ,Control and Systems Engineering ,Control theory ,Differential game ,0202 electrical engineering, electronic engineering, information engineering ,Key (cryptography) ,Initial value problem ,020201 artificial intelligence & image processing ,0503 education ,Software ,Mathematics - Abstract
In this paper, we derive conditions for the existence of Pareto efficient strategy and Pareto solution under H∞ constraint for the linear quadratic (LQ) finite horizon cooperative differential game of stochastic systems with state-, control- and disturbance-multiplicative noise. Firstly, we present a stochastic bounded real lemma (SBRL) with any initial condition for the considered stochastic system. Next, a necessary and sufficient condition for Pareto optimal strategy under the H∞ constraint is researched by two cross-coupled generalized differential Riccati equations (GDREs), which is the key contribution of this paper. Another contribution is that the Pareto solution for every controller is given under the Pareto efficient strategy and worst-case external disturbance . Finally, a practical example is given to illustrate the effectiveness of our results.
- Published
- 2020
25. A refined Hölder’s inequality for Choquet expectation by Cauchy-Schwarz’s inequality
- Author
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Hamzeh Agahi
- Subjects
Information Systems and Management ,Series (mathematics) ,Inequality ,media_common.quotation_subject ,05 social sciences ,050301 education ,02 engineering and technology ,Measure (mathematics) ,Computer Science Applications ,Theoretical Computer Science ,Submodular set function ,Monotone polygon ,Choquet integral ,Artificial Intelligence ,Control and Systems Engineering ,Converse ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0503 education ,Mathematical economics ,Cauchy–Schwarz inequality ,Software ,Mathematics ,media_common - Abstract
Recently, Torra, Narukawa and Sugeno [Fuzzy Sets and Systems, 292 (2016) 364–379] obtained the Cauchy-Schwarz inequality for Choquet integral. In this paper, we first introduce a refined Holder’s inequality in Choquet calculus. Then by this inequality, we show that Cauchy-Schwarz inequality and Holder’s inequality for Choquet integral are equivalent only when the monotone measure is submodular or the integrands are comonotonic, thus closing the series of papers in this literature. Note that it is obvious that Holder’s inequality implies Cauchy-Schwarz’s inequality. But the converse is an interesting subject. This paper focuses on this subject.
- Published
- 2020
26. On the f-divergence for discrete non-additive measures
- Author
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Michio Sugeno, Yasuo Narukawa, and Vicenç Torra
- Subjects
Pure mathematics ,Information Systems and Management ,05 social sciences ,050301 education ,f-divergence ,02 engineering and technology ,Interval (mathematics) ,Absolute continuity ,Measure (mathematics) ,Computer Science Applications ,Theoretical Computer Science ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Hellinger distance ,0503 education ,Software ,Sign (mathematics) ,Mathematics - Abstract
In this paper we study the definition of the f-divergence and the Hellinger distance for non-additive measures in the discrete case. As these measures are based on the derivatives of the measures, we consider the problem of defining the Radon–Nikodym derivative of a non-additive measure. While Radon–Nikodym derivatives for additive measures exist for absolutely continuous measures, this is not the case in the non-additive case. In this paper we will define set-directional and upper, lower and interval derivatives. We will also define when two measures have the same sign. These definitions will be used to introduce alternative definitions of the f-divergence, all extending the classical definition to non-additive measures.
- Published
- 2020
27. Equivalence of 2-rotation symmetric quartic Boolean functions
- Author
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Younhwan Cheon, Thomas W. Cusick, and Kelly Dougan
- Subjects
Monomial ,Sequence ,Information Systems and Management ,05 social sciences ,050301 education ,02 engineering and technology ,Function (mathematics) ,Computer Science Applications ,Theoretical Computer Science ,Combinatorics ,Artificial Intelligence ,Control and Systems Engineering ,Quartic function ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Invariant (mathematics) ,Boolean function ,0503 education ,Equivalence (measure theory) ,Rotation (mathematics) ,Software ,Mathematics - Abstract
A Boolean function in n variables is 2-rotation symmetric if it is invariant under even powers of ρ ( x 1 , … … , x n ) = ( x 2 , … , x n , x 1 ) , but not under the first power (ordinary rotation symmetry); we call such a function a 2-function. A 2-function is called monomial rotation symmetric (MRS) if it is generated by applying powers of ρ2 to a single monomial. If the quartic MRS 2-function in 2n variables has a monomial x1xqxrxs, then we use the notation 2-(1, q, r, s)2n for the function. This paper gives a detailed theory of equivalence of quartic MRS 2-functions in 2n variables. Such a theory was provided for the cubic MRS 2-functions in two 2015 papers of Cusick and Johns. As in the earlier papers, the two main topics in the theory are describing the affine equivalence classes of the functions under certain groups of permutations; and giving details of the linear recursions that the Hamming weights of any sequence of functions 2-(1, q, r, s)2n (with q n = s , s + 1 , … can be shown to satisfy. The discussion for both of these topics uses new ideas because the quartic theory naturally divides into two cases.
