广义梯形模糊数相似性度量的新方法及其应用  

New similarity measure for generalized trapezoidal fuzzy numbers:methods and applications

作　　者：李俊红[1,2] 曾文艺[1] 

机构地区：[1]北京师范大学信息科学与技术学院,北京100875 [2]河北师范大学数学与信息科学学院,石家庄河北050024

出　　处：《北京师范大学学报（自然科学版）》2015年第2期120-125,共6页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10971243)

摘　　要：针对模糊数相似度计算问题,提出一种新的基于广义梯形模糊数的相似度量方法,在保证度量有效性的前提下,降低相似度的计算复杂性,提高其区分度,扩大其适用范围.给出区分性、无效率和不合理率三个评价指标,以对不同相似度方法进行比较.实验结果表明新方法具有较好的性能.最后,通过基于DS证据理论的故障诊断实例说明所提方法的合理性和可用性.Aimed at the similarity measure of fuzzy numbers,a new method to calculate similarity measure for Generalized Trapezoidal Fuzzy Numbers(GTFN)was proposed.This method can ensure the effectiveness of similarity measure,reduce complexity of computation and extend its distinguishability and application scope.Three evaluation indexes were also introduced:distinction property,inefficient rate,unreasonable rate to evaluate different similarity measures.Data showed that this proposed method gave improved performance.The method was then applied to fault diagnosis based on DS evidence theory to illustrate the proposed similarity measure being reasonable and available.

关 键 词：相似度 广义梯形模糊数 模糊决策 故障诊断 DS证据理论 

分 类 号：O159[理学—数学]