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In our paper, we continue the study of the theory of fuzzy soft sets and their properties. Based on the singular values of the corresponding matrix, we define the energy of a fuzzy soft set, as well as the λ-energy of a fuzzy soft set, allowing us to introduce an effective method for decision-making. Then, we consider the limits of the defined energies, which are essentially non-negative numerical values. The paper demonstrates through examples how the introduced method can be successfully applied to many problems containing uncertainties. Additionally, the paper includes comparisons of the introduced method with other methods addressing similar problems. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach to obtaining analytical solutions for fuzzy fractional differential equations in the context of weighted Caputo-type generalized Hukuhara derivatives. The paper proposes the use of non-singular kernels to improve the accuracy of fractional calculus in fuzzy space and establishes the uniqueness of solutions for fuzzy fractional differential equations. The paper also introduces the concept of fuzzy Laplace transforms to facilitate the solution of these equations. Practical examples, such as the fuzzy fractional Newton’s law of heating and cooling, are provided to demonstrate the effectiveness of the proposed method. Overall, this paper contributes to the development of practical solutions for real-world problems in fuzzy space and enhances the accuracy of fractional calculus in this context. [ABSTRACT FROM AUTHOR]

Process monitoring using control charts is a common quality control method to plot the manufacturing process data and compare it to the control limits in the manufacturing process. Construction of the statistical control charts is recently suggested on the basis of the flexible triangular fuzzy quality rather than common interval-valued quality. Two new percentile-based approaches are investigated in this paper to construct mean and range control charts for the degree of belonging observations to the triangular fuzzy quality. A real-world case study about automobile engine piston rings is presented to show the performance of the proposed control charts. [ABSTRACT FROM AUTHOR]

Many dynamic processes are characterized by parametric or structural uncertainties due to internal and external disturbances. Existing deterministic models could not handle the uncertainties inherent in these processes. A valuable alternative to control these processes is the use of a type-3 fuzzy system. Since type-3 fuzzy systems use threedimensional membership functions, they have more capacity to model uncertainties. This paper introduces the design of a type-3 fuzzy logic system (FLS) for the control of dynamic plants. Utilizing type-3 fuzzy logic, the architecture of the type-3 fuzzy control system (T3FCS) is proposed. The knowledge base of the controller is constructed and its design stages are presented. The inference mechanism of type-3 FLS is developed using α slices and interval type-3 membership functions. The proposed type-3 FLS is utilized for controlling nonlinear dynamic plants. The modeling of the proposed T3FCS is performed and transient response characteristic is derived using different stepwise excitation signals. A comparison of the designed system with the type-1 FLS-based system is provided. The obtained simulation result demonstrates the efficiency of using the proposed type-3 FLS in the control of dynamic systems characterized by uncertainties. [ABSTRACT FROM AUTHOR]

Nowadays the cloud computing environment is widely utilized for transmitting and receiving data securely. Inorder to secure the data the encryption method is used but still due to some limitations the security process is diminished. Therefore, this paper proposes a new algorithm to provide better security while transmitting data through the network. At first, the sensitivity of data is determined using a lightweight convolutional neural network (LWCNN) model which is used to categorize the unclassified data into two categories normal sensitive data and highly sensitive data. After determining the level of data sensitivity, the encryption process is performed further. The efficient hash function-based duplication detection approach is employed to maintain confidential information before outsourcing it to a cloud server. Subsequently, the ideal keys are generated for each data based on its sensitivity level using the proposed fuzzy tuna swarm (FTS) algorithm. Finally, the data is encrypted by converting plain text into ciphertext which is only visible to authorized users. The experimental results show that the LWCNN model utilized for data sensitivity classification achieved 94% accuracy and the FTS algorithm proposed for optimal key generation took much less communication time of about 1800 µs than other compared techniques. [ABSTRACT FROM AUTHOR]

Uninorms are a special type of associative aggregation functions, which have received widespread attention in the theoretical and practical fields since their introduction. Durante and Sarkoci introduced the migrativity property in 2008. Afterwards, this property was widely applied in numerous fields like image processing and decision analysis, which has sparked a series of studies. There have been a large number of research results on the migrativity involving uninorms, but the work has mainly focused on the uninorms internal on the boundary. In this paper, we will concentrate on the uninorms not internal on the boundary. First, we discuss the characterization of the α-migrativity of conjunctive uninorms over continuous t-norms according to the value of α. Then, the consequences of the α-migrativity of disjunctive uninorms over continuous t-conorms can be obtained dually. [ABSTRACT FROM AUTHOR]

