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

Author

Listed:
  • Beza Lamesgin Derseh
  • Berhanu Assaye Alaba
  • Yohannes Gedamu Wondifraw
  • Sergejs Solovjovs

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.

Suggested Citation

  • Beza Lamesgin Derseh & Berhanu Assaye Alaba & Yohannes Gedamu Wondifraw & Sergejs Solovjovs, 2022. "t-Intuitionistic Fuzzy Structures on PMS-Ideals of a PMS-Algebra," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-13, September.
    • Handle: RePEc:hin:jijmms:5101293
    DOI: 10.1155/2022/5101293
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