Role of operator semirings in characterizing $\Gamma$-semirings in terms of fuzzy subsets

TL;DR

This paper explores how operator semirings can be used to characterize $$-semirings through fuzzy subsets, establishing relationships and lattice isomorphisms between their fuzzy ideals.

Contribution

It introduces a novel approach using operator semirings to analyze $$-semirings via fuzzy ideals, revealing structural relationships.

Findings

Lattice isomorphism between fuzzy ideals of $$-semirings and their operator semirings.

Relationships established between fuzzy ideals of $$-semirings and their operator semirings.

Framework for characterizing $$-semirings using fuzzy subset theory.

Abstract

The operator semirings of a $\Gamma$-semiring have been brought into use to study $\Gamma$-semiring in terms of fuzzy subsets. This is accomplished by obtaining various relationships between the set of all fuzzy ideals of a $\Gamma$-semiring and the set of all fuzzy ideals of its left operator semiring such as lattice isomorphism between the sets of fuzzy ideals of a $\Gamma$-semiring and its operator semirings.