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Ordered semigroups characterized by (∈, ∈ ∨q k)-fuzzy generalized bi-ideals

Khan, Asghar and Young, Bae Jun and Sarmin, Nor Haniza and Khan, Faiz Muhammad (2012) Ordered semigroups characterized by (∈, ∈ ∨q k)-fuzzy generalized bi-ideals. Neural Computing and Applications, 21 (SUP. 1). pp. 121-132. ISSN 0941-0643

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Official URL: http://dx.doi.org/10.1007%2Fs00521-011-0731-2

Abstract

In this paper, we introduce a considerable machinery that permits us to characterize a number of special (fuzzy) subsets in ordered semigroups. In this regard, we generalize (Davvaz and Khan in Inform Sci 181:1759–1770 2011) and define (∈,∈∨qk)-fuzzy generalized bi-ideals in ordered semigroups, which is a generalization of the concept of an (α, β)-fuzzy generalized bi-ideal in an ordered semigroup. We also define (∈,∈∨qk)-fuzzy left (resp. right)-ideals. Using these concept, some characterization theorems of regular, left (resp. right) regular, completely regular and weakly regular ordered semigroups are provided. The upper/lower parts of an (∈,∈∨qk)-fuzzy generalized bi-ideal and (∈,∈∨qk)-fuzzy left (resp. right)-ideal are given, and some characterizations are provided.

Item Type:Article
Uncontrolled Keywords:ordered semigroups, regular, fuzzy generalized bi-ideals
Subjects:Q Science > QA Mathematics > QA76 Computer software
Divisions:Science
ID Code:47337
Deposited By: Narimah Nawil
Deposited On:22 Jun 2015 05:56
Last Modified:25 Apr 2019 01:18

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