Abstract
In this paper, we introduce the concepts of Alexandrov L-fuzzy pre-proximities on complete residuated lattices. Moreover, we investigate their relations among Alexandrov L-fuzzy pre-proximities, Alexandrov L-fuzzy topologies, L-fuzzy upper approximate operators, and L-fuzzy lower approximate operators. We give their examples.
Highlights
Pawlak [1,2] introduced the concept of rough set theory as a formal tool to deal with imprecision and uncertainty in data analysis
Ward et al [3] introduced the concept of the complete residuated lattice, which is an algebraic structure for many-valued logic
Kim [10,11,12,13,14,15] investigated the properties of Alexandrov L-fuzzy topologies, Alexandrov L-fuzzy quasi-uniformities, and L-fuzzy approximate operators in complete residuated lattices
Summary
Pawlak [1,2] introduced the concept of rough set theory as a formal tool to deal with imprecision and uncertainty in data analysis. Kim [10,11,12,13,14,15] investigated the properties of Alexandrov L-fuzzy topologies, Alexandrov L-fuzzy quasi-uniformities, and L-fuzzy approximate operators in complete residuated lattices. We introduce the concepts of Alexandrov L-fuzzy pre-proximities on complete residuated lattices, which are a unified approach to the three spaces: Alexandrov L-fuzzy topologies, L-fuzzy lower approximate operators, and L-fuzzy lower approximate operators as an extension of Pawlak’s rough sets. We investigate their relations among Alexandrov L-fuzzy pre-proximities, Alexandrov L-fuzzy topologies, L-fuzzy lower approximate operators, and L-fuzzy lower approximate operators.
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