- Published
- 2020
28. Extended Karush-Kuhn-Tucker condition for constrained interval optimization problems and its application in support vector machines
- Author
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Debdas Ghosh, Kaushal K. Shukla, Abhishek Kumar Singh, and Kartik Manchanda
- Subjects
Information Systems and Management ,Optimization problem ,Karush–Kuhn–Tucker conditions ,05 social sciences ,050301 education ,02 engineering and technology ,Interval (mathematics) ,Computer Science Applications ,Theoretical Computer Science ,Support vector machine ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,0503 education ,Software ,Mathematics - Abstract
In this paper, we correct some errors in the extended first and second Gordan’s theorems in a recent paper—Information Sciences 504 (2019) 276–292.
- Published
- 2019
29. Optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by Dubois-Prade family of t-norms
- Author
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Amin Ghodousian
- Subjects
Mathematical optimization ,Information Systems and Management ,Current (mathematics) ,Inequality ,media_common.quotation_subject ,05 social sciences ,Feasible region ,050301 education ,02 engineering and technology ,Fuzzy control system ,Resolution (logic) ,Composition (combinatorics) ,Fuzzy logic ,Computer Science Applications ,Theoretical Computer Science ,Intersection ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,0503 education ,Software ,media_common ,Mathematics - Abstract
In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated In doing so, the feasible region is formed by the intersection of two inequality fuzzy systems and Dubois-Prade family of t-norms which are considered as fuzzy composition. The most well-known continuous t-norms are Archimedean such as Frank, Yager, Hamacher, Sugeno-Weber and Schweizer-Sklar family. An interesting family of t-norms that is not Archimedean has been introduced by Dubois and Prade. In this paper, the resolution of the feasible region of the problem is initialy investigated when it is defined with max-Duboise-Prade composition. A necessary and sufficient condition along with three other necessary conditions are derived for determining the feasibility. of the problem. Moreover, two procedures have also been presented with the aim of simplifying the current linear problems. A method is proposed to generate random feasible max-Dubois-Prade fuzzy relational inequalities and an algorithm is accordingly presented to solve the problem. Finally, an example is described to illustrate this algorithm.
- Published
- 2019
30. Axiomatic property based consistency analysis and decision making with interval multiplicative reciprocal preference relations
- Author
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Zhou-Jing Wang, Jian Lin, and Fang Liu
- Subjects
Transitive relation ,Information Systems and Management ,05 social sciences ,Multiplicative function ,050301 education ,02 engineering and technology ,Interval (mathematics) ,Measure (mathematics) ,Computer Science Applications ,Theoretical Computer Science ,Artificial Intelligence ,Control and Systems Engineering ,Consistency (statistics) ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,Multiplication ,0503 education ,Software ,Reciprocal ,Axiom ,Mathematics - Abstract
This paper focuses on obtaining an interval extension of Saaty's consistency and eliciting normalized interval weights in analytic form from interval multiplicative reciprocal preference relations (IMRPRs) as well as checking acceptability of IMRPRs. Four axiomatic properties are presented to characterize multiplicative consistency of IMRPRs. The paper shows that six existing consistency definitions fail to satisfy all the four axiomatic properties. A constrained interval multiplication based transitivity equation is devised and an interval matrix is constructed to capture original preferences and row uncertainty proportionalities of an IMRPR. Based on the constructed interval matrix, an ordinary interval multiplication based transitivity equation is developed to define consistency of IMRPRs. A logarithmic least square model is established to find normalized interval weights from IMRPRs and its analytic solution is obtained by the Lagrangian multiplier method. The paper introduces an index to measure uniformity of row uncertainties in an IMRPR and proposes a geometric consistency index to measure inconsistency of IMRPRs. A novel method is put forward to determine acceptability of IMRPRs by checking acceptable consistency and acceptable uncertainty. The proposed models are illustrated by eight numerical examples and a hierarchical multi-criteria decision making problem dealing with recommending undergraduate students to graduate admission.
- Published
- 2019
31. The lattice and matroid representations of definable sets in generalized rough sets based on relations
- Author
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Zhaohao Wang, Hong Wang, and Qinrong Feng
- Subjects
Transitive relation ,Pure mathematics ,Information Systems and Management ,Closed set ,High Energy Physics::Lattice ,05 social sciences ,050301 education ,Distributive lattice ,02 engineering and technology ,Matroid ,Computer Science Applications ,Theoretical Computer Science ,Definable set ,Distributive property ,Artificial Intelligence ,Control and Systems Engineering ,Lattice (order) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Rough set ,0503 education ,Software ,Mathematics - Abstract
The definable set is a core concept in rough set theory . It plays an important role in the characterizations of rough sets. In this paper, we study the lattice and matroid representations of definable sets in generalized rough sets based on relations. First, we propose the lower definable lattice, consisting of all lower definable sets with set inclusion order. Then we give some conditions under which the lower definable lattice is distributive (or geometric, or Boolean). Furthermore, we discuss the relationship between distributive lattices and the lower definable lattices in generalized approximation spaces based on reflexive and transitive relations . On the one hand, we show that the lower definable lattice in a generalized approximation space based on reflexive and transitive relation is distributive. On the other hand, we obtain the result that a distributive lattice can induce a lower definable lattice in a generalized approximation space based on a reflexive and transitive relation. Finally, we investigate the combination of generalized rough sets and matroids in terms of the lower definable lattice. We show that if a lower definable lattice is a lattice of closed sets of a matroid, then it must be an open-closed set lattice of a matroid. In addition, we prove that some lower definable lattices are not the lattices of closed sets of matroids. These results of this paper will benefit to our understanding of the relationship between matroids and generalized rough sets based on relations.
