Characterizations of regular semigroups by -fuzzy ideals

✍ Scribed by Muhammad Shabir; Young Bae Jun; Yasir Nawaz

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 855 KB
• Volume: 59
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2009.07.062

✦ Synopsis

α, β)-fuzzy subsemigroups (α, β)-fuzzy ideals (α, β)-fuzzy bi-ideals (α, β)-fuzzy quasi-ideals a b s t r a c t Using the ideas of belonging and quasi-coincidence of a fuzzy point with a fuzzy set, the concepts of (α, β)-fuzzy ideals and (α, β)-fuzzy generalized bi-ideals, which are generalization of fuzzy ideals and fuzzy generalized bi-ideals, in a semigroup are introduced, and related properties are investigated. We also define the lower and upper parts of fuzzy subsets of a semigroup. Characterizations of regular semigroups by the properties of the lower part of (∈, ∈ ∨q)-fuzzy left ideals, (∈, ∈ ∨q)-fuzzy quasi-ideals and (∈, ∈ ∨q)-fuzzy generalized bi-ideals are given.