Ordered semigroups characterized by (∈, ∈ ∨q k)-fuzzy generalized bi-ideals
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, whic...
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| Main Authors: | , , , |
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| Format: | Article |
| Published: |
Springer-Verlag
2012
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/47337/ http://dx.doi.org/10.1007%2Fs00521-011-0731-2 |
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| Institution: | Universiti Teknologi Malaysia |
| Summary: | 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. |
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