No 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.

Land, marine and airborne are the three types of military robots used in the War-field. Land robots are the most crucially considered robots. Selecting a military land robot for a specific purpose is one of the challenging problems for a decision-maker to find the most preferred alternative when it includes fuzziness. Intangible factors are used while selecting the appropriate robotic system as it effectively deals with fuzziness. Intuitionistic dense fuzzy set, which is the combination of intuitionistic fuzzy set and dense fuzzy set, is capable of dealing with intangible factors. This study aims to design the integrated model on intuitionistic dense fuzzy AHP-TOPSIS to choose the most preferable military land robots under various circumstances. Robots for different types of situations, namely bomb disposal, search and rescue, surveillance and reconnaissance and war-fighter are considered. Moreover, the intuitionistic dense fuzzy AHP is utilized to calculate the subjective weights of the criteria and intuitionistic dense fuzzy TOPSIS is used to rank the alternatives. Further, a sensitivity analysis is examined to demonstrate the quality of the outcome and the results are compared with the fuzzy set, intuitionistic fuzzy set, and dense fuzzy set to show the efficiency of the proposed methodology.