On Fuzzy Subsets in Abel-Grassmann’s Semirings

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Published: Feb 6, 2019
Keywords:
Abel-Grassmann’s Semiring Abel-Grassmann’s Subsemiring Level Set Fuzzy (left, right) Ideal

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Salinthip Daengkongkho
Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok
Pairote Yiarayong
Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok

Abstract

Let R be an Abel-Grassmann’s semiring. In this paper, we introduce the concept of a fuzzy subset, fuzzy left and fuzzy right ideals in Abel-Grassmann’s semirings, and to study fuzzy left and fuzzy right ideals in Abel-Grassmann’s semirings. We show that a non-empty subset I of R is an Abel-Grassmann’s subsemiring (left ideal, right ideal, ideal) if and only if fI (tfI) is a fuzzy Abel-Grassmann’s subsemiring (fuzzy left ideal, fuzzy right ideal, fuzzy ideal) of R. Finally we show that f is a fuzzy Abel-Grassmann’s subsemiring (fuzzy left ideal, fuzzy right ideal, fuzzy ideal) of R if and only if U (f, t) is an Abel-Grassmann’s subsemiring (left ideal, right ideal, ideal) of R.

Article Details

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Vol. 29 No. 1 (2019): January-March, 2019
Section
Academic Article

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