σ-convergence theory and its applications in fuzzy lattices

Authors:
Shui-Li Chen;Sheng-Tao Chen;Xiang-Gong Wang
Affiliations:
Department of Mathematics, Teachers' College, Jimei University, Xiamen, Fujian 361021, PR China;Department of Mathematics, Jianghan Petroleum Institute, Jingzhou, Hubei 434102, PR China;Department of Mathematics, Jianghan Petroleum Institute, Jingzhou, Hubei 434102, PR China
Venue:
Information Sciences: an International Journal
Year:
2004

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Abstract

Moore-Smith convergence theory is enriched in a fuzzy lattice. The σ-limit point and σ-cluster point of a molecular net and a filter in a fuzzy lattice are defined and their various properties are discussed, and the σ-closure, the σ-interior operators and σ-topological molecular lattices are introduced by the concept of ordered pair of R-neighborhoods. Mutual relationships between σ-convergence, Moore Smith convergence, θ-convergence and Urysohn convergence of a molecular net and a filter are studied. Moreover, several applications based on the σ-convergence theory of a molecular net and a filter are provided for continuous order-homomorphisms.