Open Access

ARTICLE

Decision Making Based on Valued Fuzzy Superhypergraphs

Mohammad Hamidi^1,*, Florentin Smarandache², Mohadeseh Taghinezhad¹

1 Department of Mathematics, University of Payame Noor, Tehran, 19395-4697, Iran
2 Department of Mathematics, University of New Mexico, Gallup, 87301 NM, USA

* Corresponding Author: Mohammad Hamidi. Email:

(This article belongs to the Special Issue: Advances in Ambient Intelligence and Social Computing under uncertainty and indeterminacy: From Theory to Applications)

Computer Modeling in Engineering & Sciences 2024, 138(2), 1907-1923. https://doi.org/10.32604/cmes.2023.030284

Received 29 March 2023; Accepted 14 June 2023; Issue published 17 November 2023

Abstract

This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy (hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept. We have modeled the fuzzy superhypergraphs as complex superhypernetworks in order to make a relation between labeled objects in the form of details and generalities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzes them in the form of the part to part of objects, the part of objects to the whole group of objects, and the whole to the whole group of objects at the same time. We have investigated the properties of fuzzy (quasi) superhypergraphs based on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valued fuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based on the permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi) superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introduced in this study and it is applied in designing the real problem in the real world. Finally, the problem of business superhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world.

---

Keywords

---