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Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers (TFNs), the entropies of any two TFNs which can not be always the same type, also, have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets (TFSs) with same sizes of support intervals and different heights, the relationship of their entropies lies on their height. Finally, we point it out a mistake that Chen's assertion that the entropy of resultant fuzzy set of elevation operation is directly to that of the original one while elevation factor just acts as a propartional factor. These results should contribute to the analysis and design of a fuzzy system. 相似文献
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秦应兵 《西南师范大学学报(自然科学版)》1994,(6)
设G是群,A是ZG-模。称A为一个minimax模,如果A有一个有限的ZG-子模链:0=A_o≤A_1≤…≤A_x=A且对任意的i≤n,A_i/A_(i-1)或者满足极小条件或者满足极大条件,证明了:如果G是超有限群,则任意minimax模有f-分解. 相似文献
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