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سند علمی

Some study of (α, β)-fuzzy ideals in ordered semigroups

Faiz Muhammad Khan, Nor Haniza Sarmin, Asghar Khan

چکیده

Algebraic structures especially an ordered semigroups play a prominent role in mathematics with wide ranging applications in many disciplines such as control engineering, computer arithmetics, coding theory, sequential machines and formal languages. A theory of fuzzy sets in terms of fuzzy points on ordered semigroups can be developed. In this paper, we generalize the concept of (α, β)-fuzzy left (right) ideal of an ordered semigroup S and introduce a new sort of fuzzy left (right) ideals called (∈,∈ ∨qk)-fuzzy left (right) ideals, where k ∈ [0, 1). In particular, we describe the relationships among ordinary fuzzy ideals and (∈,∈ ∨qk)fuzzy ideals of an ordered semigroup S. Finally, we characterize regular ordered semigroups in terms of (∈,∈ ∨qk)-fuzzy left (resp. right) ideals. 2010 AMS Classification: 06F05, 20M12, 08A72

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