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Published in:
2010 | OriginalPaper | Chapter
Fuzzy Measures and Granular Computing
Authors : Ling Zhang, Bo Zhang
Published in: Rough Set and Knowledge Technology
Publisher: Springer Berlin Heidelberg
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From the view point of granular computing, by analyzing the structure of fuzzy measures based on the quotient space analytical method, we have the following results: (1) the necessary and sufficient condition of the isomorphism of fuzzy measure functions in fuzzy mathematics; (2) the necessary and sufficient condition of the fuzzy and granular monotony of fuzzy measures. The results open out the essence of fuzzy measures and provide a simple way to constructing fuzzy measures. The results also show that the quotient space analytical method is ubiquitous and effective in many fields.