- Published
- 2019
32. Consistency and optimized priority weight analytical solutions of interval multiplicative preference relations
- Author
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Zhou-Jing Wang and Jian Lin
- Subjects
Information Systems and Management ,Logarithm ,Computation ,05 social sciences ,Multiplicative function ,050301 education ,02 engineering and technology ,Interval (mathematics) ,Computer Science Applications ,Theoretical Computer Science ,Interval arithmetic ,symbols.namesake ,Artificial Intelligence ,Control and Systems Engineering ,Consistency (statistics) ,Lagrange multiplier ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Applied mathematics ,020201 artificial intelligence & image processing ,Weight ,0503 education ,Software ,Mathematics - Abstract
This paper focuses on answering the following question: How to estimate the quality of off-diagonal judgments in an interval multiplicative preference relation (IMPR) and obtain an analytical solution to the optimized interval priority weight vector of an IMPR. By generalizing IMPRs, an interval-multiplication-based transitivity equation is devised to define perfect consistency of generalized IMPRs. A basic interval multiplicative weight (IMW) vector is introduced to characterize different interval weight vectors with equivalency and used as a priority weight benchmark of a generalized IMPR. Two logarithmic least square models are established for determining basic IMWs of a generalized IMPR, and their analytical solutions are found by using the Lagrangian multiplier method. The paper demonstrates that any IMPR with uncertainty has no perfect consistency in terms of interval arithmetic , and constructs a generalized IMPR from an IMPR to introduce consistency of off-diagonal judgments in an IMPR. Two computation formulas are developed to obtain optimized basic IMWs of an IMPR, which can entirely capture off-diagonal judgments if the IMPR is consistent. Numerical examples are offered to illustrate how to apply the proposed models and a comparative study is made to show that off-diagonal judgments in an inconsistent IMPR are properly captured by the analytical solution based IMWs.
- Published
- 2019
33. Covering rough set structures for a locally finite covering approximation space
- Author
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Sang-Eon Han
- Subjects
Pure mathematics ,Information Systems and Management ,Generalization ,05 social sciences ,050301 education ,02 engineering and technology ,Space (mathematics) ,Computer Science Applications ,Theoretical Computer Science ,Set (abstract data type) ,Operator (computer programming) ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Order (group theory) ,Digital geometry ,020201 artificial intelligence & image processing ,Information geometry ,Rough set ,0503 education ,Software ,Mathematics - Abstract
The purpose of this paper is to introduce the notion of locally finite covering approximation (LFC-, for brevity) space (U, C) which is a generalization of a (finite) covering approximation space. Furthermore, for a subset X of the universe U, we develop two kinds of neighborhood systems derived from the covering C, specifically K1(X) and K2(X) which are not comparable with each other. Next, the paper establishes two topologies on U, Alexandroff, and quasi-discrete topologies generated by systems K1(X) and K2(X) as bases, respectively. After suggesting many examples explaining the above notions and systems, we develop two new types of rough set structures, an H-rough set operator (H*, H*) and a Khalimsky (K-, for short) topological rough set operator ( D K − , D K + ) . The present paper investigates various properties of these operators and refers to certain advantages of them which can be used in applied science including digital geometry, information geometry, computer vision, pattern recognition, image processing, and so on. In order to accomplish this, we use some tools such as granulations, neighborhood systems, typical Pawlak’s tools, related topologies, rough set structures associated with the K-topology, and so on. Furthermore, through this work, we can obtain strong connections between covering rough set theory and applied geometry. In the present paper all sets U, C and X(⊆U) need not be finite.
- Published
- 2019
34. On generating sets of the clone of aggregation functions on finite lattices
- Author
-
Radko Mesiar, Jozef Pócs, and Radomír Halaš
- Subjects
Information Systems and Management ,General method ,Unary operation ,Singleton ,05 social sciences ,050301 education ,Binary number ,02 engineering and technology ,Computer Science Applications ,Theoretical Computer Science ,Combinatorics ,Artificial Intelligence ,Control and Systems Engineering ,Lattice (order) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Bounded lattice ,0503 education ,Finite set ,Software ,Mathematics - Abstract
In a recent paper [12] we have shown that aggregation functions on a bounded lattice L form a clone, i.e., the set of functions closed under projections and composition of functions. Moreover, for any finite lattice L we gave a finite set of unary and binary aggregation functions on L from which the aggregation clone is generated. In this paper, a general method for constructing generating sets of the aggregation clone on L is presented. Our approach is based on extending of L-valued capacities leading to so-called full systems of aggregation functions. Several full systems on L are presented (including singleton ones) and their arities are discussed.
