Fuzzifying Closure Systems and Fuzzy Lattices

Authors:
Branimir Šešelja;Andreja Tepavčević
Affiliations:
Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, Serbia;Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, Serbia
Venue:
RSFDGrC '07 Proceedings of the 11th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
Year:
2009

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Abstract

A fuzzifying closure system is introduced as a fuzzy set on the collection of subsets of a nonempty set. It is proved that this structure is a particular fuzzy lattice ordered poset. Conversely, every lattice ordered poset is isomorphic to a fuzzifying closure system. In particular, each complete fuzzy lattice is representable by a fuzzifying closure system.