Abstract
In this paper, we define L-join meet and L-meet join approximation operators as a generalization of fuzzy rough set in complete residuated lattices. We show that L-join meet and L-meet join approximation operators are induced by various L-fuzzy relations. We investigate relations between their operations and Alexandrov L-topologies.
Highlights
Pawlak [7,8] introduced rough set theory as a formal tool to deal with imprecision and uncertainty in data analysis
Zhang [5,6] introduced Alexandrov L-topologies induced by fuzzy rough sets
Algebraic structures of fuzzy rough sets are developed in many directions [3,4,10,11]
Summary
Pawlak [7,8] introduced rough set theory as a formal tool to deal with imprecision and uncertainty in data analysis. Hajek [2] introduced a complete residuated lattice which is an algebraic structure for many valued logic. Radzikowska [9] developed fuzzy rough sets induced by various L-fuzzy relations in complete residuated lattice. Belohlavek [1] investigated information systems and decision rules in complete residuated lattices. Zhang [5,6] introduced Alexandrov L-topologies induced by fuzzy rough sets. Algebraic structures of fuzzy rough sets are developed in many directions [3,4,10,11]. We introduce L-join meet and L-meet join approximation operators as a generalization of fuzzy rough set in complete residuated lattices. We show that L-join meet and L-meet join approximation operators are induced by various L-fuzzy relations. We investigate relations between their operations and Alexandrov L-topologies
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