- Published
- 2019
35. Discrete bipolar pseudo-integrals
- Author
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Biljana Mihailovic, Endre Pap, and Mirjana Strboja
- Subjects
0209 industrial biotechnology ,Lemma (mathematics) ,Pure mathematics ,Information Systems and Management ,Order (ring theory) ,02 engineering and technology ,Characterization (mathematics) ,Type (model theory) ,Computer Science Applications ,Theoretical Computer Science ,020901 industrial engineering & automation ,Monotone polygon ,Artificial Intelligence ,Control and Systems Engineering ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Astrophysics::Solar and Stellar Astrophysics ,020201 artificial intelligence & image processing ,Astrophysics::Galaxy Astrophysics ,Software ,Mathematics - Abstract
In the authors paper (Strboja et al., 2016) [42] , the notion of the bipolar pseudo-integral has been introduced. This paper extends investigations related to this new type of bipolar integrals defined with respect to ⊕-decomposable bi-capacities. We consider the main properties of the discrete bipolar pseudo-integral. A characterization theorem for the discrete bipolar pseudo-integral is proven. Monotone convergence theorems and the Fatou type lemma for the discrete bipolar pseudo-integral are considered. In order to illustrate obtained results, many interesting examples are provided.
- Published
- 2018
36. Binary generating set of the clone of idempotent aggregation functions on bounded lattices
- Author
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Jozef Pócs, Radko Mesiar, Radomír Halaš, and Zbyněk Kurač
- Subjects
Information Systems and Management ,05 social sciences ,050301 education ,Binary number ,02 engineering and technology ,Upper and lower bounds ,Computer Science Applications ,Theoretical Computer Science ,Combinatorics ,Artificial Intelligence ,Control and Systems Engineering ,Lattice (order) ,Bounded function ,Idempotence ,0202 electrical engineering, electronic engineering, information engineering ,Generating set of a group ,020201 artificial intelligence & image processing ,Ternary operation ,0503 education ,Software ,Mathematics - Abstract
In a recent paper Botur et al. (2018) we have presented a generating set of the clone of idempotent aggregation functions on bounded lattices . As the main result we have shown that this clone is generated by certain ternary idempotent functions from which all idempotent aggregation functions of L can be obtained by usual term composition. The aim of this paper is to present an essential improvement of the result above by presenting a new generating set of this clone. A bit artificial ternary functions are substituted here by natural (binary) lattice a-medians and certain binary characteristic functions. Consequently, the clone is generated by its binary part and the result strengthens the essential role of medians within all idempotent aggregation functions. Moreover, we will show that for an n-element lattice L, the upper bound of binary generators is 2 n − 1 .
- Published
- 2018
37. A goal programming approach to deriving interval weights in analytic form from interval Fuzzy preference relations based on multiplicative consistency
- Author
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Zhou-Jing Wang
- Subjects
0209 industrial biotechnology ,Information Systems and Management ,Normalization model ,Computation ,02 engineering and technology ,Interval (mathematics) ,Fuzzy logic ,Computer Science Applications ,Theoretical Computer Science ,symbols.namesake ,020901 industrial engineering & automation ,Artificial Intelligence ,Control and Systems Engineering ,Lagrange multiplier ,Goal programming ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Applied mathematics ,020201 artificial intelligence & image processing ,Uniqueness ,Preference (economics) ,Software ,Mathematics - Abstract
This paper focuses on how to find an analytic solution of optimal interval weights from consistent interval fuzzy preference relations (IFPRs) and obtain approximate-solution-based interval weights in analytic form from inconsistent IFPRs. The paper first analyzes the popularly used interval weight additive normalization model and illustrates its drawbacks on the existence and uniqueness for characterizing ]0, 1[-valued interval weights obtained from IFPRs. By examining equivalency of ]0, 1[-valued interval weight vectors, a novel framework of multiplicatively normalized interval fuzzy weights (MNIFWs) is then proposed and used to define multiplicatively consistent IFPRs. The paper presents significant properties for multiplicatively consistent IFPRs and their associated MNIFWs. These properties are subsequently used to establish two goal programming (GP) models for obtaining optimal MNIFWs from consistent IFPRs. By the Lagrangian multiplier method, analytic solutions of the two GP models are found for consistent IFPRs. The paper further devises a two-step procedure for deriving approximate-solution-based MNIFWs in analytic form from inconsistent IFPRs. Two visualized computation formulas are developed to determine the left and right bounds of approximate-solution-based MNIFWs of any IFPR. The paper shows that this approximate solution is an optimal solution if an IFPR is multiplicatively consistent. Three numerical examples including three IFPRs and comparative analyses are offered to demonstrate rationality and validity of the developed model.
