CHARACTERIZATIONS OF HEMIRINGS BY ∊,∊∨q)-FUZZY IDEALS

Abstract

Abstract. In this paper we characterize different classes of hemirings by the properties of their (∈, ∈ ∨q)-fuzzy ideals, (∈, ∈ ∨q)-fuzzy quasi-ideals and (∈, ∈ ∨q)-fuzzy bi-ideals.

Characterizations of Ordered Semigroups in Terms of Anti-fuzzy Ideals

“…In another pioneered contribution, Jun [9] generalized the concept of ( ∈ , ∈ ∨q)-fuzzy subalgebra of a BCK/BCI-algebra and introduced a new concept of ( ∈ , ∈ ∨q k )-fuzzy subalgebras followed by the basic properties of BCK-algebras. In continuation of this idea, Shabir et al [10] and Shabir and Mahmood [11] reported the concept of generalized forms of (α, β)-fuzzy ideals and defined ( ∈ , ∈ ∨q k )-fuzzy ideals of semigroups and hemirings comprehensively. Recent developments in fuzzy ideals related to semigroups and hemirings have prompted the formulation of a precise description of numerous classes of semigroups and hemirings and their characterizations (see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]).…”

“…In continuation of this idea, Shabir et al [10] and Shabir and Mahmood [11] reported the concept of generalized forms of (α, β)-fuzzy ideals and defined ( ∈ , ∈ ∨q k )-fuzzy ideals of semigroups and hemirings comprehensively. Recent developments in fuzzy ideals related to semigroups and hemirings have prompted the formulation of a precise description of numerous classes of semigroups and hemirings and their characterizations (see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]). Moreover, new classifications of ordered semigroups have been investigated by introducing the concept of ( ∈ , ∈ ∨(k * , q k ))-fuzzy subsystems and ( ∈ , ∈ ∨(k * , q k ))-fuzzy quasi-ideals by Khan et al [27] and Mahboob et al [28], respectively.…”

Some Types of Generalized Fuzzyn-Fold Filters in Residuated Lattices

“…In particular, several types of fuzzy filters such as fuzzy Boolean filters, fuzzy fantastic filters, fuzzy implicative filters and fuzzy regular filters were introduced in [6,15]. As a further generalization of some fuzzy notions, in BLalgebras, generalized fuzzy filters [16] which are common generalizations of (∈, ∈ ∨ )-fuzzy filters [17][18][19] and (∈, ∈ ∨ )-fuzzy filters [16] were investigated, and hemirings were characterized by their (∈, ∈∨ )-fuzzy ideals [20], (∈, ∈ ∨ )fuzzy ideals [21], and fuzzy ideals with thresholds [22].…”

On generalized fuzzy hyperideals in ordered LA-semihypergroups

“…Kazanci and Yamak (2008) introduced the concept of (∈, ∈ ∨ q k )-fuzzy bi-ideals of a semigroup. Later, the concept of (∈, ∈ ∨ q k )-fuzzy sets was studied in ordered semigroups (Khan et al 2014;Tang and Xie 2014), hemirings (Mahmood 2013) and semigroups (Shabir et al 2011). Zulfiqar (2014) studied the properties of α, β -fuzzy fantastic ideals in BCHalgebras.…”