Operations on fuzzy ideals of $\Gamma$-semirings

TL;DR

This paper introduces various operations on fuzzy ideals of b3-semiring and demonstrates their resulting lattice structures, also characterizing regular b3-semiring via fuzzy subsets.

Contribution

It defines new operations on fuzzy ideals of b3-semiring and establishes their lattice structures, providing a fuzzy subset characterization of regular b3-semiring.

Findings

Operations induce complete and modular lattice structures.

Characterization of regular b3-semiring using fuzzy subsets.

New insights into fuzzy ideal structures in b3-semiring.

Abstract

The purpose of this paper is to introduce different types of operations on fuzzy ideals of $\Gamma$-semirings and to prove subsequently that these oprations give rise to different structures such as complete lattice, modular lattice on some restricted class of fuzzy ideals of $\Gamma$-semirings. A characterization of a regular $\Gamma$-semiring has also been obtained in terms of fuzzy subsets.