{"title":"模糊随机变量的均值和方差评价方法","authors":"Y. Yoshida","doi":"10.1109/IS.2006.348423","DOIUrl":null,"url":null,"abstract":"This paper discusses an evaluation method of fuzzy numbers/fuzzy random variables by mean values and variance defined by fuzzy measures, and the method is applicable to decision making with both randomness and fuzziness. Next, we compare several possible approaches regarding variances by examining them for some fuzzy random variables with values at triangle-type fuzzy numbers. We find the method with lambda-mean functions has proper properties, and we derive fundamental properties regarding the variance and the corresponding co-variance and correlation. Formulae are given to apply the results to triangle-type fuzzy numbers, trapezoidal-type fuzzy numbers, and some types of fuzzy random variables","PeriodicalId":116809,"journal":{"name":"2006 3rd International IEEE Conference Intelligent Systems","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Mean Value and Variance of Fuzzy Random Variables by Evaluation Measures\",\"authors\":\"Y. Yoshida\",\"doi\":\"10.1109/IS.2006.348423\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper discusses an evaluation method of fuzzy numbers/fuzzy random variables by mean values and variance defined by fuzzy measures, and the method is applicable to decision making with both randomness and fuzziness. Next, we compare several possible approaches regarding variances by examining them for some fuzzy random variables with values at triangle-type fuzzy numbers. We find the method with lambda-mean functions has proper properties, and we derive fundamental properties regarding the variance and the corresponding co-variance and correlation. Formulae are given to apply the results to triangle-type fuzzy numbers, trapezoidal-type fuzzy numbers, and some types of fuzzy random variables\",\"PeriodicalId\":116809,\"journal\":{\"name\":\"2006 3rd International IEEE Conference Intelligent Systems\",\"volume\":\"45 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 3rd International IEEE Conference Intelligent Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IS.2006.348423\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 3rd International IEEE Conference Intelligent Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IS.2006.348423","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mean Value and Variance of Fuzzy Random Variables by Evaluation Measures
This paper discusses an evaluation method of fuzzy numbers/fuzzy random variables by mean values and variance defined by fuzzy measures, and the method is applicable to decision making with both randomness and fuzziness. Next, we compare several possible approaches regarding variances by examining them for some fuzzy random variables with values at triangle-type fuzzy numbers. We find the method with lambda-mean functions has proper properties, and we derive fundamental properties regarding the variance and the corresponding co-variance and correlation. Formulae are given to apply the results to triangle-type fuzzy numbers, trapezoidal-type fuzzy numbers, and some types of fuzzy random variables
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