This work studies Interval Initial Value Problems (IIVPs), where the derivative is given by the generalized Hukuhara derivative (gH-derivative) and the initial condition is given by an interval. The focus of the paper is to provide the numerical approximations for the solutions associated with the gH-derivative of IIVPs. This article considers the Euler numerical method, where the classical arithmetic operation is adapted for intervals. The arithmetic considered here is obtained using sup-J extension principle, where J is a particular family of joint possibility distributions. This family gives raise to different types of interactivity and this work shows what kind of interactivity is necessary in the numerical method, in order to approximate the solution via gH-derivative. To illustrate the results, the paper focuses in the decay Malthusian model. [ABSTRACT FROM AUTHOR]

In this paper, for each commutative and integral quantale, we give the stratified Sierpinski L-algebraic closure space and a sobrification of stratified L-algebraic closure spaces. Furthermore, we show that SL-AC0–the category of stratified S0-L-algebraic closure spaces is epireflective in SL-AC–the category of stratified L-algebraic closure spaces, and SobL-AC–the category of sober L-algebraic closure spaces is epireflective and E-firm epireflective in the category SL-AC0. [ABSTRACT FROM AUTHOR]

In this paper, a new approach based on fuzzy systems is used for solving variable-order fractional delay differential algebraic equations. The fractional derivatives are considered in the Atangana-Baleanu sense that is a new derivative with the non-singular and non-local kernel. By relying on the ability of fuzzy systems in function approximation, the fuzzy solutions of variables are substituted in variable-order fractional delay differential algebraic equations. The obtained algebraic equations system is then transformed into an error function minimization problem. A learning algorithm is used to achieve the adjustable parameters of fuzzy solutions. It is shown that the variable-order fractional delay optimal control problems can be reformulated as variable-order fractional delay differential algebraic equations and solved by the proposed method. The efficiency and accuracy of the presented approach are assessed through some illustrative examples of the variable-order fractional delay differential algebraic equations. [ABSTRACT FROM AUTHOR]

In literature, for the four usual classes of uninorms, the modularity equation has been solved except for the kind of ones having continuous underlying functions. This paper is devoted to solving the modularity equation involving two uninorms with continuous underlying functions. We discuss this modularity equation in detail by dividing the main section into two parts. The structure characterization of the two uninorms is almost completely obtained and it is found that they are equal in the unit square except in a subdomain. [ABSTRACT FROM AUTHOR]

A new similarity/distance measure based on the center of nine-point circle of the isosceles triangular fuzzy numbers is recommend in this paper. Extend the similarity/distance measure based on centroid, orthocenter, circumcenter, incenter and nine-point circle center of the isosceles triangles. It is proved that this general similarity/distance measure conforms to the properties of distance. Subsequently, some examples are presented to justify the superiority and validity of the proposed similarity/distance measure between IFSs based on the center of nine-point circle, which demonstrate that this measure overcomes the disadvantage of the existing similarity measures. The application of the proposed similarity measure to deal with pattern recognition problems is described, and the results are correlated with those reported in some prevailing studies. In addition, a clustering technique to classify objects based on the proposed similarity measure is discussed. Through a detailed comparative analysis of some existing measures, it is concluded that some of the existing measures fail to discriminate the results obtained under different circumstances, such as zero division or counter intuitive cases; in contrast, the proposed similarity measure successfully overcomes this weakness. [ABSTRACT FROM AUTHOR]

As a generalization of nullnorms, semi-t-operators are interesting both in theory and practical applications. In this paper, we investigate some properties of idempotent semi-t-operators on bounded lattices. Furthermore, we propose two construction methods of idempotent semi-t-operators on bounded lattices containing only two different elements which are incomparable with a but comparable with b. These methods are the generalization of several known ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the class of S-generalized distances such that the involved t-conorms S are ordinal sums is discussed. It is shown that these S-generalized distances can be thought of as families of generalized distances with respect to some Archimedean t-conorms. We also deal with the S-generalized distance aggregations, which merge a family of Si-generalized distances into a new S-generalized distance. [ABSTRACT FROM AUTHOR]

Modelling phenomena with interval differential equations (IDEs) is an effective way to consider the uncertainties that are unavoidable when collecting data. Similarly to the theory of ordinary differential equations, IDEs have been parallelly investigated with the interval difference equations from the beginning. These two branches can be regarded as one when unifying continuous and discrete solution domains. A conspicuous advantage when merging these areas is that the proof of several analogous properties in both theories need not be repeated. The paper provides a common and efficient tool for studying IDEs not only with continuous or discrete solution domains but also with more general ones. We propose the diamond-α derivative for interval-valued functions (IVFs) on time scales with respect to the generalized Hukuhara difference. Differently from most of the studies on the derivatives of functions on time scales, using the language of epsilon-delta, the novel concept is naturally studied according to the limit of IVFs on time scales as in classical mathematics. A particular class of IDEs on time scales is then considered with respect to the diamond-α derivative. Numerical problems are elaborated to illustrate the necessity and efficiency of the latter. [ABSTRACT FROM AUTHOR]

