东华大学学报（英文版）2007，Vol.24Issue(2)：268-271,4.
Properties of Fuzzy Entropy Based on the Shape Change of Membership Function
Properties of Fuzzy Entropy Based on the Shape Change of Membership Function
摘要
Abstract
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 proportional to that of the original one while elevation factor just acts as a proportional factor. These results should contribute to the analysis and design of a fuzzy system.关键词
fuzzy entropy/membership function/entropy function/triangular fuzzy number/support intervalKey words
fuzzy entropy/membership function/entropy function/triangular fuzzy number/support interval分类
数理科学引用本文复制引用
..Properties of Fuzzy Entropy Based on the Shape Change of Membership Function[J].东华大学学报（英文版）,2007,24(2):268-271,4.基金项目
The National Natural Science Foundation of China (No. 60474022) （No. 60474022）
