In the traditional fuzzy logic, the expert’s degree of certainty in a statement is described either by a number from the interval [0, 1] or by a subinterval of such an interval. To adequately describe the opinion of several experts, researchers proposed to use a union of the corresponding sets – which is, in general, more complex than an interval. In this paper, we prove that for such set-value...

In fuzzy models, redundancy may be present in the form of similar fuzzy sets, especially in the construction of a fuzzy system from a set of given training examples. In this paper, a simple formula for calculating the degree of similarity of Trapezoidal membership functions is derived in order to merge similar membership functions and hence to obtain a more transparent rule-base with a minimum ...

Given a fuzzy variable, what is the degree of difficulty of predicting the specified value that the fuzzy variable will take? Entropy provides a measure to characterize the fuzziness. Given some constraints, there are usually multiple compatible membership functions. Which membership function shall we take? The maximum entropy principle attempts to select the membership function that maximizes ...

when describing categories analytically, most traditions of thought have treated category membership as a digital, all-or-none phenomenon. That is, much work in philosophy, psychology, linguistics, and anthropology assumes that categories are logical bounded entities, membership in which is defined by an item’s possession of a simple set of criterial features, in which all instances possessing ...

*Correspondence: [email protected] School of Science, Hebei University of Engineering, Handan 056038, China Abstract Uncertain set is a set-valued function on an uncertainty space, and attempts to model unsharp concepts. Membership function is used to describe the membership degree that a value belongs to the uncertain set. In order to estimate the membership function for an uncertain set via...

This paper proposes a fuzzy goal programming based on Taylor series for solving decentralized bilevel multiobjective fractional programming (DBLMOFP) problem. In the proposed approach, all of the membership functions are associated with the fuzzy goals of each objective at the both levels and also the fractional membership functions are converted to linear functions using the Taylor series appr...

This study examined the experiences of 13 graduate students enrolled in a closed, lock-step master’s degree of the education cohort program. Interview and observational data, collected over 10 months and across four courses, were qualitatively analyzed to explore students’ understanding of the meaning of cohort membership and how that membership both shaped their educational experience and the ...

In many applications of fuzzy set theory, the membership of an object is not defined directly. One of its attributes (like height, age, weight, . . . ) is first mapped on a real number (often by means of a physical instrument) and a parametric function then maps this real number on a membership degree in some fuzzy set (like ‘tall’, ‘old’, ‘heavy’, . . . ). A very common parametric function is ...

The purpose of this paper is to introduce multiattribute decision making based on the concept of interval neutrosophic sets. While the concept of neutrosophic sets is a powerful tool to deal with indeterminate and inconsistent data, the interval neutrosophic set is also a powerful mathematical tool as well as more flexible to deal with incompleteness. The rating of all alternatives is expressed...

in this paper, we present an application of intuitionistic fuzzyprogramming to a two person bi-matrix game (pair of payoffs matrices) for thesolution with mixed strategies using linear membership and non-membershipfunctions. we also introduce the intuitionistic fuzzy(if) goal for a choiceof a strategy in a payoff matrix in order to incorporate ambiguity of humanjudgements; a player wants to max...