- Published
- 2018
38. Quaternion polar harmonic Fourier moments for color images
- Author
-
Chuan Zhang, Yongwei Li, Zhiqiu Xia, Chunpeng Wang, and Xingyuan Wang
- Subjects
Information Systems and Management ,Color image ,Zernike polynomials ,Mathematical analysis ,Cognitive neuroscience of visual object recognition ,Phase (waves) ,020206 networking & telecommunications ,Harmonic (mathematics) ,02 engineering and technology ,Iterative reconstruction ,Computer Science Applications ,Theoretical Computer Science ,symbols.namesake ,Fourier transform ,Artificial Intelligence ,Control and Systems Engineering ,Computer Science::Computer Vision and Pattern Recognition ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,020201 artificial intelligence & image processing ,Quaternion ,Software ,Mathematics - Abstract
This paper proposes quaternion polar harmonic Fourier moments (QPHFM) for color image processing and analyzes the properties of QPHFM. After extending Chebyshev–Fourier moments (CHFM) to quaternion Chebyshev-Fourier moments (QCHFM), comparison experiments, including image reconstruction and color image object recognition, on the performance of QPHFM and quaternion Zernike moments (QZM), quaternion pseudo-Zernike moments (QPZM), quaternion orthogonal Fourier-Mellin moments (QOFMM), QCHFM, and quaternion radial harmonic Fourier moments (QRHFM) are carried out. Experimental results show QPHFM can achieve an ideal performance in image reconstruction and invariant object recognition in noise-free and noisy conditions. In addition, this paper discusses the importance of phase information of quaternion orthogonal moments in image reconstruction.
- Published
- 2018
39. Subjective foundation of possibility theory: Anscombe-Aumann approach.
- Author
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Giang, Phan H.
- Subjects
- *
PROBABILITY theory , *MATHEMATICAL variables , *MATHEMATICS , *MATHEMATICAL logic , *FUTURE contingents (Logic) - Abstract
This paper presents a new characterization of subjective possibility theory. Anscombe and Aumann [1] pioneered a multiple-variable approach to characterize the subjective probability on the basis of its relationship with objective probability. We generalize the Anscombe-Aumann approach to define subjective possibility theory. To characterize the uncertainty of the variable of interest ( H ) we consider its relationship with a variable of probability and a variable of ignorance. Our axiomatization assumes that the preference over the acts contingent on the outcomes of the variables is a weak order and satisfies a monotonicity property; the preference over probabilistic lotteries is represented by linear utility; and the preference over acts under ignorance by a recently developed τ -anchor utility theory. We show that if H and the variable of ignorance are completely reversible in Anscombe-Aumann’s sense and H and the variable of probability are partially reversible then the uncertainty of H must obey the laws of possibility theory. We outline a framework to manage heterogeneous uncertainty that includes probability, possibility and ignorance in decision making. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
40. On generating of idempotent aggregation functions on finite lattices
- Author
-
Jozef Pócs, Michal Botur, Radko Mesiar, and Radomír Halaš
- Subjects
Information Systems and Management ,Unary operation ,High Energy Physics::Lattice ,05 social sciences ,050301 education ,Binary number ,Mathematics - Rings and Algebras ,02 engineering and technology ,Computer Science Applications ,Theoretical Computer Science ,Combinatorics ,Rings and Algebras (math.RA) ,Artificial Intelligence ,Control and Systems Engineering ,Lattice (order) ,Idempotence ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Generating set of a group ,020201 artificial intelligence & image processing ,Ternary operation ,0503 education ,Software ,06B99 ,Mathematics - Abstract
In a recent paper we proposed the study of aggregation functions on lattices via clone theory approach. Observing that aggregation functions on lattices just correspond to $0,1$-monotone clones, we have shown that all aggregation functions on a finite lattice $L$ can be obtained as usual composition of lattice operations $\wedge,\vee$, and certain unary and binary aggregation functions. The aim of this paper is to present a generating set for the class of intermediate (or, equivalently, idempotent) aggregation functions. This set consists of lattice operations and certain ternary idempotent aggregation functions., Comment: 18 pages
- Published
- 2018
41. Incremental anomaly detection using two-layer cluster-based structure
- Author
-
Stan Matwin, Mahdi Mohammadi, Elnaz Bigdeli, and Bijan Raahemi
- Subjects
Information Systems and Management ,business.industry ,Probabilistic logic ,Pattern recognition ,02 engineering and technology ,Mixture model ,Automatic summarization ,Computer Science Applications ,Theoretical Computer Science ,Constant false alarm rate ,Support vector machine ,Reduction (complexity) ,ComputingMethodologies_PATTERNRECOGNITION ,Artificial Intelligence ,Control and Systems Engineering ,020204 information systems ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Anomaly detection ,Artificial intelligence ,Representation (mathematics) ,business ,Software ,Mathematics - Abstract
Anomaly detection algorithms face several challenges, including processing speed, adapting to changes in dynamic environments, and dealing with noise in data. In this paper, a two-layer cluster-based anomaly detection structure is presented which is fast, noise-resilient and incremental. The proposed structure comprises three main steps. In the first step, the data are clustered. The second step is to represent each cluster in a way that enables the model to classify new instances. The Summarization based on Gaussian Mixture Model (SGMM) proposed in this paper represents each cluster as a GMM. In the third step, a two-layer structure efficiently updates clusters using GMM representation, while detecting and ignoring redundant instances. A new approach, called Collective Probabilistic Labeling (CPL) is presented to update clusters incrementally. This approach makes the updating phase noise-resistant and fast. An important step in the updating is the merging of new clusters with existing ones. To this end, a new distance measure is proposed, which is a modified Kullback–Leibler distance between two GMMs. In most real-time anomaly detection applications, incoming instances are often similar to previous ones. In these cases, there is no need to update clusters based on duplicates, since they have already been modeled in the cluster distribution. The two-layer structure is responsible for identifying redundant instances. Ignoring redundant instances, which are typically in the majority, makes the detection phase faster. The proposed method is found to lower the false alarm rate, which is one of the basic problems for the one-class SVM. Experiments show the false alarm rate is decreased from 5% to 15% among different datasets, while the detection rate is increased from 5% to 10% in different datasets with two-layer structure. The memory usage for the two-layer structure is 20 to 50 times less than that of one-class SVM. The one-class SVM uses support vectors in labeling new instances, while the labeling of the two-layer structure depends on the number of GMMs. The experiments show that the two-layer structure is 20 to 50 times faster than the one-class SVM in labeling new instances. Moreover, the updating time of the two-layer structure is two to three times less than for a one-layer structure. This reduction is the result of using two-layer structure and ignoring redundant instances.
