Abstract
Following the idea of L -fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L -fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L -fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on L -fuzzy relations. Furthermore, if L satisfies the double negative law, then there exists an order isomorphic mapping between upper and lower approximation operators based on L -fuzzy generalized neighborhood systems; when L -fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on L -fuzzy relations are complete lattice isomorphism.
Highlights
IntroductionBy fuzzifying the notion of generalized neighborhood systems, Zhao and Li [49, 50] established a rough set model based on L-fuzzy generalized neighborhood systems
Pawlak [1, 2] defined the rough set theory to address the vagueness and granularity of information systems and data analysis
We study the lattice structures of approximation operators based on L-fuzzy generalized neighborhood systems and give the relationship between lower and upper approximation operators based on L-fuzzy generalized neighborhood systems
Summary
By fuzzifying the notion of generalized neighborhood systems, Zhao and Li [49, 50] established a rough set model based on L-fuzzy generalized neighborhood systems. Complexity operators based on L-fuzzy generalized neighborhood systems were not studied Following this idea, a natural problem arises: can the lattice structures of approximation operators based on L-fuzzy generalized neighborhood systems be given?. We study the lattice structures of approximation operators based on L-fuzzy generalized neighborhood systems (resp., L-fuzzy relations) and give the relationship between lower and upper approximation operators based on L-fuzzy generalized neighborhood systems (resp., L-fuzzy relations).
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