Abstract
The aim of this paper is to define the concept of fuzzy k 0-preproximity and show how a fuzzy closure space is induced by a fuzzy k 0-preproximity and vice versa. Also, we introduce the notion of fuzzy k 0-preproximal neighborhood system.
Highlights
Zadeh [12] introduced the theory of fuzzy sets
We study the relationships between fuzzy closure spaces, fuzzy k◦-preproximity, fuzzy cotopology and fuzzy neighborhood system
We introduced the concepts of fuzzy k◦-preproximity and fuzzy neighborhood system
Summary
Zadeh [12] introduced the theory of fuzzy sets. Kubiak [9] and Šostak [11] introduced a generalization of Chang’s fuzzy topology depending on fuzzy sets. Efremovic [5] introduced the proximity relation. Han [6] introduced the k◦-proximity space as a generalization of the Efremovic-proximity space. Katsaras [8] defined fuzzy proximities, on the base of the axioms suggested by Efremovic. Park [10] generalized the concept of the fuzzy proximity, which was called by a fuzzy k-proximity. In order to fully define and model fuzzy spatial objects such as land covers, it is necessary to investigate their fuzzy topological. We introduce the notion of fuzzy k◦-preproximity and investigate some of its properties. We study the relationships between fuzzy closure spaces, fuzzy k◦-preproximity, fuzzy cotopology and fuzzy neighborhood system
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