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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]

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]

Attitudinal Choquet integral (ACI) is a recent aggregation operator that considers in the aggregation process the criteria interaction and the DM’s attitude, both of which are specific to the decision-maker. However, this capability comes at the cost of increased complexity that hinders its applicability in big data analytics. To address the same, in this paper, we explore some heuristics-based forms of the ACI operator, so as to somehow overcome its complexity. We devise new and efficient forms of ACI, and test their validity in the real world datasets, against the backdrop of preference learning. [ABSTRACT FROM AUTHOR]

In this paper, in order to apply the concept of IVI-octahedron sets to MCDGM problems, we define some aggregation operators via IVI-octahedron sets and obtain some their properties. We define some aggregation operators via IVIoctahedron sets and obtain some their properties. We present a MCGDM method with linguistic variables in IVIoctahedron set environment. Finally, we give a numerical examples for MCGDM problems. [ABSTRACT FROM AUTHOR]

Recently, Zhao et al. [55] characterized the distributivity equations of null-uninorms with continuous and Archimedean underlying operators over overlap or grouping functions. Moreover, Liu et al. [34] studied the distributive laws of continuous t-norms over overlap functions. In this paper, we proceed with the distributivity characterization of idempotent null-uninorms over overlap or grouping functions. In order to do that, we introduce a class of weak overlap and grouping functions with weak coefficients, and obtain the full characterizations of overlap and grouping functions by considering the different values of underlying uninorms’ associated functions of idempotent null-uninorms on the interval endpoints and comparing them with the weak coefficients. Obviously, idempotent null-uninorms generalize idempotent uninorms. Thus, the obtained results also generalize the distributivity of idempotent uninorms proposed as future work in [34]. [ABSTRACT FROM AUTHOR]

The generalized interval-valued orthopair fuzzy sets provide an extension of Yager’s generalized orthopair fuzzy sets, where membership and non-membership degrees are subsets of closed interval [0, 1]. Due to the uncertainty and ambiguity of real life, it is more superior for decision makers to provide their judgments by intervals rather than crisp numbers. Moreover, in the era of huge scale and rapid updating of information, individual weights have been quietly diluted, and the integration of information one by one is time-consuming and complicated. In recent years, some cholars have conducted research on the calculus of generalized orthopair fuzzy sets, but no research has further revealed the intrinsic connection between the integrals of generalized interval-valued orthopair fuzzy sets and traditional aggregation operators, which is very important in applications such as large group decision making. In order to fill this theoretical gap, this paper aims to study the integrals of generalized interval-valued orthopair fuzzy functions. In detail, we define the indefinite integral starting from the inverse operations of the interval-valued q-rung orthopair fuzzy functions (IVq-ROFFs)’ derivatives, and some fundamental properties with rigorous mathematical proofs are also discussed. To be more practical, we continue to develop definite integrals for both simplified and generalized IVq-ROFFs. Besides, we give the corresponding Newton-Leibniz formula through limit procedure, which shows the calculation relationship between the indefinite and definite integrals of the IVq-ROFFs. After obtaining the basic calculus results under generalized interval-valued orthopair fuzzy circumstance, we further reveal the inherent link between the integrals of generalized IVq-ROFFs and the traditional discrete aggregation operators. Finally, the practicability and feasibility of the proposed definite integral models are illustrated by an example of public health emergency group decision-making, and sensitivity analysis and comparison are also carried out. [ABSTRACT FROM AUTHOR]

Recently, a new paradigm for uncertain information has been proposed that can effectively handle various types of uncertainty in decision-making problems. This approach utilizes a certainty degree, which is represented by a real number indicating the level of certainty associated with input values. However, just like intuitionistic fuzzy information can handle more problems that cannot be well modeled by fuzzy information, the certainty degree in basic uncertain information can also be intuitionistic fuzzy granule, which allows it to handle more uncertainty involved decision making situations. In this paper, we introduce the concept of intuitionistic fuzzy type basic uncertain information and explain its parameters. We also define a weighted arithmetic mean for aggregating this type of information and discuss different approaches for allocating induced weights based on trust preferred preference from four perspectives: (i) preference for higher certainty degrees; (ii) aversion to higher levels of uncertainty; (iii) preference for greater differences in certainty degrees; and (iv) preference for intuitionistic fuzzy certainties. Additionally, we explore trichotomic rules-based decision making using intuitionistic fuzzy type basic uncertain information. Finally, we present an objective-subjective evaluation numerical example utilizing these methods. [ABSTRACT FROM AUTHOR]

