Relational correspondences for L-fuzzy rough approximations defined on De Morgan Heyting algebras

07/29/2023

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by   Jouni Järvinen, et al.

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Bin Pang, Ju-Sheng Mi, and Wei Yao introduced in 2019 the L-fuzzy rough approximation operations on De Morgan Heyting algebras. They presented axiomatic characterizations of L-fuzzy rough approximation operators corresponding to mediate, Euclidean and adjoint L-fuzzy relations. In this paper, we extend these results by providing uniforms methods for obtaining characterization theorems for L-fuzzy rough approximation operators. As an application of our results, we are able to give an answer to the problem left by Pang, Mi, and Yao. We also correct a misunderstanding related to crisp positive alliance relations appearing in the literature.