Polytopic Fuzzy Sets and Their Applications to Multiple-Attribute Decision-Making Problems

The aim of this paper is to introduce the concept of polytopic fuzzy sets as an extension of spherical fuzzy sets, picture fuzzy sets, and q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-rung orthopair fuzzy sets. We define some basic operations and aggregation operators on polytopic fuzzy sets. Based on these operators, we present three new methods to deal with the multiple-attribute decision-making problem which cannot be solved with the help of existing aggregation operators. Finally, a numerical example is given to illustrate the validity of the proposed approach.