The aim of this paper is to redefine the notion of spherical fuzzy soft sets as a more general concept to make them more functional for solving multi-criteria decision-making problems. We first define the set operations under the new spherical fuzzy soft set environment and obtain some fundamental properties of them. Then, we construct the spherical fuzzy soft aggregation operator which allows establishing a more efficient and useful method to solve the multi-criteria decision-making problems. We establish an algorithm for the decision-making process which is more useful, simple, and easier than the existing methods. After constructing the method for solving the decision-making problem, we give a numerical example based on linguistic terms to show that the validity of the proposed technique. Finally, we analyze the reliability of the results of this method with the help of the comparative studies by applying this to a real-time data set and using the existing methods. [ABSTRACT FROM AUTHOR]

The preference ranking organization method for enrichment of evaluations (PROMETHEE) constitutes a family of outranking multiple-attribute decision-making (MADM) methods that has been adopted by researchers from many areas during the last years. It provides reliable and clear results thanks to the advantages of different types of preference functions. In this paper, we incorporate the benefits of q-rung orthopair fuzzy set (for short, q-ROFS) in this strategy of solution. This model, q-ROFS, is a generalized form of Pythagorean fuzzy set (PFS), as it broadens the space of acceptable orthopairs and has an ability to deal with more elaborate and vague information. The technique of our extension of the PROMETHEE method uses q-rung orthopair fuzzy numbers to render the ratings of alternatives, which allows us to express uncertain and vague information more accurately. The usual criterion preference function has been used to measure the preferences of the alternatives. A partial ordering of alternatives is obtained by considering the outgoing and incoming flows of alternatives, which is known as PROMETHEE I. Furthermore, a complete ordering is accomplished by taking into account the procedure of PROMETHEE II. As a numerical exercise, we consider the selection of a contractor for a construction project. A full analysis is performed to illustrate the application of the technique that stems from our approach. Then we compare the results that we obtain with the results from existing approaches, including q-rung orthopair fuzzy ELECTRE, q-rung orthopair fuzzy TOPSIS, q-rung orthopair fuzzy VIKOR and q-rung orthopair fuzzy aggregation operators. In this way the accuracy and effectiveness of the presented work is conclusively validated . [ABSTRACT FROM AUTHOR]

This paper introduces new similarity classifiers using the Heronian mean, and the generalized Heronian mean operators. We examine the use of these operators at the aggregation step within the similarity classifier. The similarity classifier was earlier studied with other operators, in particular with an arithmetic mean, generalized mean, OWA operators, and many more. The two classifiers here are tested on four real world data sets, i.e., echocardiogram, fertility, horse-colic, and lung cancer. Three previously studied similarity classifiers are used as benchmarks to the new approaches. We observe that the similarity classifier with a generalized Heronian mean produces good classification results for the tested data sets, and is therefore more suitable for use in these classification problems. [ABSTRACT FROM AUTHOR]

Throughout this paper, our main idea is to analyze the Arrovian approach in a fuzzy context, paying attention to different extensions of the classical Arrow's model arising in mathematical Social Choice to aggregate preferences that the agents define on a set of alternatives. There is a wide set of extensions. Some of them give rise to an impossibility theorem as in the Arrovian classical model. But others lead to possibility results. We explore the main grounds that lead to impossibility or possibility. In this analysis, representative examples arise. One of them corresponds to an impossibility result, and the other ones allow the aggregation of fuzzy individual preferences to an individual one. We introduce new techniques for the proofs, specially for the one that leads to impossibility. [ABSTRACT FROM AUTHOR]

Global challenge and the speedy growth of information technologies compel organizations to constantly change their ways. At the present time, associations need IT personnel who create a difference by creative thoughts and who preserve with the rapid amendments. Since the evaluation of IT personnel selection (ITPS) consists of different alternatives and criteria, therefore, IT personnel selection could be regarded as a multi-criteria decision making (MCDM) problem. The doctrine of intuitionistic fuzzy sets (IFSs) is an effective tool to elucidate the uncertain information in an MCDM problem. The main objective of the paper is to choose the best IT personnel candidate by integrating intuitionistic fuzzy Additive Ratio Assessment (IF-ARAS) method with divergence measure, improved score function and IF-aggregation operators. In the developed methodology, the weights of criteria and decision experts (DEs) are computed based on proposed IF-divergence measure method intuitionistic fuzzy preference evaluation method, respectively. Next, the decision experts’ judgments are aggregated of the proposed method to evade the loss of data. Finally, the proposed IF-ARAS method is implemented to solve the IT-personnel selection (ITPS) problem to indicate the applicability of the presented approach. In addition, a comparative analysis is provided to discuss the obtained results for validating the developed methodology. The analysis illustrates that the IF-ARAS method is effective and well consistent with the existing ones. [ABSTRACT FROM AUTHOR]

