On t-Intuitionistic Fuzzy PMS-Subalgebras of a PMS Algebra

Abstract

In this paper, the authors extend the concept of a t-intuitionistic fuzzy set to PMS-subalgebras of PMS-algebras. The authors define the t-intuitionistic fuzzy PMS-subalgebra of a PMS-algebra and show that any intuitionistic fuzzy PMS-subalgebra of a PMS-algebra is a t-intuitionistic fuzzy PMS-subalgebra. The authors provide the condition for an intuitionistic fuzzy set in a PMS-algebra to be a t-intuitionistic fuzzy PMS-subalgebra. The authors use their (α,β) level cuts to characterize the t-intuitionistic fuzzy PMS-subalgebras of PMS-algebra. The authors investigate whether the homomorphic images and inverse images of t-intuitionistic fuzzy PMS-subalgebras are also t-intuitionistic fuzzy PMS-subalgebras. Furthermore, the authors show that the homomorphic images and inverse images of the nonempty (α,β) level cuts of the t-intuitionistic fuzzy PMS-subalgebras of a PMS-algebra are again PMS-subalgebras of a PMS-algebra. Finally, the authors show that the Cartesian product of the t-intuitionistic fuzzy PMS-subalgebras of a PMS-algebra is itself a t-intuitionistic fuzzy PMS-subalgebra and characterize it in terms of its (α,β) level cuts.