The axiomatic characterizations on L-generalized fuzzy neighborhood system-based approximation operators |
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Authors: | Fangfang Zhao Qiu Jin |
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Affiliation: | Department of Mathematics, Liaocheng University, Liaocheng, P.R. China. |
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Abstract: | The rough sets based on L-fuzzy relations and L-fuzzy coverings are the two most well-known L-fuzzy rough sets. Quite recently, we prove that some of these rough sets can be unified into one framework—rough sets based on L-generalized fuzzy neighborhood systems. So, the study on the rough sets based on L-generalized fuzzy neighborhood system has more general significance. Axiomatic characterization is the foundation of L-fuzzy rough set theory: the axiom sets of approximation operators guarantee the existence of L-fuzzy relations, L-fuzzy coverings that reproduce the approximation operators. In this paper, we shall give an axiomatic study on L-generalized fuzzy neighborhood system-based approximation operators. In particular, we will seek the axiomatic sets to characterize the approximation operators generated by serial, reflexive, unary and transitive L-generalized fuzzy neighborhood systems, respectively. |
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Keywords: | Rough set L-generalized fuzzy neighborhood system upper approximation operator lower approximation operator complete residuated lattice |
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