Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...

Yager’s ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts’ individual opinions or preferences for achieving an overall decision. The traditional Yager’s OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic te...

Because of the complexity of decision-making environment, the uncertainty of fuzziness and the uncertainty of grey maybe coexist in the problems of multi-attribute group decision making. In this paper, we study the problems of multi-attribute group decision making with hybrid grey attribute data (the precise values, interval numbers and linguistic fuzzy variables coexist, and each attribute val...

As we may have a set of possible values when comparing alternatives (or criteria), the hesitant fuzzy preference relation becomes a suitable and powerful technique to deal with this case. This paper mainly focuses on the multiplicative consistency of the hesitant fuzzy preference relation. First of all, we explore some properties of the hesitant fuzzy preference relation and develop some new ag...

The concept of trapezoidal valued hesitant fuzzy set is introduced. Notion for distance between any two trapezoidal valued hesitant fuzzy elements is given. Using this proposed distance measure, we extend the technique for order preference by similarity to ideal solution for trapezoidal valued hesitant fuzzy sets. An example is constructed to show usefulness of this extension for multicriteria ...

Single valued neutrosophic hesitant fuzzy set has three independent parts, namely the truth membership hesitancy function, indeterminacy membership hesitancy function, and falsity membership hesitancy function, which are in the form of sets that assume values in the unit interval [0, 1]. Single valued neutrosophic hesitant fuzzy set is considered as a powerful tool to express uncertain, incompl...

The soft set theory is a newly mathematical tool to deal with uncertain problems. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, we introduce the average function and propose the interval-valued intuitionistic hesitant fuzzy soft sets (IVIHFSSs) which are a combination of the interval-valued intuitionistic hesitant fuzzy sets and...

Here are many situations in real applications of decision making where we deal with uncertain conditions.  Due to the different sources of uncertainty,  since its original definition of fuzzy sets in 1965 cite{zadeh1965},  different generalizations and extensions of fuzzy sets have been introduced: Type-2 fuzzy sets cite{6,13}, Intuitionistic fuzzy sets cite{1}, fuzzy multi-sets cite{37} and et...