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The structural analysis of fuzzy measures |
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| Authors: | ZHANG Ling ZHANG Bo & ZHANG YanPing Computer Science College Anhui University Hefei China State Key Lab of Intelligent Technology & Systems Tsinghua National Lab for Information Science & Technology Information Science & Technology College Computer Science & Technology Tsinghua University Beijing |
| Affiliation: | ZHANG Ling1,ZHANG Bo2 & ZHANG YanPing1 1 Computer Science College,Anhui University,Hefei 230039,China,2State Key Lab of Intelligent Technology & Systems,Tsinghua National Lab for Information Science & Technology,Information Science & Technology College,Computer Science & Technology,Tsinghua University,Beijing 100084 |
| Abstract: | From quotient space based granular computing theory we explore the fuzzy measures of fuzzy sets. Based on the structural analysis of fuzzy sets,we present anisotropismassumption.Under this assumption we achieved the following insights:(1)the uniqueness of a fuzzy measure being isotropic on a finite complete semi-ordered set;(2)the necessary and suffcient condition of the isomorphism for fuzzy measure functions in fuzzy mathematics;(3)the necessary and suffcient condition that fuzzy measures have fuzzy and g... |
| Keywords: | quotient space fuzzy set fuzzy measure rough set structural analysis |
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