Iranian journal of fuzzy systems
Volume:16 Issue: 3, May-June 2019

In this contribution connections between input fuzzy relations R1, . . . ,Rn on a set X and the output fuzzy relationRF = F(R1, . . . ,Rn) are studied. F is a function of the form F : [0, 1]n → [0, 1] and RF is called an aggregated fuzzyrelation. In the literature the problem of preservation, by a function F, diverse types of properties of fuzzy relationsR1, . . . ,Rn is examined. Here, it is considered the converse approach. Namely, fuzzy relation RF = F(R1, . . . ,Rn) isassumed to have a given property and then it is checked if fuzzy relations R1, . . . ,Rn have this property. Moreover, adiscussion on the mentioned two approaches is provided. The properties, which are examined in this paper, depend ontheir notions on binary operations B : [0, 1]2 → [0, 1]. By incorporating operation B these properties are generalizedversions of known properties of fuzzy relations.

In this paper, we present a new fuzzy reasoning method based on the compensating fuzzy reasoning (CFR). Its basicidea is to obtain a new fuzzy reasoning result by moving and deforming the consequent fuzzy set on the basis of themoving, deformation, and moving-deformation operations between the antecedent fuzzy set and observation information.Experimental results on real-world data sets show that proposed method signi ficantly improve the accuracy and timeperformance of fuzzy neural network learning.

Decision matrix in group decision making problems depends on a lot of criteria. It is essential to know the necessity ofweight or coefficient of each criterion. Accurate and precise selection of weight will help to achieve the intended goal.The aim of this article is to introduce a linear programming model for recognizing the importance of each criterion inmulti criteria group decision making with intuitionistic fuzzy data through similarity measure between each alternativeand ideal alternative. Based on this model, decision makers and experts will be prevented from making mistakes inrecognizing the weight and shape of standardization of their mental measurement units. By using of determined weights,the alternatives will be ranked according to a new method based on ELECTRE III method. An applied and numericalexample is presented and the obtained results are compared with other methods.

Using alternative fuel vehicles is one of the ways to reduce the consumption of fossil fuels which have many negative environmental effects. An alternative fuel vehicle needs special planning for its refueling operations because of some reasons, e.g. limited number of refueling stations, uncertain refueling queue times in the stations, variable alternative fuel prices among the stations, etc. In this paper, a new problem as refueling an alternative fuel vehicle on a given path is formulated to minimize the cost of refueling and waiting times in the stations for refueling operations, simultaneously. To be more close to real-world situations, the waiting times are considered as intuitionistic fuzzy numbers in order to reflect uncertainty as well as hesitation due to various uncontrollable factors. To cope with the uncertainty of the problem, an intuitionistic fuzzy chance constrained method based on credibility measure is proposed to convert the fuzzy formulation to a crisp model. In order to tackle the bi-objective crisp formulation, a new interactive fuzzy solution method is proposed. A computational study on a real case from Turkey shows that the performance of the presented method is either better or the same as the approaches of the literature.}

Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$.  In this paper, we intend to offer a novel fuzzy radial basis function by the concept of source distance. Then, we will construct a fuzzy linear combination of such basis functions in order to introduce a fully fuzzy quasi-interpolation in the form of $widetilde{f}^{*}:F(mathbb{R})rightarrow F(mathbb{R})$. Also the error estimation of the proposed method is proved in terms of the fully fuzzy modulus of continuity which will be introduced in this paper. Finally some examples have been given to emphasize the acceptable accuracy of our method.

Galois connection in category theory play an important role inestablish the relationships between different spatial structures. Inthis paper, we prove that there exist many interesting Galoisconnections between the category of Alexandroff $L$-fuzzytopological spaces, the category of reflexive $L$-fuzzyapproximation spaces and the category of Alexandroff $L$-fuzzyinterior (closure) spaces. This indicates that there is a closeconnection between the three structures.

Myerson treated various situations of cooperation in the field of cooperative games and proposed the communication structure. In this paper, we define and characterize an allocation rule in terms of the position value, called an average spanning tree solution, for communication situations by introducing a concept of cooperation relationship which says that two players are deemed to possess this relationship if there is a communication path through them. Considering the fact that the extent to what players participate in a coalition may be partially restricted for uncertain possibilities, we construct a graph game in multilinear extension form and continue to explore the fuzzy average spanning tree solution on a framework of communication situation with fuzzy coalition.

For many decision problems with uncertainty, triangular intuitionistic fuzzy number is a useful tool in expressing ill-known quantities. This paper develops a novel decision method based on zero-sum game for multiple attribute decision making problems where the attribute values take the form of triangular intuitionistic fuzzy numbers and the attribute weights are unknown. First, a new value index is defined for triangular intuitionistic fuzzy numbers on the basis of the centroid. Thereby, a new ranking approach is presented for comparing triangular intuitionistic fuzzy numbers. We formulate a multiple attribute decision making problem as a two-person zero-sum game with payoffs of triangular intuitionistic fuzzy numbers. Then, following the new ranking approach, the fuzzy matrix game is converted as a pair of crisp linear programming models, and the optimal strategies are objectively derived by solving such models. Therefore, the ranking order of alternatives is determined by the expected scores of alternatives. An example of video monitoring system selection is demonstrated to illustrate the effectiveness of the proposed methodology.

