基于模糊数结构元相似度的模糊风险分析
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摘要
基于模糊数结构元理论,定义了模糊数结构元相似度。通过12组模糊集对结构元相似度的性质进行对比研究。结果表明,结构元相似度是实数相似度的拓展,具有良好的性质且计算简单。最后给出了基于结构元相似度的模糊风险分析模型,模型中评估项的值是语言值。
Structured-element similarity of fuzzy numbers is definition based on structured element theory.A comparative study of structured-element similarity is presented by 12 sets of fuzzy numbers.Results show structured-element similarity is an extension of the similarity of real numbers,and has good properties and simple calculation.Finally,we present a fuzzy risk analysis algorithm based on structured-element similarity,where the values of the evaluating items are represented by linguistic values.
Structured-element similarity of fuzzy numbers is definition based on structured element theory.A comparative study of structured-element similarity is presented by 12 sets of fuzzy numbers.Results show structured-element similarity is an extension of the similarity of real numbers,and has good properties and simple calculation.Finally,we present a fuzzy risk analysis algorithm based on structured-element similarity,where the values of the evaluating items are represented by linguistic values.
引文
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[11]岳立柱,马卫民,郭永升.求解模糊排队性状指标隶属函数的通用方法[J].系统工程理论与实践,2014,34(4):925~935.
[2] Chen S J,Chen S M.Fuzzy risk analysis based on similarity of generalized fuzzy numbers[J].IEEE Transactions on Fuzzy Systems,2003,11(1):45~56.
[3] Wei S H,Chen S M.A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers[J].Expert Systems with Applications,2009,36(1):589~598.
[4] Schmucker K J.Fuzzy sets,natural language computations,and risk analysis[M].Rockville,MD:Computer Science Press,1984.
[5] Bustince H,Pagola M,Barrenechea E.Construction of fuzzy indices from fuzzy DI-subsethood measures:Application to the global comparison of images[J].Information Sciences,2007,177(3):906~929.
[6] Chen S J,Chen S M.A new method to measure the similarity between fuzzy numbers[C]//IEEE International Conference on Fuzzy Systems,2001,3:1123~1126.
[7]郭嗣琮.模糊分析中的结构元方法(Ⅰ)、(Ⅱ)[J].辽宁工程技术大学学报,2002,21(5):670~673;21(6):808~810.
[8]郭嗣琮.模糊实数空间与[-1,1]上同序单调函数类的同胚[J].自然科学进展,2004,14(11):1318~1321.
[9]岳立柱.基于结构元理论的模糊数的贴近度[J].模糊系统与数学,2011,25(6):10~15.
[10] Wu D,Mendel J M.A comparative study of ranking methods,similarity measures and uncertainty measures for interval type-2fuzzy sets[J].Information Sciences,2009,179(8):1169~1192.
[11]岳立柱,马卫民,郭永升.求解模糊排队性状指标隶属函数的通用方法[J].系统工程理论与实践,2014,34(4):925~935.