区间值模糊集的分解定理及相似度的计算

Decomposition theorem of interval-valued fuzzy sets and calculation of similarity measure

针对区间值模糊集相似度公式只是经验公式并没有理论依据问题.建立了区间值模糊集新的截集概念,研究了相似度计算方法.结果表明:所建立的新截集概念是以往截集概念的推广.在新截集理论的基础上,进一步给出了区间值模糊集的分解定理;根据该截集发展出一种推导区间值模糊集相似度的方法,建立了模糊集相似度与区间值模糊集相似度之间的联系,可进一步应用到模糊风险分析研究中.

The similarity formulas of interval-valued fuzzy sets proposed in the past years are empirical formulas without a theoretical basis.In order to provide a theoretical basis,a new concept of cut set of interval-valued fuzzy sets is established and the method of calculating the similarity between interval-valued fuzzy sets is investigated.The results show that the newly proposed concept is an extension of existing concept.The decomposition theorem of interval-valued fuzzy set is derived and a new method of calculating the similarity formula of interval-valued fuzzy sets is proposed based on the new cut set.In addition,the connection between the similarity of fuzzy set and the similarity of interval-valued fuzzy set is established.The new method can be applied in the study of fuzzy risk analysis and has a theoretical significance in fuzzy risk analysis.