Journal•ISSN: 0165-0114

# Fuzzy Sets and Systems

Elsevier BV

About: Fuzzy Sets and Systems is an academic journal published by Elsevier BV. The journal publishes majorly in the area(s): Fuzzy logic & Fuzzy set. It has an ISSN identifier of 0165-0114. Over the lifetime, 8867 publications have been published receiving 445661 citations.

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TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

Abstract: A definition of the concept 'intuitionistic fuzzy set' (IFS) is given, the latter being a generalization of the concept 'fuzzy set' and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

13,376 citations

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TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.

Abstract: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable. More specifically, if F is a fuzzy subset of a universe of discourse U={u} which is characterized by its membership function μF, then a proposition of the form “X is F,” where X is a variable taking values in U, induces a possibility distribution ∏X which equates the possibility of X taking the value u to μF(u)—the compatibility of u with F. In this way, X becomes a fuzzy variable which is associated with the possibility distribution ∏x in much the same way as a random variable is associated with a probability distribution. In general, a variable may be associated both with a possibility distribution and a probability distribution, with the weak connection between the two expressed as the possibility/probability consistency principle. A thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is, in the main, possibilistic rather than probabilistic in nature. Thus, by employing the concept of a possibility distribution, a proposition, p, in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p. Several types of conditional translation rules are discussed and, in particular, a translation rule for propositions of the form “X is F is α-possible,” where α is a number in the interval [0, 1], is formulated and illustrated by examples.

8,918 citations

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TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.

Abstract: In the recent past numerous models and methods have been suggested to solve the vectormaximum problem. Most of these approaches center their attention on linear programming problems with several objective functions. Apart from these approaches the theory of fuzzy sets has been employed to formulate and solve fuzzy linear programming problems. This paper presents the application of fuzzy linear programming approaches to the linear vectormaximum problem. It shows that solutions obtained by fuzzy linear programming are always efficient solutions. It also shows the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution.

3,357 citations

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TL;DR: The rating of each alternative and the weight of each criterion are described by linguistic terms which can be expressed in triangular fuzzy numbers and a vertex method is proposed to calculate the distance between two triangular fuzzyNumbers.

Abstract: The aim of this paper is to extend the TOPSIS to the fuzzy environment. Owing to vague concepts frequently represented in decision data, the crisp value are inadequate to model real-life situations. In this paper, the rating of each alternative and the weight of each criterion are described by linguistic terms which can be expressed in triangular fuzzy numbers. Then, a vertex method is proposed to calculate the distance between two triangular fuzzy numbers. According to the concept of the TOPSIS, a closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to both the fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) simultaneously. Finally, an example is shown to highlight the procedure of the proposed method at the end of this paper.

3,109 citations

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TL;DR: The problems of structure identification of a fuzzy model are formulated and an algorithm for identifying a structure is suggested and a successive identification algorithm of the parameters is suggested.

Abstract: The problems of structure identification of a fuzzy model are formulated. A criterion for the verification of a structure is discussed. Using the criterion, an algorithm for identifying a structure is suggested. Further, a successive identification algorithm of the parameters is suggested. The proposed methods are applied to an example.

2,649 citations