GENERAL TYPES OF(∈,∈∨q_k)-FUZZY SUBSEMIGROUPS IN SEMIGROUPS

Abstract

Abstract. More general form of an (∈, ∈ ∨ q k )-fuzzy subsemigroup is considered. The notions of (∈, q

Generalization of (∈,∈∨q_k )-fuzzy subnear-rings and (∈,∈∨q_k )-fuzzy ideals of near-rings

“…(v) x t q k δ λ if λ(x)+t > δ−k, where k, δ ∈ [0, 1] such that k < δ. In this case, x t is said to be (δ, k)-quasi-coincident with a fuzzy subset λ (see [16]).…”

“…In [11], Jun and Oztürk introduced the notions of (∈, ∈ ∨q δ 0 )-fuzzy subrings and (∈, ∈ ∨q δ 0 )-fuzzy ideals of a ring and obtained some properties. Kang [16] introduced the notion of (∈, ∈ ∨q k δ )-fuzzy subsemigroup in a semigroup and investigated some of its properties. Khan et al [18] defined the concept of (∈, ∈ ∨q k δ )-fuzzy left (resp.…”

On the Generalization of Interval Valued $left( in ,in vee q_{widetilde{k}}right) $-Fuzzy bi-Ideals in Ordered Semigroups

“…The notion of general form of the quasi-coincidence of a fuzzy point with a fuzzy set is initiated by Jun in [7]. In [11], Kang generalized the concept of (∈, ∈ ∨q δ k )-fuzzy subsemigroup and initiated the notion of (∈, ∈ ∨q k )-fuzzy subsemigroup of semigroups. Interval valued fuzzy sets were introduced independently by Zadeh [26], Grattan-Guiness [4], John [5], in the same year, where the value of the membership functions are intervals of numbers in place of the numbers.…”