- Published
- 2018
42. Autocratic multiattribute group decision making for hotel location selection based on interval-valued intuitionistic fuzzy sets
- Author
-
Shou-Hsiung Cheng
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Information Systems and Management ,Degree (graph theory) ,Group (mathematics) ,business.industry ,Intuitionistic fuzzy ,02 engineering and technology ,Ideal solution ,Interval valued ,Computer Science Applications ,Theoretical Computer Science ,Group decision-making ,020901 industrial engineering & automation ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Artificial intelligence ,business ,Software ,Selection (genetic algorithm) ,Mathematics ,Drawback - Abstract
In this paper, we propose a new autocratic multiattribute group decision making (AMAGDM) method for hotel location selection based on interval-valued intuitionistic fuzzy sets (IVIFSs), where the evaluating values of the attributes for alternatives and the weights of the attributes given by decision makers are represented by interval-valued intuitionistic fuzzy values (IVIFVs). The proposed method calculates the changing of the weights of the decision makers until the group consensus degree (GCD) of the decision makers is larger than or equal to a predefined threshold value. We also apply the proposed AMAGDM method to deal with the hotel location selection problem. The main contribution of this paper is that we propose a new AMAGDM method which is simpler than Wibowo's method (2013), where the drawback of Wibowo's method is that it is too complicated due to the fact that it adopts the concept of ideal solutions for determining the overall performance of each hotel location alternative with respect to all the selection criteria. The proposed AMAGDM method provides us with a very useful way for AMAGDM in interval-valued intuitionistic fuzzy environments.
- Published
- 2018
43. Twist tensor total variation regularized-reweighted nuclear norm based tensor completion for video missing area recovery
- Author
-
Sudhish N. George and Baburaj Madathil
- Subjects
Information Systems and Management ,MathematicsofComputing_NUMERICALANALYSIS ,Matrix norm ,Tensor completion ,020206 networking & telecommunications ,02 engineering and technology ,Topology ,Computer Science Applications ,Theoretical Computer Science ,Singular value ,Artificial Intelligence ,Control and Systems Engineering ,Norm (mathematics) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Tensor ,Twist ,Algorithm ,Software ,Mathematics - Abstract
This paper focuses on recovering multi-dimensional signal called tensor which is corrupted by random missing areas. The performance of the conventional tensor completion techniques deteriorate when the tensor multi-rank is large and/or large missing areas. Moreover, these techniques are weak in preserving the edges in the signals like images/videos. This paper proposes an efficient method to overcome these problems by simultaneously combining novel twist tensor total variation norm to exploit spatio-temporal correlation and tensor-Singular Value Decomposition (t-SVD) based reweighted nuclear norm to improve low multi-rank tensor recovery. The twist tensor total variation norm takes care of edges in the recovered data and aids the recovery of missing areas by utilising the similarities in the adjacent samples. The reweighted nuclear norm handles corrupted large rank tensors by sparsity enhancement via reweighting its singular values. The effectiveness of the proposed method is established by applying to video completion problem, and experimental results reveal that the algorithm outperforms its counterparts.
- Published
- 2018
44. ELECTRE methods in prioritized MCDM environment
- Author
-
Xiuli Qi, Suojuan Zhang, Xiaohan Yu, and Xianglin Liao
- Subjects
Multicriteria decision ,Information Systems and Management ,Management science ,020209 energy ,Data_MISCELLANEOUS ,Assertion ,02 engineering and technology ,Multiple-criteria decision analysis ,Fuzzy logic ,Computer Science Applications ,Theoretical Computer Science ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Special case ,ELECTRE ,Software ,Mathematics - Abstract
In most cases, ELECTRE methods just apply to traditional multicriteria decision making (MCDM) problems with independent criteria. However, there exist more or less interdependences among criteria in actual situations. A special case is MCDM with prioritizations among criteria, called prioritized MCDM. In recent years, how to deal with MCDM problems in the environment of prioritized criteria becomes hot topic increasingly. Lots of existing methods, including PROMETHEE, are modified for the prioritized MCDM, but the advantages of ELECTRE have not been exploited to the prioritized MCDM. In my opinion, design specific ELECTRE methods for prioritized MCDM problems will benefit the developments of both ELECTRE and prioritized MCDM. In this paper, we firstly reformulate the expressions of concordance and discordance indices for use in the MCDM problems with dependent criteria, especially prioritized criteria, based on the concepts of fuzzy measures and digraphs respectively. After replacing the fuzzy measure by a prioritized measure, we successfully validate the concordance of an assertion under prioritized criteria. Furthermore, we design an approach to validate the discordance of the assertion based on a digraph constructed by the criteria and their prioritizations. Finally, we design three procedures to construct outranking relations in the prioritized MCDM environment according to the ideas of ELECTRE-I, ELECTRE-Iv, and ELECTRE-IS respectively. It is meaningful of this paper to provide a new idea to solve the prioritized MCDM problems and widen the application scope of ELECTRE methods by means of the reformulations of concordance and discordance.
