The axiomatic characterizations on L-fuzzy covering-based approximation operators |
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Authors: | Ling Qiang Li Kai Hu Fang Fang Zhao |
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Affiliation: | Department of Mathematics, Liaocheng University, Liaocheng, P.R. China. |
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Abstract: | Axiomatic characterization is the foundation of L-fuzzy rough set theory: the axiom sets of approximation operators guarantee the existence of L-fuzzy relations or L-fuzzy coverings that reproduce the approximation operators. Axiomatic characterizations of approximation operators based on L-fuzzy coverings have not been fully explored, although those based on L-fuzzy relations have been studied thoroughly. Focusing on three pairs of widely used L-fuzzy covering-based approximation operators, we establish an axiom set for each of them, and their independence is examined. It should be noted that the axiom set of each L-fuzzy covering-based approximation operator is different from its crisp counterpart, with an either new or stronger axiom included in the L-fuzzy version. |
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Keywords: | L-fuzzy rough set L-fuzzy covering axiom set residuated lattice |
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