Haar and Yager’s Ranking Methods for Intuitionistic Dense Fuzzy Set

Abstract

The world is full of uncertainties. To deal with the uncertain nature mathematically, fuzzy set came into being. Fuzzy set was then extended to intuitionistic fuzzy set where the set itself contains its membership, non-membership and its hesitancy. When the entire components converge at a crisp numberin a set as n→ ∞, dense fuzzy set was identified. Thus, by introducing dense fuzzy set into the field of intuitionistic set theory, intuitionistic dense fuzzy set was introduced. In this present study, an effort has been made in ranking an intuitionistic dense fuzzy set. Ranking plays a vital role in fuzzy decision making problems and in numerous fuzzy applications. Ranking a fuzzy tuples is not as easy as an ascending order ranking. There are numerous methods for ranking a fuzzy number. But in all the cases it is found that, they end up in giving unsatisfactory results due to the complexity of the problem in one way or the other. Thus, this paper paves a way in finding a ranking method for the intuitionistic dense fuzzy set by means of Haar ranking and Yager’s ranking. Numerical examples are given and Cauchy’s sequence has been utilized for better illustration.

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