The aim of this manuscript is to present a new concept of hesitant q-rung orthopair fuzzy sets (Hq-ROFSs) by combining the concept of the q-ROFSs as well as Hesitant fuzzy sets. The proposed concept is the generalization of the fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and Pythagorean fuzzy sets as well as intuitionistic hesitant fuzzy sets (IHFSs) and hesitant Pythagorean fuzzy sets (HPFSs).Furthermore some basic operational laws of hesitant q-rung orthopair fuzzy have been investigated. The score and accuracy functions are defined which play a vital role in decision making process for making comparison between the hesitant q-rung orthopair fuzzy numbers (Hq-ROFNs). Under the Hq-ROF environment, Hq-ROF weighted averaging (Hq-ROFWA) and Hq-ROF weighted geometric (Hq-ROFWG) operators are introduced and various properties of these aggregation operators are studied. Additionaly, a numerical application shows that how the proposed operators are utilized to solve multi-criteria decision making (MCDM) problems in which experts added their optimistic and pessimistic preferences. Finally the analysis of proposed method with other methods is presented which show that the method presented in this paper is more exible and superior than existing methods. [ABSTRACT FROM AUTHOR]

The interval-valued intuitionistic fuzzy set (IVIFS) which is an extension of the Atanassov's intuitionistic fuzzy set is a powerful tool for modeling real life decision making problems. In this paper, we propose the generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral (GIVIFHGSCI) and the interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral (IVIFHGSCI) operators, which consider the importance of the ordered positions and correlations among the arguments with the assumption that the aggregated arguments are interrelated. Furthermore, some of the properties and special cases of these operators are discussed. An approach for multicriteria decision making based on these operators is developed. Finally an illustrative example follows. [ABSTRACT FROM AUTHOR]

Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al. [7], in this paper a fuzzy disjunction D on the set H of finite and nonempty subsets of the unit interval and a t-conorm S on the set H of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negations Nn on H and μn on B are proposed. Particularly, their De Morgan's laws are investigated with respect to binary operations C and D on H, as well as T and S on B respectively, where C is a commutative fuzzy conjunction on (H,≤H) and T is a t-norm on (B, ≤B). Finally, the new hesitant fuzzy aggregation operators are presented on H and B and their more general forms are given. Moreover, the validity of the aggregation operations is illustrated by a numerical example on decision making. [ABSTRACT FROM AUTHOR]

Molodtsov initiated soft set theory that provided a general mathematical framework for handling with uncertainties in which we encounter the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as bipolar fuzzy set theory. The main object of this paper is to lay a foundation for providing a new application of bipolar fuzzy soft tool in considering many problems that contain uncertainties. In present study, aggregation of bipolar fuzzy soft numbers have so far not yet been applied for ranking of alternatives in decision-making problems. To this propose, bipolar fuzzy soft weighted arithmetic averaging (BFSWAA) operator, bipolar fuzzy soft weighted geometric averaging (BFSWGA) operator have been used to compare two bipolar fuzzy soft numbers (BFSNs) for aggregating different bipolar fuzzy soft input arguments in bipolar fuzzy soft environment. Then, their related properties have been investigated. Finally, a practical example for selection of alternatives is given to demonstrate the utility and application of the proposed work. [ABSTRACT FROM AUTHOR]

