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...

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in amedical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised...

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 article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define extended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm...

In this work, we present definition of intuitionistic fuzzy parameterized (ifp) intuitionistic fuzzy soft set and its operations. Then we define ifp-aggregation operator to form ifp-intuitionistic fuzzy soft decision making method which allows constructing more efficient decision processes. Keyword 0.1 Soft set, intuitionistic fuzzy set, intuitionistic fuzzy soft set, intuitionistic fuzzy param...

Decision making is a process common to human beings. The uncertainty and fuzziness of problems demand the use of the fuzzy linguistic approach to model qualitative aspects of problems related to decision. The recent proposal of hesitant fuzzy linguistic term sets supports the elicitation of comparative linguistic expressions in hesitant situations when experts hesitate among different linguisti...