An Overview on Intuitionistic Fuzzy Multi-Hypergroup

Abstract

The major goal of this work is to introduce the Intuitionistic Fuzzy Multi-Hypergroup and to introduce non membership on multihyper group to provide new path way in the field of hypergroup.

Introduction

I. INTRODUCTION

In 1934, Frederic Marty defined a hypergroup as a natural extension of a group. Composing two elements in a group results in an element, but in a hypergroup, the result is a non-empty set. The law characterizing suchhyperstructure theory refers to algebraic structures that have at least one multi-valued operation.

Marty's motivation for introducing hypergroups is that the quotient of a group modulo any subgroup (not necessarily normal) is a hypergroup.

Since the 1970s, there has been significant progress in hyperstructure theory, including the introduction of new structures such as hyperrings, hypermodules, hyperlattices, and hyperfields. There are several forms of hyperstructures are employed in various contexts, including automata theory, topology, cryptography, geometry, graphs and hypergraphs, convex system analysis, finite group character theory, fuzzy and rough set theory, probability theory, ethnology, and the economy.

Zadeh proposed a fuzzy set, which is comparable to a set but with degrees of membership to the generation of fuzzy set. Intuitionistic Fuzzy Multi-Hypergroup is a generalization of  Fuzzy Multi-Hypergroup.

Intuitionistic Fuzzy Multi-Hypergroup can  be further extended in the field of Plus weighted grammar[3,4,5]. Intuitionistic Fuzzy Multi-Hypergroup can be linked with fuzzy hyper graph in the field of medical diagnosis[6].

Intuitionistic Fuzzy Multi-Hypergroup have many scope in the field of graph labeling and Coloring[2, 7,8,9,10].

Section 1, gives the general notion of Fuzzy multi hyper group. Some basic concepts which are needed for the succeeding sections are discussed in Section 2. Intuitionistic Fuzzy Multi-Hypergroup is introduced in Section 3 and related theorems are proved.

Conclusion

Intuitionistic fuzzy multi hypergroup has been introduced and it is proved that if is a hypergroup and be a intuitionistic fuzzy multiset of , if is an intuitionistic fuzzy multi-hypergroup of ,then . This work can be further extended in the field of Plus weighted grammar and Plus weighted automata which will give fruitful result in the field of automata theory.

References

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Copyright

Copyright © 2024 Saridha S, Emily Denina S. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.