The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The operation law, score function, accuracy function , and certainty function for interval-valued intuitionistic linguistic varibales (IVILVs) are defined. Hereby a lexicographic method is proposed to rank the IVILVs. Then, three kinds of interval-valued intuitionistic linguistic arithmetic average operators are defined, including the interval-valued intuitionistic linguistic weighted arithmetic average (IVILWAA) operator, interval-valued intuitionistic linguistic ordered weighted arithmetic (IVILOWA) operator, and interval-valued intuitionistic linguistic hybrid arithmetic (IVILHA) operator, and their desirable properties are also discussed. Based on the IVILWAA and IVILHA operators, two methods are proposed for solving multi-attribute group decision making problems with IVILVs. Finally, an investment selection example is illustrated to demonstrate the applicability and validity of the methods proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making (MADM) problems with 2-tuple intuitionistic fuzzy linguistic information. Then, we utilize arithmetic and geometric operations to develop some 2-tuple intuitionistic fuzzy linguistic aggregation operators. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the 2-tuple intuitionistic fuzzy linguistic MADM problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function. The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria. Based on the Lukasiewicz triangular norm, we first propose a prioritized arithmetic mean to IVIF multi-criteria decision making (MCDM) problem where there is a linear ordering among the criteria. The proposed aggregation operator overcomes the existing prioritized aggregation operator’s shortcomings that it is not monotone with respect to the total order on interval-valued intuitionistic fuzzy values (IVIFVs). We also prove that it is bounded and monotone with respect to the total order on IVIFVs, and therefore is a true generalization of such operations. We finally propose an aggregation operators-based two-step procedure to IVIF MCDM in the situation that more than one criteria exist at some priority level. [ABSTRACT FROM AUTHOR]

In this contribution connections between input fuzzy relations R1, . . . ,Rn on a set X and the output fuzzy relation RF = F(R1, . . . ,Rn) are studied. F is a function of the form F : [0, 1]n → [0, 1] and RF is called an aggregated fuzzy relation. In the literature the problem of preservation, by a function F, diverse types of properties of fuzzy relations R1, . . . ,Rn is examined. Here, it is considered the converse approach. Namely, fuzzy relation RF = F(R1, . . . ,Rn) is assumed to have a given property and then it is checked if fuzzy relations R1, . . . ,Rn have this property. Moreover, a discussion on the mentioned two approaches is provided. The properties, which are examined in this paper, depend on their notions on binary operations B : [0, 1]2 → [0, 1]. By incorporating operation B these properties are generalized versions of known properties of fuzzy relations. [ABSTRACT FROM AUTHOR]

In some multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intuitionistic fuzzy set on a real number set and have better capability to model ill-known quantities. Firstly, the weighted possibility means of membership and non-membership functions for TrIFNs are defined. Hereby, a new lexicographic ranking method for TrIFNs is presented. Then, a series of trapezoidal intuitionistic fuzzy prioritized aggregation operators are developed, including trapezoidal intuitionistic fuzzy prioritized score (TrIFPS) operator, trapezoidal intuitionistic fuzzy prioritized weighted average (TrIFPWA) operator, trapezoidal intuitionistic fuzzy prioritized and (TrIFP-AND) operator and trapezoidal intuitionistic fuzzy prioritized or (TrIFP-OR) operator. Some desirable properties of these operators are also discussed. By utilizing the TrIFPWA operator, the attribute values of alternatives are integrated into the overall ones, which are used to rank the alternatives. Thus, a new method is proposed for solving the prioritized MADM problems with TrIFNs. Finally, the applicability of the proposed method is illustrated with a supply chain collaboration example. [ABSTRACT FROM AUTHOR]

Based on the classical works of Clifford inducing partial order from semigroups, recently, Gupta and Jayaram explored the order ⊑F from an associative operation F through local left identity (LLI). Inspired by their works, we further present an order ⊑∗ F obtained from non-commutative operation F which has the local right identity (LRI) since the non-commutativity of F implies that the local left and right identity may be different for each element, which means that both orders may not coincide in the same domain. Firstly, we determine an equivalent characterization for two orders induced by non-commutative operation F. Secondly, we investigate both orders induced by semi-t-operators and deeply study their properties. Finally, we characterize both orders obtained from semi-uninorm (resp. semi-nullnorm) under the condition that semi-uninorm (resp. semi-nullnorm) is locally continuous. [ABSTRACT FROM AUTHOR]

In this paper, we firstly show th a t the TV-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary V-distributive left semi-uninorm, is the right residual coimplication induced by its TV-dual operation. As a dual result, the TV-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary A-distributive left semi-uninorm, is the right residual implication induced by its TV-dual operation. Then, we demonstrate th a t the TV-dual operations of the left semi-uninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left semi-uninorms. Finally, we reveal the relationships between conjunctive right arbitrary Vdistributive left semi-uninorms induced by implications and disjunctive right arbitrary A-distributive left semi-uninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle. [ABSTRACT FROM AUTHOR]