Plenty of researches have been carried out, focusing on the measures of distance, similarity, and correlation between intuitionistic fuzzy sets (IFSs).However, most of them are single-valued measures and lack of potential for efficiency validation.In this paper, a new vector valued similarity measure for IFSs is proposed based on OWA operators.The vector is defined as a two-tuple consisting of the similarity measure and uncertainty measure, in which the latter is the uncertainty of the former.OWA operators have the ability to aggregate all values in the universe of discourse of IFSs, and to determine the weights according to specific applications.A framework is built to measure similarity between IFSs.A series of definitions and theorems are given and proved to satisfy the corresponding axioms defined for IFSs.In order to illustrate the effectiveness of the proposed vector valued similarity measure,a classification problem is used as an application.

This paper gives a decentralized approach to the problem of failure prognosis in the framework of fuzzy discrete event systems (FDES). A notion of co-predictability is formalized for decentralized prognosis of FDESs, where several local agents with fuzzy observability rather than crisp observability are used in the prognosis task. An FDES is said to be co-predictable if each faulty event can be predicted prior to its occurrence by at least one local agent using the observability of fuzzy events. The verification of the decentralized predictability is performed by constructing a fuzzy co-verifier from a given FDES. The complexity of the fuzzy co-verifier is polynomial with respect to the FDES being predicted, and is exponential with respect to the number of the local prognosis agents. Then, a necessary and sufficient condition for the co-predictability of FDESs is given. In addition, we show that the proposed method may be used to deal with the decentralized prognosis for both FDESs and crisp DESs. Finally, to illustrate the effectiveness of the approach, some examples are provided.

The purpose of this paper is to develop a new two-stage method for fuzzy multi-objective linear program and apply to engineering project portfolio selection. In the fuzzy multi-objective linear program, all the objective coefficients, technological coefficients and resources are trapezoidal fuzzy numbers (TrFNs). An order relationship for TrFNs is introduced by using the interval expectation of TrFNs. In the first stage, the fuzzy multi-objective linear program with TrFNs is transformed into an interval multi-objective linear program according to the order relationship of TrFNs. Combining the ranking order relation between intervals with the satisfactory crisp equivalent forms of interval inequality relations, the interval multi-objective linear program is further transformed into a crisp multi-objective linear program. In the second stage, the positive and negative ideal solutions are calculated as well as the closeness degrees from the positive ideal solution to all objectives on the basis of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). Then, using the closeness degrees, we convert the crisp multi-objective linear program into mono-objective program to solve. The proposed method is not only mathematically rigorous, but also can adequately consider the acceptance degree of decision maker that the fuzzy constraints may be violated. The other possible cases of the fuzzy multi-objective linear program are also discussed. The proposed method is illustrated by means of a project portfolio selection problem.

This article formulates a new technique for behavior analysis of systems through fuzzy Kolmogorov's differential equations and Particle Swarm Optimization. For handling the uncertainty in data, differential equations have been formulated by Markov modeling of system in fuzzy environment. First solution of these derived fuzzy Kolmogorov's differential equations has been found by Runge-Kutta fourth order method and thereafter the solution has been improved by Particle Swarm Optimization. Fuzzy availability is estimated in its transient as well as steady states. Sensitivity analysis has also been done to find the relative importance of a particular component of the system. Butter oil processing plant as an industrial system has been studied as a case for application of the proposed approach.

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varepsilon)$ is called a generalized GL-monoid if$(L,*,varepsilon)$ is a commutative unital quantale and the operation $*$ is$otimes$-semi-distributive. For generalized GL-monoid $L$ as thetruth value table, we systematically propose the stratified$L$-generalized convergence spaces based on stratified $L$-filters,which makes various existing lattice-valued convergence spaces asspecial cases. For $L$ being a commutative unital quantale, wedefine a fuzzy Scott convergence structure on $L$-fuzzy dcpos anduse it to induce a stratified $L$-topology. This is the inducing wayto the definition of quantale-valued fuzzy Scott topology, whichseems an appropriate way by some results.

By considering the supreme-utilities among fuzzy sets and the weights among participants simultaneously, we introduce the supreme-weighted value on fuzzy transferable-utility games. Further, we provide some equivalent relations to characterize the family of all solutions that admit a potential on weights. We also propose the dividend approach to provide alternative viewpoint for the potential approach. Based on these equivalent relations, several axiomatic results are also proposed to present the rationality for the supreme-weighted value.