Decision making under uncertainty is a crucial issue and most demanding area of research now a days. Intuitionistic hesitant fuzzy set plays important role in dealing with the circumstances in which decision makers judge an alternative with a collection membership grades and a collection of non-membership grades. This paper contributes a novel and advanced distance measure between Intuitionistic Hesitant fuzzy sets (IHFSs). A comparative analysis of the present distance measure with existing measures is performed first. Afterwards, a case study is carried in multi-criteria decision making problem to exhibit the applicability and rationality of the proposed distance measure. The advantage of the proposed distance measure over the existing distance measures is that in case of deficit number of elements in IHFs, a decision maker can evaluate distance measure without adding extra elements to make them equivalent and furthermore, it works in successfully in all the situations.

/pdf/fuzzy-multi-criteria-decision-making-algorithm-under-4uku42a77j.pdf

Fuzzy Multi-Criteria Decision Making Algorithm under Intuitionistic Hesitant Fuzzy Set with Novel Distance Measure

A study on generalized hesitant intuitionistic Fuzzy soft sets

Generalized intuitionistic fuzzy soft matrices and their application

Some properties of new hesitant fuzzy operators


 In this paper, we introduce an extension theory of the trapezoidal intuitionistic fuzzy numbers under intuitionistic hesitant fuzzy sets called trapezoidal hesitant intuitionistic fuzzy number (THIF-number). This new theory provides very effectively to model uncertainties of some events by several different trapezoidal intuitionistic fuzzy numbers based on the same support set in the set of real numbers R. Also, to demonstrate the application of this theory, a new multi-criteria decision-making(MCDM) method based on THIF-numbers is presented. To do this, we first propose

operations of THIF-numbers with properties. We second give score, standard deviation degree, deviation degree of THIF-numbers to compare THIF-numbers. We third develop geometric operators and arithmetic operators of THIF-number. Finally, a numerical example is presented to illustrate the application of the developed method in THIF-numbers.

/pdf/trapezoidal-hesitant-intuitionistic-fuzzy-numbers-and-their-csvx2phms8.pdf

Trapezoidal Hesitant Intuitionistic Fuzzy Numbers and Their Applications to Multiple-Criteria Decision Making Problems

This paper aims to extend the hesitant fuzzy soft sets to hesitant intuitionistic fuzzy soft sets by merging the concept of hesitant intuitionistic fuzzy sets and soft sets. The authors define some operations on hesitant intuitionistic fuzzy sets, such as complement, union and intersection, and obtain related properties. The similar operations are defined on hesitant intuitionistic fuzzy soft sets, and also some properties such as assosiative and De Morgan’s laws are obtained.

Hesitant intuitionistic fuzzy soft sets

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Hesitant intuitionistic fuzzy soft sets