A new generalization of fuzzy ideals in LA-semigroups

Abstract. In this article, the concept of (∈γ, ∈γ ∨ q δ )-fuzzy LAsubsemigroups, (∈γ, ∈γ ∨ q δ )-fuzzy left(right) ideals, (∈γ, ∈γ ∨ q δ )-fuzzy generalized bi-ideals and (∈γ, ∈γ ∨ q δ )-fuzzy bi-ideals of an LA-semigroup are introduced. The given concept is a generalization of (∈, ∈ ∨ q)-fuzzy LA-subsemigroups, (∈, ∈ ∨ q)-fuzzy left(right) ideals, (∈, ∈ ∨ q)-fuzzy generalized bi-ideals and (∈, ∈ ∨ q)-fuzzy bi-ideals of an LA-semigroup. We also give some examples of (∈γ, ∈γ ∨ q δ )-fuzzy LA-subsemigroups ( left, right, generalized bi-and bi) ideals of an LA-semigroup. We prove some fundamental results of these ideals. We characterize (∈ γ , ∈γ ∨ q δ )-fuzzy left(right) ideals, (∈γ, ∈γ ∨ q δ )-fuzzy generalized bi-ideals and (∈γ, ∈γ ∨ q δ )-fuzzy bi-ideals of an LA-semigroup by the properties of level sets

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity