On Homomorphism and Cartesian Products of Intuitionistic Fuzzy PMS-subalgebra of a PMS-algebra

Beza Lamesgin Derseh; Berhanu Assaye Alaba; Yohannes Gedamu Wondifraw

doi:10.18778/0138-0680.2023.08

Authors

Beza Lamesgin Derseh Bahir Dar University, College of Science, Department of Mathematics Bahir Dar, Ethiopia
Berhanu Assaye Alaba Bahir Dar University, College of Science, Department of Mathematics, Bahir Dar, Ethiopia
Yohannes Gedamu Wondifraw Bahir Dar University, College of Science, Department of Mathematics, Bahir Dar, Ethiopia

DOI:

https://doi.org/10.18778/0138-0680.2023.08

Keywords:

PMS-algebra, intuitionistic fuzzy PMS-subalgebra, homomorphism, cartesian product and strongest intuitionistic fuzzy relation

Abstract

In this paper, we introduce the notion of intuitionistic fuzzy PMS-subalgebras under homomorphism and Cartesian product and investigate several properties. We study the homomorphic image and inverse image of the intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, which are also intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, and find some other interesting results. Furthermore, we also prove that the Cartesian product of intuitionistic fuzzy PMS-subalgebras is again an intuitionistic fuzzy PMS-subalgebra and characterize it in terms of its level sets. Finally, we consider the strongest intuitionistic fuzzy PMS-relations on an intuitionistic fuzzy set in a PMS-algebra and demonstrate that an intuitionistic fuzzy PMS-relation on an intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra if and only if the corresponding intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra of a PMS-algebra.

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