Quantitative and qualitative fuzzy measures have been proposed to hesitant fuzzy sets 9 (HFSs) from different points. However, few of the existing HFSs fuzzy measures refer to the grey 10 relational analysis (GRA) theory. Actually, the GRA theory is very useful in the fuzzy measure 11 domain, which has been developed for such the intuitionistic fuzzy sets. Therefore, in this paper, 12 we apply ...

In intuitionistic fuzzy sets, there is a natural symmetry between degrees of truth and falsity. As a result, for such sets, natural similarity measures are symmetric relative to an exchange of true and false values. It has been recently shown that among such measures, the most intuitively reasonable are the ones which are also symmetric relative to an arbitrary permutation of degrees of truth, ...

—Experts are often not 100% con dent in their statements. In traditional fuzzy logic, the expert's degree of con dence in each of his or her statements is described by a number from the interval [0, 1]. However, due to similar uncertainty, an expert often cannot describe his or her degree by a single number. It is therefore reasonable to describe this degree by, e.g., a set of numbers. In this ...

Complex numbers can capture compound features and convey multifaceted information; thereby providing means for solving complicated problems. In this paper, we combine the degree of membership and a degree of non-membership of members of Intuitionistic Fuzzy Sets via complex numbers to characterize these fuzzy sets. This approach enables extending several concepts such as classical fuzzy sets, P...

This paper examines the fuzzy system for function approximation in a macroscopic level. The rules of a fuzzy function approximation system are expressed in the form of polynomials such that each rule forms a local approximator. We show that this kind of fuzzy function approximation is equivalent to piecewise polynomial interpolation between turning points when normalized fuzzy function membersh...

Intuitionistic fuzzy sets are generalized fuzzy sets whose elements are characterized by a membership, as well as a non-membership value. The membership value indicates the degree of belongingness, whereas the nonmembership value indicates the degree of non-belongingness of an element to that set. The utility of intuitionistic fuzzy sets theory in computer vision is increasingly becoming appare...

In this paper, we deal with a two-person zero-sum games with fuzzy payoffs and fuzzy goals. The aim of the paper is to explain new concepts of solutions for a two-person zero-sum games with fuzzy payoffs and fuzzy goals. We assume that each player has a fuzzy goal for each of the payoffs. A degree of attainment of the fuzzy goal is defined and the max-min strategy with respect to the degree of ...

The Arrow index of a fuzzy choice function C is a measure of the degree to which C satisfies the Fuzzy Arrow Axiom, a fuzzy version of the classical Arrow Axiom. The main result of this paper shows that A(C) characterizes the degree to which C is full rational. We also obtain a method for computing A(C). The Arrow index allows to rank the fuzzy choice functions with respect to their rationality...

A new approach for testing fuzzy hypotheses based on fuzzy data is introduced. According to the proposed approach, a method is first developed based on the defined fuzzy point estimation, which are then used to make a procedure for testing fuzzy hypotheses. This approach has been used to test simple, one-sided and two-sided fuzzy hypotheses. Two new criteria, called degree of acceptance (DA) an...

at early stages of new product development, the effort tooptimize is low and effects on the whole innovation process are high.therefore, a deeper understanding of fuzzy front end and its successcan help firms to be more successful in developing new products. wepresented and tested a conceptual model of relationships among keyvariable sre lated to the fuzzy front end,execution phase of new produ...