t-Intuitionistic Fuzzy Structures on PMS-Ideals of a PMS-Algebra

Abstract

In this article, we apply the concept of a t -intuitionistic fuzzy set to PMS-ideals in PMS-algebras. The notion of the t -intuitionistic fuzzy PMS-ideal of PMS-algebra is introduced, and several related properties are studied. The relationships between a t -intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, as well as the relationships between an intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-ideal are discussed in detail. A condition for an intuitionistic fuzzy set to be a t -intuitionistic fuzzy PMS-ideal is provided. The t -intuitionistic fuzzy PMS-ideals of PMS-algebra are described using their α , β level cuts. The homomorphism of a t -intuitionistic fuzzy PMS-ideal of a PMS-algebra is studied, and its homomorphic image and inverse image are explored. The Cartesian product of any two t -intuitionistic fuzzy PMS-ideals is discussed, and some related results are derived. The Cartesian product of the t -intuitionistic fuzzy PMS-ideals is also characterized using its α , β level cuts. The strongest t -intuitionistic fuzzy PMS-relation in a PMS-algebra is defined. Finally, the relationships between the strongest t -intuitionistic fuzzy PMS-relation and t -intuitionistic fuzzy PMS-ideal are studied.