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L-Fuzzy Rough Approximation Operators Based on Co-Implication and Their (Single) Axiomatic Characterizations

For L a complete co-residuated lattice and R an L-fuzzy relation, an L-fuzzy upper approximation operator based on co-implication adjoint with L is constructed and discussed. It is proved that, when L is regular, the new approximation operator is the dual operator of the Qiao–Hu L-fuzzy lower approximation operator defined in 2018. Then, the new approximation operator is characterized by using an axiom set (in particular, by single axiom). Furthermore, the L-fuzzy upper approximation operators generated by serial, symmetric, reflexive, mediate, transitive, and Euclidean L-fuzzy relations and their compositions are characterize through axiom set (single axiom), respectively.