Titlebook: Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing; 10th International C Dominik ?l?zak,Guoyin Wang,Yiyu Yao Conference proceeding

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Algebraic Approach to Generalized Rough Setsor any atomic complete Boolean algebra . with the set . of atoms, a map . is an algebraic lower approximation operator if and only if there exists a binary relation . on . such that . = .., where .. is the lower approximation defined by the binary relation .. This generalizes the results given by Ya

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Logic for Rough Sets with Rough Double Stone Algebraic Semanticser approximation set, upper approximation set>. An important result is that the collection of rough sets of an approximation space can be made into a regular double Stone algebra. In this paper, a logic for rough sets, i.e., the sequent calculus corresponding to rough double Stone algebra, is propos

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Pairwise Cores in Information Systemsall reducts of the information system). A notion of a pairwise core (2-core), which naturally extends the definition of a core into the case of pairs of attributes is presented. Some useful features concerned with the graph representation of pairwise cores are discussed..The paper presents also prac

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Proximity Spaces of Exact Setsssociated modal Boolean algebra of exact sets. The present essay generalizes the axiomatic notion of a PFS to tolerance (reflexive, symmetric) relations, where the universe of exact sets forms a modal ortho-lattice. An example of this general notion is provided by the tolerance relation of “matching” over ..