In this paper we have defined anti fuzzy interior ideal in semigroups. We characterize regular, intra-regular and left (right) quasi-regular semigroups by the properties of their anti fuzzy ideals, anti fuzzy bi-ideals, anti fuzzy generalized bi-ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals.

In this paper we introduce the concept of fuzzy generalized bi-ideal of a Γsemigroup, which is an extension of the concept of a fuzzy bi-ideal of a Γsemigroup and characterize regular Γ-semigroups in terms of fuzzy generalized bi-ideals. AMS Mathematics Subject Classification(2000): 08A72, 20M12, 3F55

More general forms of the paper by O. Kazanci and S. Yamak (Generalized fuzzy bi-ideals of semigroups, Soft Comput. 12, 1119–1124, 2008) are discussed. The notion of (∈,∈∨ qk)-fuzzy bi-ideals in a semigroup S is introduced, and several properties are investigated. Characterizations of an (∈,∈∨ qk)-fuzzy bi-ideal in a semigroup S are discussed.

In this paper, we introduce the notion of ($epsilon $, $epsilon $ $vee$ q_{k})− fuzzy subnear-ring which is a generalization of ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnear-ring. We have given examples which are ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy ideals but they are not ($epsilon $, $epsilon $ $vee$ q)−fuzzy ideals. We have also introduced the notions of ($epsilon $, $epsilon $ $vee$ ...

We introduced and study fuzzy Γ-hypersemigroups, according to fuzzy semihypergroups as previously defined [33] and prove that results in this respect. In this regard first we introduce fuzzy hyperoperation and then study fuzzy Γ-hypersemigroup. We will proceed by study fuzzy Γ-hyperideals and fuzzy Γ-bihyperideals. Also we study the relation between the classes of fuzzy Γ-hypersemigroups and Γ-...

In this paper we introduce bipolar fuzzy subsemigroup, bipolar fuzzy left (right) ideals and bipolar fuzzy bi-ideal in ordered semigroups. We characterize different classes of ordered semigroups by the properties of their bipolar fuzzy ideals and bipolar fuzzy bi-ideals.

In this paper, we give some characterizations of intraregular semigroups by the properties of their (∈,∈ ∨qk)-fuzzy right ideals, (∈,∈ ∨qk)-fuzzy left ideals, (∈,∈ ∨qk)-fuzzy interior ideals, (∈,∈ ∨qk)fuzzy bi-ideals and (∈,∈ ∨qk)-fuzzy generalized bi-ideals. 2010 AMS Classification: 03E72, 20M12

In this paper we de ne interval valued fuzzy h-quasi-ideals and interval valued fuzzy h-bi-ideals. We characterize h-hemiregular and h-intra-hemiregular hemirings by the properties of their interval valued fuzzy h-ideals, interval valued fuzzy h-quasiideals, and interval valued fuzzy h-bi-ideals.

A bounded linear operator T on a complex Hilbert space H is irreducible if it has no reducing subspace other than the trivial ones (0) and H; it is strongly irreducible if every operator similar to T is irreducible. Equivalently, T is irreducible (resp. strongly irreducible) if the only projections (resp. idempotent operators) commuting with T are 0 and I. Since (strongly) irreducible operators...