Distributions with fuzziness and randomness

Proceedings of 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society Pub Date : 1995-03-17 DOI:10.1109/ISUMA.1995.527774

Ru-Jen Chao, B. Ayyub

{"title":"Distributions with fuzziness and randomness","authors":"Ru-Jen Chao, B. Ayyub","doi":"10.1109/ISUMA.1995.527774","DOIUrl":null,"url":null,"abstract":"Both cognitive and noncognitive uncertainties can be present in the same variable. The non-cognitive uncertainty of a variable can be described by its own probability density function (PDF); whereas the cognitive uncertainty of a random variable can be described by the membership function for its fuzziness and its /spl alpha/-cuts. A PDF called fuzzy-random PDF is proposed in this paper based on considering the combined effects of both cognitive and non-cognitive uncertainties for the variable. The variable is assumed to have a fuzzy mean and a non-fuzzy standard deviation. The fuzzy-random PDF is defined as the marginal density function of the multiplication of its normalized membership function and its random distribution. Relationships for the means and variances among the fuzzy-random distribution, normalized membership function, and random distribution were developed. The moments method and discrete method were proposed for dealing with the fuzzy-random PDF.","PeriodicalId":298915,"journal":{"name":"Proceedings of 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society","volume":"70 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1995-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISUMA.1995.527774","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 10

Abstract

Both cognitive and noncognitive uncertainties can be present in the same variable. The non-cognitive uncertainty of a variable can be described by its own probability density function (PDF); whereas the cognitive uncertainty of a random variable can be described by the membership function for its fuzziness and its /spl alpha/-cuts. A PDF called fuzzy-random PDF is proposed in this paper based on considering the combined effects of both cognitive and non-cognitive uncertainties for the variable. The variable is assumed to have a fuzzy mean and a non-fuzzy standard deviation. The fuzzy-random PDF is defined as the marginal density function of the multiplication of its normalized membership function and its random distribution. Relationships for the means and variances among the fuzzy-random distribution, normalized membership function, and random distribution were developed. The moments method and discrete method were proposed for dealing with the fuzzy-random PDF.

查看原文本刊更多论文

具有模糊性和随机性的分布

认知不确定性和非认知不确定性可以同时存在于同一变量中。变量的非认知不确定性可用其自身的概率密度函数(PDF)来描述;而随机变量的认知不确定性可以用隶属函数来描述，因为它具有模糊性和/spl alpha/-cuts。本文在综合考虑变量的认知不确定性和非认知不确定性影响的基础上，提出了一种模糊随机PDF。假设变量具有模糊均值和非模糊标准差。模糊随机PDF定义为其归一化隶属函数与其随机分布相乘的边际密度函数。建立了模糊随机分布、归一化隶属函数和随机分布之间的均值和方差关系。提出了矩量法和离散法处理模糊随机PDF的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Proceedings of 3rd International Symposium on Uncertainty Modeling and Analysis and Annual Conference of the North American Fuzzy Information Processing Society

自引率

0.00%

发文量