A new type of generalized fuzzy quasi-ideals of ordered semigroups

In this paper, the concept of (∈,∈ ∨ qk)-fuzzy quasi-ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, which is a generalization of fuzzy quasi-ideal of S, and related properties are investigated. Furthermore, we introduce the concepts of prime and completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals of ordered semigroups, and characterize bi-regular ordered semigroups in terms of completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals. Moreover, characterizations of regular ordered semigroups and intra-regular ordered semigroups by the properties of (∈,∈∨ qk)-fuzzy ideals, (∈,∈∨ qk)-fuzzy bi-ideals and (∈,∈∨ qk)-fuzzy quasi-ideals are given. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of (∈,∈ ∨ qk)-fuzzy quasi-ideals. 2010 AMS Classification: 06F05, 08A72