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Article type: Research Article
Authors: Ameen, Zanyar A.a; * | Mohammed, Ramadhan A.b | Al-shami, Tareq M.c; d; e | Asaad, Baravan A.f; g
Affiliations: [a] Department of Mathematics, College of Science, University of Duhok, Duhok, Iraq | [b] Department of Mathematics, College of Basic Education, University of Duhok, Duhok, Iraq | [c] Department of Mathematics, Sana’a University, Sana’a, Yemen | [d] Jadara University Research Center, Jadara University, Jordan | [e] Department of Engineering Mathematics & Physics, Faculty of Engineering & Technology, Future University, New Cairo, Egypt | [f] Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Iraq | [g] Department of Computer Science, College of Science, Cihan University-Duhok, Iraq
Correspondence: [*] Corresponding author. Zanyar A. Ameen, Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq. E-mail: [email protected].
Abstract: This paper introduces a new fuzzy structure named “fuzzy primal.” Then, it studies the essential properties and discusses their basic operations. By applying the q-neighborhood system in a primal fuzzy topological space and the Łukasiewicz disjunction, we establish a fuzzy operator (·) ⋄ on the family of all fuzzy sets, followed by its core characterizations. Next, we use (·) ⋄ to investigate a further fuzzy operator denoted by Cl⋄. To determine a new fuzzy topology from the existing one, the earlier fuzzy operators are explored. Such a new fuzzy topology is called primal fuzzy topology. Various properties of primal fuzzy topologies are found. Among others, the structure of a fuzzy base that generates a primal fuzzy topology. Furthermore, the concept of compatibility between fuzzy primals and fuzzy topologies is introduced, and some equivalent conditions to that concept are examined. It is shown that if a fuzzy primal is compatible with a fuzzy topology, then the fuzzy base that produces the primal fuzzy topology is itself a fuzzy topology.
Keywords: Fuzzy primal, fuzzy grill, fuzzy ideal, primal fuzzy topology, fuzzy ideal topology
DOI: 10.3233/JIFS-238408
Journal: Journal of Intelligent & Fuzzy Systems, vol. Pre-press, no. Pre-press, pp. 1-10, 2024
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