By J. Stepaniuk
The publication "Rough-Granular Computing in wisdom Discovery and knowledge Mining" written by way of Professor Jaroslaw Stepaniuk is devoted to tools in line with a mixture of the subsequent 3 heavily comparable and quickly turning out to be components: granular computing, tough units, and information discovery and information mining (KDD). within the publication, the KDD foundations in accordance with the tough set method and granular computing are mentioned including illustrative purposes. In looking for proper styles or in inducing (constructing) classifiers in KDD, other kinds of granules are modeled. during this modeling technique, granules known as approximation areas play a unique rule. Approximation areas are outlined by means of neighborhoods of gadgets and measures among units of items. within the e-book, the writer underlines the significance of approximation areas in trying to find correct styles and different granules on dfferent degrees of modeling for compound thought approximations. Calculi on such granules are used for modeling computations on granules in trying to find goal (sub) optimum granules and their interactions on diversified degrees of hierarchical modeling. The equipment in line with the combo of granular computing, the tough and fuzzy set techniques let for an effcient development of the top of the range approximation of compound concepts.
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Extra info for Rough – Granular Computing in Knowledge Discovery and Data Mining
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9. For every object x ∈ U and the Boolean function defined by gA∪{d},x (a∗1 , . . , a∗m ) = a∗ y∈U,d(y)=d(x) a∈cx,y the following conditions are equivalent: 1. {ai1 , . . , aik } is a relative reduct for the object x ∈ U in the decision table DT. 2. a∗i1 ∧ . . ∧ a∗ik is a prime implicant of the Boolean function gA∪{d},x . 10. For the Boolean function defined by gA∪{d} (a∗1 , . . , a∗m ) = a∗ x,y∈U,d(y)=d(x) a∈cx,y 50 Data Reduction Fig. 3. Idea of Object Related Reducts the following conditions are equivalent: 1.
R). 1. The positive region of the classification {X1 , . . , Xr } with respect to the approximation space AS#,$ is defined by r P OS AS#,$ , {X1 , . . , Xr } = LOW AS#,$ , Xi . i=1 2. The quality of approximation of the classification {X1 , . . , Xr } in the approximation space AS#,$ is defined by γ AS#,$ , {X1 , . . , Xr } = card P OS AS#,$ , {X1 , . . , Xr } card (U ) . 3. The quality of approximation of the classification coefficient expresses the ratio of the number of all AS#,$ -correctly classified objects to the number of all objects in the data table.
It is necessary 40 Rough Sets to induce approximations of concepts (models of concepts) from available experimental data. The data models developed so far in such areas as statistical learning, machine learning, pattern recognition are not satisfactory for approximation of complex concepts that occur in the perception process. , [18, 208]). The main reason for this is that these complex concepts are, in a sense, too far from measurements which renders the searching for relevant features in a huge feature space infeasible.