Journal
INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS
Volume 10, Issue 10, Pages 2669-2690Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s13042-018-0893-7
Keywords
Decision-theoretic rough set; Double quantification; Graded rough set; Incremental information; Uncertainty measure
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Funding
- Natural Science Foundation of China [11671109, 11671111, 61472463, 61772002]
- Science and Technology Research Program of Chongqing Municipal Education Commission [KJ1709221]
- China Scholarship Council [201606120161]
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Double-quantitative decision-theoretic rough set (Dq-DTRS), as a new model considering double quantification to reflect the distinct degrees of quantitative information, satisfies the quantitative completeness properties and exhibits much stronger fault tolerance capabilities than decision-theoretic rough set (DTRS) and graded rough set (GRS). Since the Dq-DTRS was proposed, there have been few studies on the uncertainty analysis of the model. In this paper, we investigate the uncertainty measure of the four disjoint regions in Dq-DTRS models by introducing a fuzziness formula for rough set, and then describe the changing regularities of fuzziness of disjoint regions in DqI-DTRS model and DqII-DTRS model along with the variation of two parameters alpha, beta and the grade k, respectively. In addition, three kinds of incremental information for Dq-DTRS model, namely useful incremental information, useless incremental information and error-correction incremental information are presented being formed with regard to the changes of boundary regions, and also the related assessment methods for these special types of incremental information are discussed in the form of several important theorems.
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