- Published
- 2018
45. A modified PSO algorithm for linear optimization problem subject to the generalized fuzzy relational inequalities with fuzzy constraints (FRI-FC)
- Author
-
Maryam Raeisian Parvari and Amin Ghodousian
- Subjects
Mathematical optimization ,Information Systems and Management ,Fuzzy classification ,Linear programming ,05 social sciences ,050301 education ,Particle swarm optimization ,T-norm ,02 engineering and technology ,Fuzzy logic ,Computer Science Applications ,Theoretical Computer Science ,Fuzzy transportation ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Fuzzy set operations ,Fuzzy number ,020201 artificial intelligence & image processing ,0503 education ,Software ,Mathematics - Abstract
In this paper, optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t-norm is considered as fuzzy composition, and fuzzy inequality replaces ordinary inequality in the constraints. Unlike most optimization algorithms, in fuzzy relational inequalities with fuzzy constraints (FRI-FC) we find a near-feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp (ordinary) inequality constraints. Such solutions are called super-optima in this paper. Subsequently, an algorithm is proposed to find a super-optimum with pre-specified desirable infeasibility. For this purpose, we firstly study some structural properties of the FRI-FC problem and present a new formulization that is independent of t-norms used in the constraints of the problem. This new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters. However, it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super-optimum under a certain sufficient condition. Finally, a modified PSO is presented in which the ability of PSO to solve unconstrained problems with continuous domain, the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized FRI-FC problems. The modified PSO algorithm has been applied to the generalized FRI-FC problem defined with ten well-known continuous t-norms. Additionally, an idea of the FRI-FC problems as outer approximators for FRI problems with ordinary inequalities is also investigated.
- Published
- 2017
46. Results on highly nonlinear Boolean functions with provably good immunity to fast algebraic attacks
- Author
-
Meicheng Liu and Dongdai Lin
- Subjects
Discrete mathematics ,Information Systems and Management ,020206 networking & telecommunications ,02 engineering and technology ,Upper and lower bounds ,Addition theorem ,Computer Science Applications ,Theoretical Computer Science ,Nonlinear system ,Integer ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Algebraic function ,Algebraic number ,Boolean function ,Stream cipher ,Software ,Mathematics - Abstract
In the last decade, algebraic and fast algebraic attacks are regarded as the most successful attacks on LFSR-based stream ciphers . Since the notion of algebraic immunity was introduced, the properties and constructions of Boolean functions with maximum algebraic immunity have been researched in a large number of papers. However, there are few results with respect to Boolean functions with provably good immunity against fast algebraic attacks. In previous literatures, only Carlet–Feng function was proven to have good immunity to fast algebraic attacks. In this paper, we first study a large family of highly nonlinear Boolean functions in terms of the immunity to fast algebraic attacks, which includes the functions of Tu–Deng, the functions of Tang et al. and the functions of Jin et al. Based on a sufficient and necessary condition for measuring the immunity of Boolean functions against fast algebraic attacks using bivariate polynomial representation , we propose an efficient method for estimating the immunity of the functions of such family. Then we prove that a family of 2 k-variable Boolean functions, including the function recently constructed by Tang et al., are almost perfect algebraic immune for any integer k ≥ 3. More exactly, they achieve optimal algebraic immunity and almost perfect immunity to fast algebraic attacks. The functions of such family are balanced and have optimal algebraic degree. Besides, we prove a lower bound on their nonlinearity based on the work of Tang et al. which is better than that of Carlet–Feng function. It is also checked for 3 ≤ k ≤ 9 that the exact nonlinearity of such functions is very good, which is slightly smaller than that of Carlet–Feng function, and some functions of this family even have a slightly larger nonlinearity than Tang’s et al. function. To sum up, among the known functions with provably good immunity against fast algebraic attacks, the functions of this family make a trade-off between the exact value and the lower bound of nonlinearity.
