L -fuzzy soft sets based on complete Boolean lattices

Authors:
Zhaowen Li;Dingwei Zheng;Jing Hao
Affiliations:
College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, PR China;College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, PR China;College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

In this paper, the concept of L-fuzzy soft sets based on complete Boolean lattices, which can be seen as a generalization of fuzzy soft sets, is introduced. The topological and lattice structure of L-fuzzy soft sets are obtained. Some operations on L-fuzzy soft sets are discussed, and new types of L-fuzzy soft sets such as full, keeping intersection and keeping union L-fuzzy soft sets are defined and supported by some illustrative examples. A pair of L-fuzzy soft rough approximations is proposed and their properties are given. Based on L-fuzzy soft rough approximations, the concept of L-fuzzy soft rough sets is introduced and their structures are studied. The fact that every finite L-fuzzy topological space is an L-fuzzy soft approximation space is revealed. In addition, we obtain two one-to-one correspondence relationships associated with L-fuzzy soft sets, which expounds the broad application prospect of L-fuzzy soft sets.