Introducing Fuzzy Almost m-Ideals, Fuzzy Generalized Almost m-Ideals and Related Objects in Semigroups

Kausar N.

MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES, vol.14, no.3, pp.351-371, 2020 (ESCI)

  • Publication Type: Article / Article
  • Volume: 14 Issue: 3
  • Publication Date: 2020
  • Journal Name: MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.351-371
  • Yıldız Technical University Affiliated: No

Abstract

In this article, we present the concepts of almost m-ideals, generalized almost m-ideals, fuzzy almost m-ideals, and fuzzy generalized almost m-ideals. We present the results illustrating their mutual differences and similarities. Along these lines, we bring about their examples and then characterize semigroups through their properties. One of the distinguished properties of the almost m-ideals respectively the related objects is that their intersection is not an almost m-ideal respectively related objects, while their union is. A subsemigroup of a semigroup is the almost m-ideals if and only if its characteristic function is the fuzzy almost m-ideals. Through these four closely related concepts of m-ideals, we show that this field will open new avenues of research and applications of semigroups