In this article, multitrial vector-based differential evolution algorithm (MTDE) is proposed as energy and cost management controller under Time of Use (TOU) tariff in grid associated domestic PV-wind power system tied with battery storages. To enrich the energy efficiency of a proposed power system, two optimisation algorithms are proposed in the scheduling operation. TOU billing is a cost- reflective power pricing strategy that has been found as an effective way to reduce peak energy consumption in the residential segment everywhere the world, mainly in industrialised nations. In the optimisation maximizing the cost benefit of the household energy is taken as the objective and the dispatching ratio of electricity sold to the grid and used locally is treated as the optimisation variable. Using MATLAB, the performance of proposed MTDE in the aspect of daily cost benefit and revenue growth rate are presented with the comparative analysis of gravitational search algorithm and conventional self-made for self-consumed and rest for sale (SFC&RFS) mode-based energy management controller. In comparison to the SFC&RFS mode, the GSA-based cost optimization offers a 21.46% increase in revenue growth, while it is improved to 38.7% using proposed MTDE algorithm. The paper also addresses the significance of fuzzy logic based maximum power point tracking (MPPT) of solar PV in enhancing the energy management of the proposed system. The prototype of fuzzy logic MPPT for 10 W solar panel is presented and the tracked maximum power is visualized using Thingspeak IoT cloud server. The tracking speed of the MPPT can be increased by introducing machine learning algorithms at the cost of memory and complexity. In this article, the linear regression-based machine learning algorithm is implemented in the hardware prototype by utilizing the dataset aggregated from fuzzy MPPT and hence the proposed MPPT inherits the characteristics of the fuzzy MPPT with increased tracking speed. Around 75 % data are used for training, 25% of data are used to test the model and it is observed that the root mean square error (rmse) is 5.1334 and mean square error is 26.3521 and the model is utilized as MPPT for the real-time inputs. [ABSTRACT FROM AUTHOR]

A new image encryption scheme using the advanced encryption standard (AES), a chaotic map, a genetic operator, and a fuzzy inference system is proposed in this paper. In this work, plain images were used as input, and the required security level was achieved. Security criteria were computed after running a proposed encryption process. Then an adaptive fuzzy system decided whether to repeat the encryption process, terminate it, or run the next stage based on the achieved results and user demand. The SHA-512 hash function was employed to increase key sensitivity. Security analysis was conducted to evaluate the security of the proposed scheme, which showed it had high security and all the criteria necessary for a good and efficient encryption algorithm were met. Simulation results and the comparison of similar works showed the proposed encryptor had a pseudo-noise output and was strongly dependent upon the changing key and plain image. [ABSTRACT FROM AUTHOR]

As a proper generalization of the ordinal sum t-norm construction on bounded lattices proposed in [E. Aşıcı, R. Mesiar, New constructions of triangular norms and triangular conorms on an arbitrary bounded lattice, International Journal of General Systems, 49(2) (2020), 143-160], the present paper studies a new extension of a triangular norm on a subinterval [0, α] via an interior operator to the underlying entire bounded lattice, where the necessary and sufficient conditions under which the constructed operation is again a t-norm are given. By comparing the graphic structures of two t-norms on a common bounded lattice which are constructed in different ways, it is shown that the new method in this paper is essentially different from the ones existing in the literature. As an end, this new construction is generalized to construct ordinal sums of finitely many t-norms by recursion on bounded lattices. The dual results for ordinal sum construction of t-conorms via closure operators on bounded lattices are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new optimization problem with respect to a generalized form of fuzzy relational equations (FRE) in which fuzzy equality replaces ordinary equality in the constraints (FRE-FC). Fuzzy constraints enable us to attain optimal points (called super-optima in this paper) that are better solutions than those resulted from the resolution of the similar problems with ordinary equality constraints. Some structural properties of the FRE-FC problems are studied and a new formulation is presented in which the fuzzy constraints (equations) are precisely modeled. Subsequently, a new PSO-based algorithm is proposed to solve the FRE-FC problems defined by arbitrary continuous t-norms. The proposed algorithm is tested with different test problems generated by ten well-known continuous t-norms used in the literature. Moreover, the generated solutions for these problems, are also compared with some well-known meta-heuristic methods which have been applied to many practical optimization problems. It is shown that the optimal intensity of electromagnetic radiation problem can be formed as a special case of FRE-FC problems in which fuzzy composition is defied by max-product composition. [ABSTRACT FROM AUTHOR]

Software quality is an important research direction in software engineering domain, which is a multi-dimen-sional evaluation problem. The VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) technique is a comprehensive method for handing the multi-dimensional evaluation problems. The projection is commonly used to measure the closeness between two decision objects in decision science. However, two research questions are found in this work: (1) There is no specific concrete regret matrix in current VIKOR technique; (2) The existing projection measures are not always reasonable in interval-valued intuitionistic fuzzy setting. Two research gaps are filled systematically in this paper: (1) A specific concrete regret matrix is provided in this extended VIKOR-based group decision-making method; (2) A new normalized projection measure is provided in order to measure the closeness between two decision matrices. The decision procedures are also provided in this paper. A practical application to the software quality assessment is introduced. Some experimental comparisons are provided in order to illustrate the feasibility and practicability of introduced method. [ABSTRACT FROM AUTHOR]

