Characterizations of regular semigroups by (α,β)-fuzzy ideals

Generalised roughness in (∈,∈Vq)-fuzzy substructures of LA-semigroups

“…Khan et al (2010a;2010b) applied this concept in AG-groupoids. Shabir et al (2010) have applied this concept in semigroups. Rehman and Shabir (2012) initiated the study of (α, β)-fuzzy substructure in ternary semigroups.…”

“…                                                                                                                                                                                                        Notion of lower and upper part of a fuzzy set is given inShabir et al (2010). In the following this notion is defined for                                                                                                                                                                                                                                                                             …”

A novel generalization of fuzzy ideals in semigroups

“…Yuan et al [12] provided a generalization of fuzzy subgroups and (∈, ∈ ∨ q δ 0 )-fuzzy subgroups. The aim of this paper is to generalize the notions and results in the paper [11]. We introduce the notions of ( α, β)-fuzzy left (right, bi-) ideals in semigroups, and investigate related properties.…”

“…In [9] Kazanci and Yamak study (∈, ∈ ∨ q)-fuzzy bi-ideals of a semigroup. Shabir et al [11] introduced the concept of (α, β)-fuzzy ideal, (α, β)-fuzzy generalized bi-ideal, and characterized regular semigroups by the properties of these ideals. Jun et al [6] considered more general form of quasi-coincident fuzzy point, and they [7] introduced the notions of ( α, β)-fuzzy subsemigroups in semigroups, and investigate related properties.…”

A New Form of Fuzzy Generalized Bi-Ideals in Ordered Semigroups

“…In addition, Davvaz and Khan [5] discussed some characterization regular ordered semigroups in terms of (α, β)-fuzzy generalized bi-ideals, where α, β ∈ {∈,q,∈ ∨q,∈ ∧q} and α =∈ ∧q. Moreover, in the semigroup theory the notions of generalized fuzzy (interior, bi-, left, right, quasi) ideals was studied respectively in ( [6][7][8][9]). Kazanchi and Yamak [7] gave (∈, ∈ ∨ q k )-fuzzy bi-ideals of a semigroup and in [10] Shabir et.…”