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 $\left(\alpha ,\beta \right)$ 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 $\left(\alpha ,\beta \right)$ 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.