Copyright of Iranian Journal of Fuzzy Systems is the property of University of Sistan & Baluchestan and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Generally exploring the exact solution of linear programming problems in which all variables and parameters are Z-numbers, is either not possible or difficult. Therefore, a few numerical methods to find the numerical solutions do act an important role in these problems. In this paper, we concentrate on introducing a new numerical method to solve such problems based on the ranking function. After proving the necessary theories, for more illustrations and the correctness of the topic, some theoretical and practical examples are also provided. Finally, the results obtained from the proposed method have been compared with some existing methods. [ABSTRACT FROM AUTHOR]

In this paper, by using the notion of prime filter, we show representation theorem of hoops and we prove that every nontrivial ∨-hoop is a subdirect product of hoop-chains. In the following, by using the concept of maximal filter of hoops, we introduce radical of hoops. Then some equivalence definitions of it and some related properties are investigated. Then by using this notion, we introduce the concepts of r-filters and p-filters on hoops and the relation between them and other filters of hoops are investigated. Finally, by using p-filters on hoops, we define new open sets on hoop that could be used to construct a Zarisky topology. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the fuzzy stability of a fractional Lorenz system in the sense of the Caputo-Fabrizio derivative and a fractional financial crisis in the sense of ♄−Hilfer derivative. Defining a new type of fuzzy control function that has a dynamic situation helps us to investigate new stability results for these mathematical models. [ABSTRACT FROM AUTHOR]

The imprecision related to measurements can be managed in terms of fuzzy features, which are characterized by two components: Center and spread. Outliers affect the outcome of the clustering models. In trying to overcome this problem, this paper proposes a fuzzy clustering model for L-R fuzzy data, which is based on a dissimilarity measure between each pair of fuzzy data defined as an adaptive weighted sum of the L1-norms of the centers and the spreads. The proposed method is robust based on the metric and weighting approaches. It estimates the weight of a given fuzzy feature on a given fuzzy cluster by considering the relevance of that feature to the cluster; if outlier fuzzy features are present in the dataset, it tends to assign them weights close to 0. To deeply investigate the capability of our model, i.e., alleviating undesirable effects of outlier fuzzy data, we provide a wide simulation study. We consider the ability to classify correctly and the ability to recover the true prototypes, both in the presence of outliers. The comparison made with other existing robust methods indicates that the proposed methodology is more robust to the presence of outliers than other methods. Moreover, the performance of our method decreases more slowly than others when the percentage of outliers increases. An application of the suggested method to a real-world categorical dataset is also provided. [ABSTRACT FROM AUTHOR]

This paper introduces a novel adaptive nonsingular fast terminal sliding mode approach that benefits from an interval type-2 fuzzy logic estimator and a gain for control and synchronization of chaotic systems in the presence of uncertainty. The nonsingular fast terminal sliding mode controller is developed to increase the convergence rate and remove the singularity problem of the system. Using the proposed method, the finite-time convergence has been ensured. To eliminate the chattering phenomenon in the conventional sliding mode controller, the discontinuous sign function is estimated using an interval type-2 fuzzy inference system (FIS) based on the center of sets type reduction followed by defuzzification. By adding the proportionate gain to the interval type-2 FIS, the robustness and speed of the controller system is enhanced. An appropriate Lyapunov function is utilized to ensure the closed-loop stability of the control system. The performance of the controller is evaluated for a nonlinear time-varying second-order magnetic space-craft chaotic system with different initial conditions in the presence of uncertainty. The simulation results show the efficacy of the proposed approach for the tracking control problems. The time and frequency domain analysis of the control signal demonstrates that the chattering phenomenon is successfully diminished. [ABSTRACT FROM AUTHOR]

Ranking fuzzy numbers have become of growing importance in recent years, especially as decision-making is increasingly performed under greater uncertainty. In this paper, we extend the concept of magnitude to rank fuzzy numbers to a more general definition to increase flexibility and generality. More precisely, we propose a multidimensional approach to rank fuzzy numbers considering alternative magnitude definitions with three novel features: Multidimensionality, normalization, and a ranking based on a parametric distance function. A multidimensional magnitude definition allows us to consider multiple attributes to represent and rank fuzzy numbers. Normalization prevents meaningless comparisons among attributes due to scaling problems, and the use of the parametric Minkowski distance function becomes a more general and flexible ranking approach. The main contribution of our multidimensional approach is the representation of a fuzzy number as a point in a n-dimensional normalized space of attributes in which the distance to the origin is the magnitude value. We illustrate our methodology and provide further insights into different normalization approaches and parameters through several numerical examples. Finally, we describe an application of our ranking approach to a multicriteria decision-making problem within an economic context in which the main goal is to rank a set of credit applicants considering different financial ratios used as evaluation criteria. [ABSTRACT FROM AUTHOR]

