Hesitant fuzzy set (HFS), which allows the membership degree of an element to a set represented by several possible values, is considered as a powerful tool to express uncertain information in the process of multi-attribute decision making (MADM) problems. In this paper, we develop a novel approach based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and the maximizi...

Abstract. This paper proposes the concept of an interval neutrosophic hesitant fuzzy set (INHFS) and the operational relations of INHFSs. Then, we develop correlation coefficients of INHFSs and investigate the relation between the similarity measures and the correlation coefficients. Furthermore, a multiple attribute decision making method based on the correlation coefficients is established un...

Recently, a novel hesitant fuzzy set (HFS) ranking technique based on the idea of lexicographical ordering is proposed and an example is presented to demonstrate that the proposed ranking method is invariant with multiple occurrences of any element of a hesitant fuzzy element (HFE). In this paper, we show by examples that the HFS lexicographical ordering method is sometimes invalid, and a modif...

In medical science, disease diagnosis is one of the difficult tasks for medical experts who are confronted with challenges in dealing with a lot of uncertain medical information. And different medical experts might express their own thought about the medical knowledge base which slightly differs from other medical experts. Thus, to solve the problems of uncertain data analysis and group decisio...

Due to importance of correlation measure in data analysis, some researchers have shown great interest in the concept of correlation measure for extensions of fuzzy sets, in particular, for a new extension known as hesitant fuzzy set (HFS). Recently, an extension of HFS called the weighted hesitant fuzzy set (WHFS) has been developed by Zhang and Wu [1] to allow the membership of a given element...

We introduce the concepts of entropy and cross-entropy for hesitant fuzzy information, and discuss their desirable properties. Several measure formulas are further developed, and the relationships among the proposed entropy, cross-entropy, and similarity measures are analyzed, from which we can find that three measures are interchangeable under certain conditions. Then we develop two multiattri...

The concept of dual hesitant fuzzy sets (DHFSs), which was first introduced as a new extension of fuzzy sets and hesitant fuzzy sets in 2012, is a useful tool to deal with the vagueness and ambiguity in many practical problems under hesitant fuzzy environment. Normally, we use the definition of distance to describe the relationship of two DHFSs. However, considering that the existing distance m...

The Maclaurin symmetric mean (MSM) was originally introduced by Maclaurin. The prominent characteristic of the MSM is that it can capture the interrelationship among the multi-input arguments. However, the researches on MSM are very rare, especially in fuzzy decision making. In this paper, we investigate the MSM operator and extend the MSM operator to hesitant fuzzy environment and develop the ...

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...

In this paper we introduce the notion of interval valued hesitant fuzzy soft topological space. Also the concepts of interval valued hesitant fuzzy soft closure; interior and neighbourhood are introduced here and established some important results.