In this paper, we study countably compact fuzzy sets using the definition of C. K. Wong [10] and obtain its several properties. 1. Introduction The concept of fuzzy set and fuzzy set operations were first introduced by L. A. Zadeh [11] in1965. Several other mathematicians studied fuzzy sets in various areas in mathematics. Firstly, C. L. Chang [2] in 1968 developed the theory of fuzzy topologic...

Alternative rules for the aggregation of different sources of information are discussed in the ambit of random set theory, which gives a general framework in the field of the uncertainty measures, containing probabilistic measures, set-based models (interval analysis or more generally convex models), fuzzy sets and possibility theory as particular extreme cases. Analogies and extensions of the ...

in this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. it would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. we give the main properties of the operations defined and prove som...

Each fuzzy set can be represented by a nested system of ordinary sets—its a-cuts. There is an extensive literature on fuzzy sets devoted to problems of the following kind: is it possible to reduce operations with fuzzy sets to operations with their a-cuts? Is it possible to reduce properties of fuzzy relations to properties of their a-cuts? More generally, can a fuzzy concept be represented by ...

This research addresses system reliability analysis using weakest t-norm based approximate intuitionistic fuzzy arithmetic operations, where failure probabilities of all components are represented by different types of intuitionistic fuzzy numbers. Due to the incomplete, imprecise, vague and conflicting information about the component of system, the present study evaluates the reliability of sy...

In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

Manufacturing flexibility is a competitive weapon for surviving today’s highly variable and volatile markets. It is critical therefore, to select the appropriate type of flexibility for a given manufacturing system, and to design effective strategies for using this flexibility in a way to improve the system performance. This study focuses on full routing flexibility which includes not only alte...

Let us consider the Analytic Hierarchy Process in which the labels are structured as graded numbers. To obtain the scoring that corresponds to the best alternative, or the ranking of the alternatives, we need to use a total order for the graded numbers involved in the problem. In this article, we consider a definition of such a total order, which is based upon two subjective aspects: the degree...

The purpose of this paper is to extend a new balancing and ranking method to handle uncertainty for a multiple attribute analysis under a hesitant fuzzy environment. The presented hesitant fuzzy balancing and ranking (HF-BR) method does not require attributes’ weights through the process of multiple attribute decision making (MADM) under hesitant conditions. For the rating of possible alternati...

A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect t...