L-fuzzy closure systems

Authors:
Jinming Fang;Yueli Yue
Affiliations:
Department of Mathematics, Ocean University of China, 23 Hong Kong East Road, Qingdao 266071, China;Department of Mathematics, Ocean University of China, 23 Hong Kong East Road, Qingdao 266071, China
Venue:
Fuzzy Sets and Systems
Year:
2010

Citing 3
Cited 1

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Abstract

This paper studies the generalization of fuzzy closure operators and fuzzy closure systems, introduced by Belohlavek in 2001, and introduces the concepts of strong L-fuzzy closure systems and strong L-fuzzy closure operators. It is shown that a strong L-fuzzy closure system is precisely the fuzzy system in opposition to the crisp system, and a strong L-fuzzy closure operator is a suitable closure operator that has a close relation to a strong L-fuzzy closure system. It is also shown that there is a Galois correspondence between the category of (strong) L-fuzzy closure system spaces and that of (strong) L-fuzzy closure spaces.