Characterizations of regular semigroups by (α,β) -fuzzy ideals

Authors:
Muhammad Shabir;Young Bae Jun;Yasir Nawaz
Affiliations:
Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan;Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Republic of Korea;Department of Basic Sciences, HITEC University, Taxila Cantt, Pakistan
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

Using the ideas of belonging and quasi-coincidence of a fuzzy point with a fuzzy set, the concepts of (@a,@b)-fuzzy ideals and (@a,@b)-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.