The structure-preservation under consistent functions for interior and closure of fuzzy neighborhood systems
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The neighborhood system(NS) is one of the most general structures for granular computing. The concept of consistent function is a tool to study the structure-preservation for closure and interior operators of NS. In this paper, the definition of interior and closure operators are generalized for fuzzy neighborhood system(FNS) via fuzzy implicator and triangular norm, some properties of FNS under consistent functions are investigated. The consistent functions satisfy structural preservation properties on the universe, and surjective functions also preserve properties for FNS on the image universe with left-continuous triangular norm operator. In addition, the Lukasiewicz operators for FNS satisfy the duality.
Abstract
The neighborhood system(NS) is one of the most general structures for granular computing. The concept of consistent function is a tool to study the structure-preservation for closure and interior operators of NS. In this paper, the definition of interior and closure operators are generalized for fuzzy neighborhood system(FNS) via fuzzy implicator and triangular norm, some properties of FNS under consistent functions are investigated. The consistent functions satisfy structural preservation properties on the universe, and surjective functions also preserve properties for FNS on the image universe with left-continuous triangular norm operator. In addition, the Lukasiewicz operators for FNS satisfy the duality.
참고문헌 (26)
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