Novel fuzzy topologies from old through fuzzy primals
Zanyar A. Ameen, Ramadhan A. Mohammed, Tareq M. Al-shami, and Baravan, A. Asaad

TL;DR
This paper introduces the concept of fuzzy primals and primal fuzzy topologies, exploring their properties, operators, and relationships to extend fuzzy topology theory.
Contribution
It proposes a new fuzzy structure called fuzzy primal, along with operators and methods to generate and analyze primal fuzzy topologies.
Findings
Defined fuzzy primal and primal fuzzy topology.
Introduced fuzzy operators (.)$^ riangle$ and Cl$^ riangle$ for topology construction.
Established conditions for compatibility between fuzzy primals and topologies.
Abstract
In this paper, we introduce a novel fuzzy structure named "fuzzy primal". We study the essential properties and discuss basic operations on it. A fuzzy operator (.) on the family of all fuzzy sets is introduced here by applying the q-neighborhood structure to a primal fuzzy topological space along with the Lukasiewicz disjunction. We explore the main characterizations of (.). Then, we define another fuzzy operator, symbolized by Cl, with the utilization of (.). These fuzzy operators are studied in order to deduce a new fuzzy topology from the original one. Such a new fuzzy topology is called primal fuzzy topology. The fundamental structure, particularly a fuzzy base that generates primal fuzzy topologies, as well as many relationships between different fuzzy primals and fuzzy topologies, are also analyzed. Lastly, the concept of compatibility…
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Taxonomy
TopicsFuzzy and Soft Set Theory