In a cross-docking system, doors can be used exclusively for receiving or sending operations, or they can be flexible enough to be used for both. Flexible doors have gained attention for improving cross-docking system performance, but their implementation incurs additional costs due to the need for dual-function equipment to handle both receiving and sending operations. Despite the advantages of flexible doors, applying them is usually associated with additional costs due to the need for dual-function equipment to receive and send. Moreover, the distance that goods move within crossdocking facilities, from receiving to sending dock doors, significantly affects how well these facilities work. This paper presents a new bi-objective mixed-integer linear programming model for scheduling the inbound and outbound trucks in a cross-docking facility. The model objectives are to minimize total system costs, including additional costs of applying flexible doors and transshipment (maximize efficiency) and to minimize outbound trucks’ tardiness from predetermined due dates (maximize responsiveness). As a result of the uncertainties in cross-dock truck scheduling problems, the parameters are considered triangular interval-valued fuzzy (IVF) numbers. Moreover, a new IVF-uncertain solution approach based on the max-min operator and compromise programming concepts is proposed to solve multi-objective mathematical programming problems with triangular IVF numbers. The proposed model and IVF-solution approach are used for cross-docking operations planning at a well-known food manufacturing group. The results are also analyzed according to their sensitivity to changes in key parameters of the cross-docking problem. Comparison of the proposed approach with other known fuzzy methods for solving multi-objective models demonstrates the superior performance of the proposed approach in the real case study. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to make a novel interpretation of relation between (N̅,p,q) method and P-convergence for double sequences of fuzzy numbers. In accordance with this aim, we derive some Tauberian conditions, controlling O-oscillatory behavior of a double sequence of fuzzy numbers in certain senses, from (N̅,p,q) summability to P- convergence with some restrictions on the weight sequences. As special cases, we indicate that O-condition of Hardy type with respect to (Pm) and Qn are Tauberian conditions for (N̅,p,q) summability under some additional conditions. In the sequel, we prove a fuzzy Korovkin-type approximation theorem by using the (N̅,p,q) summability method for fuzzy positive linear operators. [ABSTRACT FROM AUTHOR]

In this paper, we provide new several Jackson-type approximations results for continuous fuzzy-number-valued functions which improve several previous ones. We use alternative techniques adapted from Interval Analysis which rely on the gH-difference (which might not exist) and the generalized difference (which might lack the cancellation law) of fuzzy numbers. [ABSTRACT FROM AUTHOR]

The immediate consequences operator has been a widely studied and used operator for defining the semantics of a logic program. For instance, it has been considered in the fuzzy case for handling datasets with imperfect, imprecise or vague information. The natural generalization of this operator to the mentioned fuzzy framework is based on the supremum operator, which preserves the strict nature of the universal quantifier. As a consequence, errors in the data, which are usual in the uncertainty environment of the considered dataset, can cause loss of information. This is the main reason why this paper makes different generalizations of this operator by using weighted aggregation operators and introducing interesting results. [ABSTRACT FROM AUTHOR]

In the real world, the parameters of a problem may not be the crisp values. The fuzzy theory among the theories in which uncertainty plays a crucial role. Type-2 fuzzy sets generalize fuzzy sets. We consider a special type of such sets here. In this paper, we consider two issues. First, we review the method proposed by Javanmard and Mishmast Nehi for solving an interval type-2 triangular fuzzy linear programming problem, and improve it. Then, we express a bilevel linear programming problem, that, to the best of our knowledge, has not been investigated so far. We consider the bilevel linear programming problem with uncertainty where all the coefficients in the problem are interval type-2 triangular fuzzy numbers. We convert an interval type-2 triangular fuzzy bilevel linear programming problem into an interval bilevel linear programming problem using Grzegorzewski’s nearest interval approximation method. Finally, we obtain five problems, and by solving them, we achieve the solution of interval type-2 triangular fuzzy bilevel linear programming problem as an interval type-2 triangular fuzzy number. [ABSTRACT FROM AUTHOR]

