In this paper, we research the relationship between entropy and similarity of interval valued intuitionistic fuzzy sets in detail and prove eight theorems that entropy and similarity of interval valued intuitionistic fuzzy sets can be transformed to each other based on their axiomatic definitions. Finally, we propose some formulaes to calculate entropy and similarity of interval valued intuitio...

In this paper, we define the concept of incomplete hesitant fuzzy preference relations to deal with the cases where the decision makers express their judgments by using hesitant fuzzy preference relations with incomplete information, and investigate the consistency of the incomplete hesitant fuzzypreference relations and obtain the reliable priority weights. We first establish a goal programmin...

This paper deals with interval-valued fuzzy sets and I-fuzzy sets, Atanassov's intuitionistic fuzzy sets. They are treated in a systematic way as two, formally equivalent, natural extensions of methods of representing incomplete knowledge about sets. We define and investigate triangular norm-based areas of uncertainty of interval-valued fuzzy sets and I-fuzzy sets, and study some properties of ...

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 practical situations, interval-valued fuzzy sets are frequently encountered. In this paper, firstly, we present shadowed sets for interpreting and understanding interval fuzzy sets. We also provide an analytic solution to computing the pair of thresholds by searching for a balance of uncertainty in the framework of shadowed sets. Secondly, we construct errorsbased three-way approximations of...

Abstract The hesitant fuzzy set has been an important tool to address problems of decision making. There are several various improved sets, such as dual set, interval-valued and intuitionistic however, no one kind sets could reflect attitude characteristics makers on time-sequences. In reality, time-sequence is sector situations might have different knowledges the same alternative at moments. T...

We begin the paper studying the axioms that the indicators of the grade of inclusion of a fuzzy set in another fuzzy set must satisfy. Next, we present an expression of such indicator, ®rst for fuzzy sets and then for interval-valued fuzzy sets, analyzing in both cases their main properties. Then, we suggest an expression for the similarity measure between interval-valued fuzzy sets. Besides, w...

We continue to develop a construction of an L-fuzzy valued measure by extending a measure defined on a σalgebra of crisp sets to an L-fuzzy valued measure defined on a TM-tribe in the case when operations with L-sets and L-fuzzy numbers are defined by using the minimum triangular norm TM . We introduce an L-fuzzy valued integral over an L-set with respect to an L-fuzzy valued measure, consider ...