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A New Type of Fuzzy Quasi-ideals of Ordered Semigroups
Irina Cristea, Ahsan Mahboob and Noor Mohammad Khan

In this paper, we generalize the concept of an (∈,∈ ∨qk)-fuzzy quasi-ideal of an ordered semigroup, using the notion of (k∗, q)-quasi-coincidence of an ordered fuzzy point with a fuzzy subset of the support ordered semigroup. First we define and characterize in different ways the (∈,∈ ∨(k, qk))-fuzzy quasi-ideals of an ordered semigroup. Secondly, we present some relationships between these generalized fuzzy quasi-ideals and similar generalizations of fuzzy left/right ideals or fuzzy bi-ideals (based on the (k, q)-quasi-coincidence relation). Similarities with quasi-ideals in ordered semigroups are discussed at the end of the paper.

Keywords: Ordered semigroup, fuzzy subsets, (∈,∈ ∨(k, qk))-fuzzy quasi-ideals

AMS Mathematics Subject Classification: 06F05, 08A72

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