Hesitant fuzzy linguistic term set (HFLTS) is an approach giving ability to obtain more flexible decision-making (DM) process by integrating linguistic fuzzy modeling (LFM) with hesitative expert judgments. Although HFLTS is widely-studied in the literature and many enhancements are made on HFLTS procedure, none of these enhancements gives ability to continue with precise fuzzy modeling (PFM) in decision process. LFM has a big drawback about accuracy because of the dependency between the size of term set and the comprehensiveness of fuzzy sets (FSs). This issue creates a very critical difficulty in modeling of DM problems that need sensitive evaluations by using HFLTS. This paper aims to solve this problem by proposing a novel HFLTS methodology that is usable for DM problems that need sensitive calculations in the decision stage. The proposed methodology integrates 2-tuple LFM and linguistic fuzzy modifiers with HFLTS to overcome the accuracy problem and obtain more sensitive and flexible decision procedure. This paper also presents an envelopment transformation technique to aggregate expert assessments as a fuzzy membership function instead of membership grades. It becomes possible to keep interpretability in a certain level and achieve sensitive results at the same time with the help of these modifications. The proposed HFLTS approach is analyzed on a real case example from manufacturing industry for acceptance sampling plans (ASP) that is a DM problem requiring sensitive calculations. As another originality of the paper, the main formulations of ASP are derived based on hesitant fuzzy defectiveness information. The obtained results are also compared with some existing enhancements of the HFLTS and the success of the proposed methodology is proved in terms of sensitive calculation. [ABSTRACT FROM AUTHOR]

One of the main goals of network planners is the protection of important nodes in a network against natural disasters, security threats, attacks, and so on. Given the importance of this issue, a new model is presented in this paper for protecting an important node in a typical network based on a defensive location problem where the two agents threaten this node. The protecting facilities location problem with two agents is formulated as a three-level programming problem. The decision maker in the upper level is a network planner agent. The planner agent wants to find the best possible location of protecting facilities to protect the important node against threatening agents. The second and third levels problems are stated as the shortest path problems in the network in which the edges are weighted with positive values. In this work, the genetic, variable neighborhood search, simulated annealing algorithms are used to solve the problem. The performance of the used metaheuristic algorithms on this class of problems is investigated by a test problem that is generated randomly. Then, t-test are used to compare the performance of these algorithms. The best results are obtained by the variable neighborhood search algorithm. [ABSTRACT FROM AUTHOR]

Copyright of Iranian Journal of Fuzzy Systems is the property of University of Sistan & Baluchestan and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Recently in [17, 18], new algebras, called weak pseudo EMV-algebras, wPEMV-algebras for short, were introduced generalizing pseudo MV-algebras, generalized Boolean algebras and pseudo EMV-algebras. For these algebras a top element is not assumed a priori. For this class of algebras, we define a state as a finitely additive mapping from a wPEMV-algebra into the real interval [0, 1] which preserves a partial addition of two non-interactive elements and attaining the value 1 in some element. It can happen that some commutative wPEMV-algebras are stateless, e.g. cancellative ones. The paper is divided into two parts. Part I deals with basic properties of states and state-morphisms which are wPEMVhomomorphisms from a wPEMV-algebra into the real interval [0, 1] endowed as a commutative wPEMV-algebra. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal and normal ideals having a special property. In Part II, we present an analogue of the Krein-Mil’man theorem applied to the set of states. We characterize the space of the state-morphisms of a wPEMV-algebra without top element as a Hausdorff locally compact space in the weak topology of states and we present its Alexandroff’s one-point compactification. Moreover, we give an integral representation of any (finitely additive) state by a unique regular Borel σ-additive probability measure. Recently in [17, 18], new algebras, called weak pseudo EMV-algebras, wPEMV-algebras for short, were introduced generalizing pseudo MV-algebras, generalized Boolean algebras and pseudo EMV-algebras. For these algebras a top element is not assumed a priori. For this class of algebras, we define a state as a finitely additive mapping from a wPEMV-algebra into the real interval [0, 1] which preserves a partial addition of two non-interactive elements and attaining the value 1 in some element. It can happen that some commutative wPEMV-algebras are stateless, e.g. cancellative ones. The paper is divided into two parts. Part I deals with basic properties of states and state-morphisms which are wPEMVhomomorphisms from a wPEMV-algebra into the real interval [0, 1] endowed as a commutative wPEMV-algebra. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal and normal ideals having a special property. In Part II, we present an analogue of the Krein-Mil’man theorem applied to the set of states. We characterize the space of the state-morphisms of a wPEMV-algebra without top element as a Hausdorff locally compact space in the weak topology of states and we present its Alexandroff’s one-point compactification. Moreover, we give an integral representation of any (finitely additive) state by a unique regular Borel σ-additive probability measure. [ABSTRACT FROM AUTHOR]

The concept of fuzzy random variable has been applied in several papers to model the present value of life insurance liabilities. It allows the fuzzy uncertainty of the interest rate and the probabilistic behaviour of mortality to be used throughout the valuation process without any loss of information. Using this framework, and considering a triangular interest rate, this paper develops closed expressions for the expected present value and its defuzzified value, the variance and the distribution function of several well-known actuarial liabilities structures, namely life insurances, endowments and life annuities. [ABSTRACT FROM AUTHOR]