Weighted average with normalized weights is a widely used aggregation operator that takes into account the varying degrees of importance of the numbers in a data set. It possesses some important properties, like monotonicity, continuity, additivity, etc., that play an important role in practical applications. The inputs of the aggregation as well as the normalized weights are usually not known precisely. In such a case, their values can be expressed by fuzzy numbers, and the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights needs to be employed in the model. The aim of the paper is to reveal whether and in which way the properties of the weighted average operator can be observed also for its fuzzy extension. It is shown that it possesses three conditions characteristic for aggregation operators { identity, monotonicity and boundary conditions, and besides that, also compensation, idempotency, stability for linear transformation, 1-lipschitzianity, and continuity. Furthermore, it is proved that it preserves strict monotonicity in case of positive fuzzy weights, and symmetry in case of equal fuzzy weights, although it does not coincide with the fuzzy arithmetic mean operator in such a case. One of the most valuable result of the study is the fact that in contrast to the crisp weighted average operator, it is not additive. The importance of the obtained results is discussed and illustrated by several illustrative examples. [ABSTRACT FROM AUTHOR]

There are many vague and uncertain issues in real-life. To address these problems, many models and theories have been developed. Therefore, the present study aims to describe the concept of trapezoidal fuzzy multi-number aggregation operators and also provide its application in architecture. Our main focus is on the trapezoidal fuzzy multi-number weighted arithmetic average (TFMNWAA) operator, the trapezoidal fuzzy multi-number weighted geometric average (TFMNWGA) operator and trapezoidal fuzzy multi-number hybrid aggregation (TFMNHA) operator. And then, we investigate the fundamental properties of the operators in detail such as idempotency, commutativity and boundedness. Then the notion of a new score function of ranking the trapezoidal fuzzy multi-numbers is defined. We apply the TFMNHA operator to multi-criteria decision-making trapezoidal fuzzy multi-number. Finally, a discussion is presented with a numerical example is provided to show its applicability and usefulness. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the idea of traditional arithmetic operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic weighted average (HFLWA) operator, hesitant fuzzy linguistic ordered weighted average (HFLOWA) operator and hesitant fuzzy linguistic hybrid average (HFLHA) operator. Furthermore, we propose the concept of the dual hesitant fuzzy linguistic set and develop some aggregation operators with dual hesitant fuzzy linguistic information. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

The cross-migrativity has been investigated for families of certain aggregation operators, such as t-norms, t-subnorms and uninorms. In this paper, we aim to study the cross-migrativity property for semi-t-operators, which are generalizations of t-operators by omitting commutativity. Specifically, we give all solutions of the cross-migrativity equation for all possible combinations of semi-t-operators. Moreover, it is shown that if a semi-t-operator F is α-cross-migrative over another semi-t-operator G, then G must be a semi-nullnorm except one case. Finally, it is pointed out that the cross-migrativity property between two semi-t-operators is always determined by their underlying operators except a few cases. [ABSTRACT FROM AUTHOR]

Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t- operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and so on. Therefore, the aim of this paper is to investigate the left (right) distributivity of semi-t-operators over 2-uninorms. We consider five subclasses of 2-uninorms and characterize the corresponding left (right) distributive equations of semi-t-operators over 2-uninorms. [ABSTRACT FROM AUTHOR]

Recently, the TODIM1 (an acronym in Portuguese of interactive and multi-criteria decision making) method has attracted increasing attention and many researchers have extended it to deal with multiple attribute decision making (MADM) problems under different situations. However, none of them can be used to handle MADM problems with positive, independent, and negative interactions among attributes, which restricts the applicability of TODIM method. Therefore, in this paper, we propose the 2-additive fuzzy Choquet integral-based hesitant fuzzy TODIM method to deal with this situation. To begin with, we propose the novel measured function to compare the magnitude of hesitant fuzzy elements, which has been proved to be more rational and efficient than existing approaches. Then we use nonlinear programming to obtain 2-additive fuzzy measures and then put forward novel Choquet integral based-dominance degree to calculate the dominance degree of one alternative over another under all attributes. Consequently, we then calculate the global value of each alternative whereby we can rank all the alternatives. Finally, an illustrate example is used to demonstrate the efficiency and applicability of the proposed approach with sensitivity analysis. [ABSTRACT FROM AUTHOR]

