Centroid and Graded Mean Ranking Methods for Intuitionistic Trapezoidal Dense Fuzzy Set to Solve MCDM Problems of Robot Selection

Abstract

Fuzzy ranking plays a vital role in decision-making problems and various fuzzy applications. There are plenty of ranking methods that are used to rank fuzzy numbers. However, they fail to give satisfactory results in certain situations due to the complexity of the problem. In this present study, an attempt has been made to introduce four types of ranking methods in the field of intuitionistic dense fuzzy (IDF) depending on centroid and graded mean ranking. Also, arithmetic operations based on lambda 1,lambda 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _1, \lambda _2$$\end{document}-cuts, fuzzy numbers, and extension principles are defined for IDF environment. A model is framed to rank MCDM problems, which are aggregated using a weighted aggregation operator and ordered using the proposed and extended ranking methods. To illustrate the proposed MCDM model under the field of IDF, the problem of robot selection is taken for war fighter robots and exoskeleton robots to help and replace humans in war and help assistive walking patients with spinal cord injuries. The result reveals that the Ripsaw and Rewalk emerge as preferable options for substituting humans in the contexts of war fighters and exoskeleton robots, respectively. To analyze the effectiveness of the ranking results, comparative and sensitivity analyses are examined. Thus, the results provide a satisfactory output.