This paper characterizes a uninorm distributive over a noncontinuous t-(co)norm, where the uninorm is locally internal on the boundary. Firstly, when the uninorm is disjunctive, the necessary conditions (resp. the sufficient conditions) for a uninorm distributive over a noncontinuous t-norm are analyzed under the certain condition. Secondly, the distributivity of a conjunctive uninorm over a noncontinuous t-conorm is characterized by duality. In particular, this paper is related to the open question recalled by Klement in the Linz2000 closing session, which provides the noncontinuous solutions of that question. [ABSTRACT FROM AUTHOR]

The primary aim of the notion of consistency fuzzy set (CFS) is to model the uncertain information given in a fuzzy multi environment and so to obtain meaningful data from the fuzzy multi-sets and to present this data in a compact form via some statistical tools. The data collected by fuzzy multi-sets are processed via CFSs and a sort of data science is done in the fuzzy environment. In this paper, we present a cross entropy measure and a sine entropy measure between CFSs to contribute to the processing and modeling of data obtained by statistical methods. Also, we construct a new VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method by using CFSs that is called CF-VIKOR to carry out decision process in multi-criteria decision making. Finally, we give a comparison analysis between the obtained results and the existing results in literature with the help of Spearman’s, Kendall’s rank correlation coefficient measures and Wang and Triantaphyllou validity test to show the efficiency and rationality of the proposed CF-VIKOR method. [ABSTRACT FROM AUTHOR]

Fuzzy soft set is a general mathematical tool to deal with uncertain and fuzziness information. But inadequacy lies in which cannot express various uncertainty in a more natural and accurate manner, due to the reason of adopting the fuzzy membership which restricts to [0, 1]. As a result, it merely concerns non-negative fuzzy belongingness of elements, so as to be incapable of capturing the conflict information that supporting, neutral and opposing scenarios regarding belongingness of elements in a set to taken into account. To overcome the limitation, this paper extends fuzzy soft set to bilateral fuzzy soft set (BFSS), which considers both non-negative and negative sides for fuzzy membership and normalizes the range to [−1, 1]. Then defines some basic operations on BFSS, as well as a detail study of relevant properties. In order to eliminate redundant parameters and draw the essential part of BFSS, the parameters reduction on BFSS is also investigated, and the significance of parameters is introduced accordingly. On this basis, an assessment approach for multi-criteria multi-person decision making under conflict information, together with the algorithm for implementation is presented. Finally, a typical numerical example regarding voting demonstrates the validity and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates a novel distributed fuzzy adaptive iterative learning control protocol of exact consensus for second-order unknown nonlinear strict-feedback multi-agent systems with partially unknown time-varying control di- rections. Fuzzy logic system estimates the unknown nonlinear dynamics of each agent. Based on Nussbaum function, the control protocols of all follower agents with partially unknown virtual and actual control directions are designed by the backstepping method. The proposed protocol guarantees that the output of every follower agent could exactly track the desired output trajectory on a finite time interval. As an extension, the formation control results can also be solved. Finally, two simulation examples prove that the proposed control scheme is effective and rigorous. [ABSTRACT FROM AUTHOR]

This paper presents two approaches for testing quality to make a decision based on the extended process capability indices. Common methods in measuring quality of the manufactured product have widely focused on the precise specification limits, but in this study the lower and upper specification limits are considered as non-precise/fuzzy sets. Based on a general statistical approach using an extended process capability index, the purpose of this study is estimating a critical value to determine whether the process meets the customer requirements. Moreover, a simulation approach to analyze the manufacturing process capability has been suggested for testing quality based on fuzzy specifications by normal data. Meanwhile, this paper discusses how well the Monte Carlo simulation approach can be used for non-normal data. Finally, the real application of the proposed methods is investigated in a real case study. [ABSTRACT FROM AUTHOR]

Fuzzy modeling is a well-known solution for simplified modeling and predicting nonlinear systems behavior. Dynamic TSK Fuzzy Systems are an important branch in fuzzy modeling and are used for complex nonlinear dynamic systems modeling vastly. High order fuzzy systems have been developed recently in the fuzzy modeling field, aiming to reduce number of the fuzzy model rules compared to zero and first order systems, not in cost of a larger modeling error. Employing high order TSK in dynamic TSK fuzzy systems, motivates finding a better model for nonlinear dynamic systems. Closed loop control system design is an important usage of dynamic TSK models, including the stability analysis as the first step. While stability investigation is a main part of any Controller design process, in this paper, a criterion has been investigated based on Lyapunov second method, for High Order Dynamic TSK Fuzzy System stability. Although the controller design process is not totally discussed in this paper, however some examples are provided to verify the proposed stability criterion. [ABSTRACT FROM AUTHOR]

