Applications of hesitant fuzzy sets to ternary semigroups

Abstract

The aim of this paper is to introduce a new concept of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals on ternary semigroups. We extend the concept of fuzzy bi-ideals and fuzzy interior ideals to the context of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals, respectively. Some characterizations of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals are obtained. Moreover, we investigate relationships between hesitant fuzzy ideals and hesitant fuzzy interior ideals on ternary semigroups. Finally, we obtain necessary and sufficient conditions of hesitant fuzzy interior ideal in order to be a hesitant fuzzy ideal.

An (α,β)-Hesitant Fuzzy Set Approach to Ideal Theory in Semigroups

“…A hesitant fuzzy set theory is an excellent tool to handle the uncertainty in case of insufficient data. Many authors studied different aspects of hesitant fuzzy sets (see [1,5,14,19,20]). Also, hesitant fuzzy set theory is used in decision making problem etc.…”

“…In 2019, Arulmozhi, Chinnadurai and Swaminathan [3] introduced the notion of interval valued η, δ bipolar fuzzy ideal, bi-ideal,interior ideal, (∈, ∈ ∨q)-bipolar fuzzy ideal of ordered Γ-semigroups and established some properties of bipolar fuzzy ideals in terms of ( ∈, ∈ ∨ q)-bipolar fuzzy ideals. In 2020, Yairayong [17] applied the theory of hesitant fuzzy sets to completely regular semigroups and introduced the notion of hesitant fuzzy semiprime sets and hesitant fuzzy idempotent sets on semigroups, which is a generalization of fuzzy semiprime and fuzzy idempotent sets. He also proved that the every hesitant fuzzy two-sided ideal on a semigroup S is a hesitant fuzzy interior ideal if and only if S is a semisimple semigroup.…”

Soft ideals of soft ternary semigroups

“…In this paper, we discuss about soft ternary semigroup. We are motivated by the papers of Ali, Shabir [7], Abbasi, Kahan and Ali [19], Yiarayong [20], Chinram, Panitykul [21] and also try to extend the properties of prime ideal, semiprime ideal, irreducible ideal, prime bi-ideal in view of soft set and characterized completely regular soft https://doi.org/10.1016/j.heliyon. ternary semigroup by using these soft ideals.…”