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

Abstract

Abstract. In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory, the use of fuzzified algebraic structures especially ordered semigroups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (∈, ∈ ∨q k )-fuzzy subsystems of ordered semigroups namely (∈, ∈ ∨q k )-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (∈, ∈ ∨q k )-fuzzy generalized bi-ideals. Moreover, different classes of ordered semigroups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (∈, ∈ ∨q k )-fuzzy generalized bi-ideal is defined and some characterizations are discussed.

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.…”