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02-01-2020 | Original Article | Issue 5/2020

International Journal of Machine Learning and Cybernetics 5/2020

Using single axioms to characterize L-rough approximate operators with respect to various types of L-relations

Journal:
International Journal of Machine Learning and Cybernetics > Issue 5/2020
Authors:
Bin Pang, Ju-Sheng Mi
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Abstract

Considering L being a complete Heyting algebra, this paper mainly proposes a general framework of L-rough approximate operators in which constructive and axiomatic approaches are used. In the constructive approach, upper and lower L-rough approximate operators are introduced and their connections with L-relations are investigated. In the axiomatic approach, various types of set-theoretic L-operators are defined. It is shown that each type of L-rough approximate operators corresponding to special kind of L-relations, including serial, reflexive, symmetric, transitive, mediate, Euclidean and adjoint L-relations as well as their compositions, can be characterized by single axioms.

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