- Published
- 2017
47. Training-less color object recognition for autonomous robotics
- Author
-
Tamer Rabie
- Subjects
Information Systems and Management ,Color normalization ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,02 engineering and technology ,Theoretical Computer Science ,Computer Science::Robotics ,symbols.namesake ,Artificial Intelligence ,Robustness (computer science) ,Histogram ,0202 electrical engineering, electronic engineering, information engineering ,Taylor series ,Computer vision ,Mathematics ,business.industry ,Cognitive neuroscience of visual object recognition ,Histogram matching ,020207 software engineering ,Robotics ,Pattern recognition ,Computer Science Applications ,ComputingMethodologies_PATTERNRECOGNITION ,Control and Systems Engineering ,Computer Science::Computer Vision and Pattern Recognition ,symbols ,Robot ,020201 artificial intelligence & image processing ,Artificial intelligence ,business ,Software - Abstract
This paper looks at the challenge of object recognition from the perspective of achieving the final goals of practical real-world autonomous robot-vision applications; that of identifying a target of interest in the robot’s field of view and properly localizing its position in preparation for the higher-level goal of tracking and navigation. A unified framework is introduced that combines a multidimensional feature histogram approach with a multiscale pyramid approach for training-less color object recognition and localization, with direct application to autonomous robotic agents. This framework addresses the high computational cost associated with multidimensional processing by deriving the Multidimensional “Laplacian Feature Histogram Pyramid”, a novel approach to a unified multidimensional-multiscale histogram representation. Furthermore, a Taylor series formulation is employed to combine the multiscale levels of the multidimensional Laplacian feature histogram pyramid into one efficient multidimensional-multiscale “Laplacian-Taylor Feature Histogram” for rapid object recognition and localization. The paper describes the criteria for target detection and localization by autonomous robots and how this newly developed framework fits these needs. Comparative results demonstrate the robustness of this recognition framework to noise and localization of target objects in cluttered scenes.
- Published
- 2017
48. Computing random consistency indices and assessing priority vectors reliability
- Author
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Bice Cavallo and Cavallo, Bice
- Subjects
Mathematical optimization ,021103 operations research ,Information Systems and Management ,Weak consistency ,Sequential consistency ,0211 other engineering and technologies ,Strong consistency ,Causal consistency ,02 engineering and technology ,Coherence (statistics) ,computer.software_genre ,Computer Science Applications ,Theoretical Computer Science ,Artificial Intelligence ,Control and Systems Engineering ,Consistency (statistics) ,0202 electrical engineering, electronic engineering, information engineering ,Local consistency ,020201 artificial intelligence & image processing ,Data mining ,computer ,Multiple-criteria evaluation, Pairwise comparison matrix, Random consistency index, Ordinal reliability measure, Priority vector ,Software ,Reliability (statistics) ,Mathematics - Abstract
The paper deals with two crucial steps in multi-criteria decision analysis, that are consistency of the judgments and priority vectors for alternatives/criteria. From a side, several consistency indices are proposed for measuring the consistency of a Pairwise Comparison Matrix. From another one, conditions weaker than consistency, such as transitivity and weak consistency, are proposed for representing further levels of coherence of a Decision Maker when he/she expresses his/her preferences by means of reciprocal Pairwise Comparison Matrix. Firstly, in this paper, a simulation is performed in order to establish a relation between random consistency index and coherence level. Then, since weak consistency ensures reliability to priority vectors proposed in literature, a second simulation is performed in order to measure, in case of no weak consistency, the reliability of these priority vectors.
- Published
- 2017
49. On attribute reduction in concept lattices: Methods based on discernibility matrix are outperformed by basic clarification and reduction
- Author
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Jan Konecny
- Subjects
Information Systems and Management ,Theoretical computer science ,05 social sciences ,050301 education ,02 engineering and technology ,Computer Science Applications ,Theoretical Computer Science ,Reduction (complexity) ,Matrix (mathematics) ,Artificial Intelligence ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,Formal concept analysis ,020201 artificial intelligence & image processing ,0503 education ,Algorithm ,Software ,Mathematics - Abstract
Several recent papers have studied the problem of attribute reduction in concept lattices by using a discernibility matrix in various extensions of formal concept analysis. We recall the clarification and reduction method by Ganter & Wille and show that it is strictly superior to the methods based on discernibility matrix. Consequently, we show how to adapt the clarification and reduction method to the extensions of formal concept analysis considered in the recent papers.
- Published
- 2017
50. Fuzzy-model-based admissibility analysis and output feedback control for nonlinear discrete-time systems with time-varying delay
- Author
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Chong Lin, Qing-Guo Wang, Bing Chen, and Jian Chen
- Subjects
0209 industrial biotechnology ,Information Systems and Management ,02 engineering and technology ,Fuzzy logic ,Computer Science Applications ,Theoretical Computer Science ,Nonlinear system ,020901 industrial engineering & automation ,Cone (topology) ,Discrete time and continuous time ,Artificial Intelligence ,Control and Systems Engineering ,Linearization ,Control theory ,Complementarity (molecular biology) ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Jensen's inequality ,Software ,Mathematics - Abstract
This paper is concerned with the admissibility analysis and stabilization problems for singular fuzzy discrete-time systems with time-varying delay. The novelty of this paper comes from the consideration of a new summation inequality which is less conservative than the usual Jensen inequality, the Abel-Lemma based inequality and the Seuret inequality. Based on the inequality, sufficient conditions are established to ensure the systems to be admissible. Moreover, the corresponding conditions for the existence of desired static output feedback controller gains are derived to guarantee that the closed-loop system is admissible. The conditions can be solved by a modified cone complementarity linearization (CCL) algorithm. Examples are given to show the effectiveness of the proposed method.
- Published
- 2017
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