Applications of Spherical Fuzzy Sets in Ternary Semigroups

Abstract

A ternary semigroup is an algebraic structure (T,(·)) such that T is a non-empty set and (·): T 3→ T is a ternary operation satisfying the associative law, i.e., (abc)de = a(bcd)e = ab(cde) for all a, b, c, d, e ∈ T, and let S be a spherical fuzzy subset of a universal set S defined by S := {< x, µS(x), ηS(x), νS(x) >| x ∈ S} where µS, ηS and νS be three fuzzy subsets of S with the condition 0 ≤ (µS(x))2 + (ηS(x))2 + (νS(x))2 ≤ 1. Then µS(x), ηS(x) and νS(x) are called the degree of membership, the degree of hesitancy and the degree of non-membership, respectively. The main purpose of this thesis is to study spherical fuzzy ternary subsemigroups and spherical fuzzy ideals in ternary semigroups by using the concepts of ternary subsemigroups and ideals in ternary semigroups. Moreover, we study roughness of spherical fuzzy sets and spherical fuzzy ideals in ternary semigroups.