There has been a growing interest in the study of the notion of α-migrativity and generalizations in recent years, and it has been investigated for families of certain operators such as t-norms, t-conorms, uninorms, nullnorms. This paper is mainly devoted to investigating the migrativity equations between semi-t-operators or semi-uninorms, and Mayor's aggregation operators. The results that we obtain are complete and different from the known ones concerning migrativity for t-norms, t-conorms, uninorms and nullnorms. [ABSTRACT FROM AUTHOR]

In this paper, a method is introduced which reduces the harmonic distortion of the inverter output current, connecting the fuel cell to the AC load. Using FUZZY LOGIC-PI (FLPI), the controlling method is engaged in optimum tuning of the PI controller coefficients of this converter. This converter has only one DC-AC boost inverter and simultaneously has the task of increasing voltage level and generating the AC power. In order to control the inverter output voltage, an internal current control loop and an external voltage control loop are used. Designing the control of each loop is done separately based on FLPI controller. Simulation results for proposed fuel cell energy system in the presence of this controller imply good performance of FLPI and suitable mitigation of inverter output current ripple. [ABSTRACT FROM AUTHOR]

Dual probabilistic linguistic term sets (DPLTSs) are more powerful compare to probabilistic linguistic term sets, probabilistic hesitant fuzzy sets, hesitant fuzzy sets and intuitionistic fuzzy sets for the reason that they deal with both belongingness grades and non-belongingness grades along with their respective probabilities. On the other hand, the generalized Dombi operators have higher flexibility due to inclusion of two parameters. MARCOS (Measurements alternatives and ranking according to compromise solution) technique was developed by utilizing the utility degrees of options using the ideal and anti-ideal solutions. Here, we combine the merits of generalized Dombi operator and MARCOS and propose a DPL-MARCOS approach under dual probabilistic linguistic setting. In this methodology, the concepts of consistency and similarity between the experts are used to calculate their weights of subjective and objective types, respectively. For aggregating experts’ preferences, we propose dual probabilistic linguistic- generalized Dombi weighted averaging aggregation operator. A biomass feedstock selection problem is furnished to show the applicability of our technique. We have considered coconut shell, coffee husk and sugarcane baggage as alternatives. The result shows that coffee husk is the most suitable option. The sensitivity assessment of parameter values reveals that our technique is stable. The comparative study proves that our model is more significant and realistic compare to the existing ones. [ABSTRACT FROM AUTHOR]

Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are a very useful means to depict the linguistic information in the process of decision making. In this article, we investigate the group decision making problems in which all the linguistic information provided by the decision makers is expressed as interval type-2 fuzzy decision matrices where each of the elements is characterized by interval type-2 fuzzy set, and the information about attribute weights is completely unknown. We first introduce the average centroid matrix of the interval type-2 fuzzy decision matrix, and then utilize the interval type-2 fuzzy averaging operator to aggregate all individual interval type-2 fuzzy decision matrices into a collective interval type-2 fuzzy decision matrix. Based on the average centroid matrix of the collective interval type-2 fuzzy decision matrix and information theory, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the interval type-2 fuzzy averaging operator, we utilize the average centroid measure to give an approach to ranking the given alternatives and then selecting the most desirable one(s). Finally, we give an illustrative example. [ABSTRACT FROM AUTHOR]

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The current study set to extend a new VIKOR method as a compromise ranking approach to solve multiple criteria decision-making (MCDM) problems through intuitionistic fuzzy analysis. Using compromise method in MCDM problems contributes to the selection of an alternative as close as possible to the positive ideal solution and far away from the negative ideal solution, concurrently. Using Atanassov intuitionistic fuzzy sets (A-IFSs) may simultaneously express the degree of membership and non-membership to decision makers (DMs) to describe uncertain situations in decision-making problems. The proposed intuitionistic fuzzy VIKOR indicates the degree of satisfaction and dissatisfaction of each alternative with respect to each criterion and the relative importance of each criterion, respectively, by degrees of membership and non-membership. Thus, the ratings for the importance of criteria, DMs, and alternatives are in linguistic variables and expressed in intuitionistic fuzzy numbers. Using IFS aggregation operators and with respect to subjective judgment and objective information, the most suitable alternative is indicated among potential alternatives. Moreover, practical examples illustrate the procedure of the proposed method. [ABSTRACT FROM AUTHOR]