Abstract

The notion of $\Gamma$-semigroups was introduced by Sen in 1981 and that of fuzzy sets by Zadeh in 1965. Any semigroup can be reduced to a $\Gamma$-semigroup but a $\Gamma$-semigroup does not necessarily reduce to a semigroup. In this paper, we study the coincidences of fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy ideals in regular, left regular, right regular, intra-regular, semisimple ordered $\Gamma$-semigroups.

Highlights

  • Introduction and PreliminariesA fuzzy subset of a set S is a function from S to a closed interval [0, 1]

  • The concept of a fuzzy subset of a set was first considered by Zadeh [32] in 1965

  • The fuzzy set theories developed by Zadeh and others have found many applications in the domain of mathematics and elsewhere

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Summary

Introduction

Introduction and PreliminariesA fuzzy subset of a set S is a function from S to a closed interval [0, 1]. Zhan and Ma [33] studied fuzzy interior ideals in semigroups. Chon [5] characterized the fuzzy bi-ideals generated by a fuzzy subset in semigroups. In 2012, Sardar, Davvaz, Majumder and Kayal [24] studied the generalized fuzzy interior ideals in Γ-semigroups. A nonempty subset A of M is called a left ideal of M if

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