In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets DHFSs , which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy...

This study is to propose a new approach for medical diagnosis using the distance between interval-valued intuitionistic fuzzy sets. For this purpose, we developed an interview chart with interval fuzzy degrees based on the relation between symptoms and diseases (three types of headache), and utilized the interval-valued intuitionistic fuzzy weighted arithmetic average operator to aggregate fuzz...

In this paper, we propose a method to calculate the correlation coefficient of generalized intuitionistic fuzzy sets by means of "centroid". The value which obtained from this method tell us the strength of relationship between the generalized intuitionistic fuzzy sets [11] and the whether the generalized intuitionistic fuzzy sets are positively or negatively related. This method looks better t...

It is known that interval-valued fuzzy sets provide a more adequate description of expert uncertainty than the more traditional “type-1” (number-valued) fuzzy techniques. In the current approaches for using interval-valued fuzzy techniques, it is usually assumed that all fuzzy sets m(x) ∈ [m(x), m(x)] are possible. In this paper, we show that it is reasonable to restrict ourselves only to fuzzy...

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 introduce the concept of interval valued (α, β)-fuzzy subnear-rings and ideal of near-rings, where α, β any two of the {∈, q,∈ ∨q,∈ ∧q} with α 6=∈ ∧q, by using belongs to relation ∈ and quasi-coincidence with relation q between interval valued fuzzy points and interval valued fuzzy sets. We also discussed some characterizations of interval valued (α,∈ ∨q)-fuzzy ideals(subnear-...

In 1965, in his pioneer paper L.A. Zadeh [9] introduced the concept of fuzzy set to handle the uncertainties in our daily life. After that many generalizations of fuzzy sets are presented, for example, interval valued fuzzy sets [10] and intuitionistic fuzzy sets [1]. Fuzzy sets are extremely useful to solve many problems in applied mathematics, information sciences and theory of automata [2]. ...