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We discuss the notion of intuitionistic fuzzy PMS-ideals under homomorphism and Cartesian product and investigate several related properties. The homomorphism of an intuitionistic fuzzy PMS-ideal of a PMS-algebra is studied, and its homomorphic image and inverse image are investigated. The Cartesian product of any two intuitionistic fuzzy PMS-ideals is discussed, and some related results are obtained. The Cartesian product of the intuitionistic fuzzy PMS-ideals is characterized in terms of their level sets. Finally, we discuss the concept of the strongest intuitionistic fuzzy relations on an intuitionistic fuzzy PMS-ideal of a PMS-algebra and investigate the relationships between the strongest intuitionistic fuzzy relations and the intuitionistic fuzzy PMS-ideals.<\/jats:p>","DOI":"10.1007\/s44196-023-00242-5","type":"journal-article","created":{"date-parts":[[2023,5,2]],"date-time":"2023-05-02T13:02:32Z","timestamp":1683032552000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Intuitionistic Fuzzy PMS-Ideals of a PMS-Algebra Under Homomorphism and Cartesian Product"],"prefix":"10.1007","volume":"16","author":[{"given":"Berhanu Assaye","family":"Alaba","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7726-5248","authenticated-orcid":false,"given":"Beza Lamesgin","family":"Derseh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yohannes Gedamu","family":"Wondifraw","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,5,2]]},"reference":[{"issue":"4","key":"242_CR1","doi-asserted-by":"publisher","first-page":"572","DOI":"10.3390\/sym12040572","volume":"12","author":"M Alshammari","year":"2020","unstructured":"Alshammari, M., et al.: Residual series representation algorithm for solving fuzzy duffing oscillator equations. 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