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.

the intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by atanassov in 1983. the aim of this paper is to develop an effective methodology for solving matrix games with payoffs of atanassov’s triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concepts and ranking order relations of atanassov’s tifns are defined. a pair of bi-object...

We de ne fuzzy h-subhemiring, fuzzy h-ideals and fuzzy generalized h-biideals with thresholds, and characterize h-hemiregular and h-intra-hemiregular hemirings by the properties of their fuzzy h-ideals, fuzzy h-bi-ideals and fuzzy h-quasi-ideals with thresholds.

In this paper, the notion of an interval valued intuitionistic fuzzy subsemiring (ideal) of a semiring with respect to t−norm T and s−norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on semirings, new interval valued intuitionistic (S, T )−fuzzy subsemirings (ideals) ...

In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, which is a generalization of fuzzy ideals in ternary semigroups. We investigate the related properties of ternary semigroups. The lower and upper parts of fuzzy subsets of a ternary semigroup are defined. Characterizations of regular ternary semigroups by the properties of the lower part of (∈,∈∨q)-fuzzy left ...

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...

In this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. We characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. We also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

Abstract: In this study we introduce a new class of a non-associative algebraic structure namely intra-regular Abel Grassmann's groupoid (AG-groupoid in short). We apply generalized fuzzy ideal theory to this class and discuss its related properties. We introduce ) , ( k q ∨ ∈ ∈ -fuzzy semiprime ideals in AG-groupoids and characterize it. Specifically we have characterized intra-regular AG-grou...

The purpose of this note is to obtain some properties of (∈,∈ ∨q)fuzzy bi-ideals in a Γ-semigroup in order to characterize regular and intra-regular Γ-semigroups. Keywords—Regular Γ-semigroup, belong to or quasi-coincident, (∈,∈ ∨q)-fuzzy subsemigroup, (∈,∈ ∨q)-fuzzy bi-ideals.