We introduce the concepts of interval-valued fuzzy mα-open sets and interval-valued fuzzy mα-continuous mappings. And we study some characterizations and properties of such concepts.

In this paper, we propose a fuzzy SVk -modes algorithm that uses the fuzzy k -modes clustering process to cluster categorical data with set-valued attributes. In the proposed algorithm, we use Jaccard coefficient to measure the dissimilarity between two objects and represent the center of a cluster with set-valued modes. A heuristic update way of cluster prototype is developed for the fuzzy par...

In this paper, the notion of the interval valued neutrosophic soft sets (ivn−soft sets) is defined which is a combination of an interval valued neutrosophic sets [36] and a soft sets [30]. Our ivn−soft sets generalizes the concept of the soft set, fuzzy soft set, interval valued fuzzy soft set, intuitionistic fuzzy soft set, interval valued intuitionistic fuzzy soft set and neutrosophic soft se...

In this Chapter, invoking the notion of signed fuzzy number valued measures on the fuzzy set, we attempt to study the Lebesgue decompositions of a signed fuzzy number valued measures. We introduce in this Chapter a new notion called singular complements to the domain of fuzzy number valued measures and derive some consequential properties. The contents of this chapter form the material of the p...

In this lecture we give several examples and lessons learned from research, development and experiments in the area of theory and applications of information technology. We will try to describe a possible synergy of theory and application too. Namely, to describe where practical needs bring new problems for theory and where theory helps to formulate methods, which should be verified in practice...

Interval-valued data can find their practical applications in such situations as recording monthlyinterval temperatures at meteorological stations, daily interval stock prices, etc. The primary objectiveof the presented paper is to compare three different methods of fuzzy clustering for interval-valuedsymbolic data, i.e.: fuzzy c-means clustering, adaptive fuzzy c-means clustering a...

The fuzzy extension principle has been widely used to extend the domain of mathematical functions and relations from elements of a referential set to fuzzy subsets of that referential set. However, there are restrictions associated with the fuzzy extension principle. This paper addresses the question how restricted is the family of “fuzzy set to fuzzy set mappings” obtained by the fuzzy extensi...

In this paper, we first introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we consider the interval valued ( , fuzzy (implicative) ideals of pseudo-MV algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy (implicative) ideals are derived. ) q ∈∈∨ −

Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Rela­ tionship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.

In this paper, we propose new methods to represent interdependence among alternative attributes and experts’ opinions by constructing Choquet integral using interval-valued intuitionistic fuzzy numbers. In the sequel, we apply these methods to solve the multiple attribute group decision-making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. First, the concept of interva...