Interval-valued picture fuzzy hypergraphs with application towards decision making

The concept of interval-valued picture fuzzy sets (IVPFSs) is the most generalized form of fuzzy sets (FSs) and is proven a useful tool to manipulate complications that arise due to incomplete information more effectively. One of the most powerful feature of IVPFSs is that it allocates the membership, non membership and neutral membership values as intervals to any element of the given data. Due to this, IVPFSs play a key role to deal uncertain data with multiple attributes. In this study, we introduce the notion of interval-valued picture fuzzy hypergraphs (IVPFHGs) which is the combination of both IVPFSs and hypergraphs and provide its application in decision making. We describe several types of IVPFHGs such as partial, simple, support, support simple, elementary IVPFHGs etc. We also initiate the concepts of dual of IVPFHGs. Moreover, ([iota,kappa],[lambda,epsilon],[rho,nu])\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$([\iota , \kappa ], [\lambda , \epsilon ], [\rho , \nu ])$$\end{document}-level cuts of IVPFHGs are also addressed. We present a comparative analysis of our newly established terms with those existing in the literature and elaborate the superiority of IVPFHGs over the other existing fuzzy hypergraphs structures. Finally, we provide an application of IVPFHGs with algorithm and flowchart towards decision making.