In testing hypotheses, we may confront with cases where data are recorded as non-precise (fuzzy) rather than crisp. In such situations, the classical methods of testing hypotheses are not capable and need to be generalized. In solving the problem of testing hypotheses based on fuzzy data, the fuzziness of the observed data leads to the fuzzy p-value. This paper has been focused to calculate fuzzy p-value based on fuzzy data using the extension principle. Also, considering that p-value method is the most widely used / popular approach for testing hypotheses among different sciences users, two fuzzy p-value-based case studies have been provided in this paper. The first case study is discussed on "the fuzzy data from a speedometer camera" and the second is deliberate about "the lifetime of produced batteries in a factory" and both of them have been solved by a novel approach considering other studies found in the literature. [ABSTRACT FROM AUTHOR]

Induction motors (IMs) are widely used in many industrial applications due to their robustness, low cost, simplicity and relative good efficiency. One of the major considerations for IMs is their speed control. PI (proportional-integrator) controllers are usually used as speed controller. Adjusting the gain of PI controller is time-consuming which needs thorough considerations. Hence, fuzzy controllers are proposed to overcome such problems. In this paper, firstly drive of a three-phase induction motor is designed based on PI controller and then fuzzy logic controller is implemented. This paper presents a novel speed control technique based on fuzzy logic with two inputs and one output for drive of an IM. The inputs are speed error and derivation of speed error and the output is speed. Finally comparison is done between the PI and fuzzy controllers which shows superiority of the fuzzy controller over PI controller. [ABSTRACT FROM AUTHOR]

In this paper, we introduce fruitful concepts of common limit range and joint common limit range for coupled mappings on modified intuitionistic fuzzy metric spaces. An illustrations are also given to justify the notion of common limit range and joint common limit range property for coupled maps. The purpose of this paper is to prove fixed point results for coupled mappings on modified intuitionistic fuzzy metric spaces. Moreover, we extend the notion of common limit range property and E.A property for coupled maps on modified intuitionistic fuzzy metric spaces. As an application, we extend our main result to integral type contraction condition and also for finite number of mappings on modified intuitionistic fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

Testing the capability of a productive process on the basis of the flexible fuzzy quality using Yongting’s index is proposed in this paper by the Monte Carlo simulation. The theoretical approach and detailed steps of an algorithm are given to simulate the critical-value-based and also p-value-based approaches to statistical testing fuzzy quality. Also, the probability of type II error of the quality test simulated by Monte Carlo approach. Moreover, a real-world case study is provided to show the performance of the proposed algorithm for triangular and trapezoidal fuzzy qualities. [ABSTRACT FROM AUTHOR]

A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant fuzzy analysis and takes some applications that were discussed in recent literature. In this paper, we develop the hesitant fuzzy arithmetic, which is based on the extension principle for hesitant fuzzy sets. Employing this principle, standard arithmetic operations on fuzzy numbers are extended to HFNs and we show that the outcome of these operations on two HFNs are an HFN. Also we use the extension principle in HFSs for the ranking of HFNs, which may be an interesting topic. In this paper, we show that the HFNs can be ordered in a natural way. To introduce a meaningful ordering of HFNs, we use a new lattice operation on HFNs based upon extension principle and defining the Hamming distance on them. Finally, the applications of them are explained on optimization and decision-making problems. [ABSTRACT FROM AUTHOR]

The problem of robust nonfragile H∞ filtering for fuzzy fractional order (FFO) systems 0 < α < 1 with uncertainties is studied. First, a new sufficient condition of H∞ control for fractional order systems is given to overcome the shortcoming of solving the complex matrix. Then, based on the condition and the linear matrix inequality (LMI) approach, the conditions of robust H∞ control for FFO systems are proposed, which can guarantee the prescribed noise attenuation level in the H∞ sense. Furthermore, the FFO filter is constructed, and sufficient conditions are proposed for FFO filter systems. Finally, two examples are given to verify the effectiveness of our conditions. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study the fuzzy stability of a fractional Lorenz system in the sense of the Caputo-Fabrizio derivative and a fractional financial crisis in the sense of h−Hilfer derivative. Defining a new type of fuzzy control function that has a dynamic situation helps us to investigate new stability results for these mathematical models. [ABSTRACT FROM AUTHOR]

In this paper, based on the weighted metric, the problem of approximating a general continuous fuzzy number u with derivable u(r) and ū(r) (left and right cut functions of level value r) for r ∈ (0, 1] by using the m − n−step type fuzzy number is studied. Two kinds of approximations (I−nearest approximation and II−nearest approximation which satisfy different conditions) of using m − n−step type fuzzy numbers to approximate general continuous fuzzy numbers are defined, and the relationship between the I−nearest approximation and II−nearest approximation is obtained. Then the methods of the two kinds of approximations are respectively presented by the theorems more specifically. At last, an example is given to show the effectiveness and usability of the methods set up by us. [ABSTRACT FROM AUTHOR]