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

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

International Journal of Fuzzy System Applications (IJFSA), 2023, vol. 12, issue 1, 1-22

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.

Date: 2023
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