Abstract
A fuzzy rough set is a fuzzy generalization of rough set. There are already several definitions for it, and most of them are given with reference to a t-norm *, a fuzzy (*-)similarity relation and the duality principle. In this paper, a generalization of fuzzy rough sets is investigated regarding a general fuzzy relation and a lower semi-continuous fuzzy conjunction logical operator in its second argument. The generalized fuzzy rough approximation operators are established by using the adjunction between the fuzzy conjunction operator and a fuzzy implication operator. Algebraic properties of the generalized fuzzy rough approximation operators are discussed. It has been shown that information with much more necessity measure and with less probability measure for a fuzzy set can be mined in comparison with existing methods of fuzzy rough sets. © Springer-Verlag Berlin Heidelberg 2007.
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Deng, T., Chen, Y., & Gao, G. (2007). Algebraic properties of adjunction-based fuzzy rough sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4482 LNAI, pp. 47–54). Springer Verlag. https://doi.org/10.1007/978-3-540-72530-5_5
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