{"title":"Analytical formulas for similarity, possibility and distinguishability measures of Cauchy type fuzzy sets with comparison to Gaussian fuzzy sets","authors":"Nelly S. Amer, H. Hefny","doi":"10.1109/INTELCIS.2015.7397257","DOIUrl":null,"url":null,"abstract":"This paper provides general analytical formulas for similarity and distinguishabilty measures of fuzzy sets of Cauchy type membership functions. A generalized analytical formula between similarity and possibility measures has also been obtained. A comparison with the case of Gaussian fuzzy sets ensures interesting monotonic characteristic charts for Cauchy type fuzzy sets compared with those of Gaussian fuzzy sets. This result represents a significant guide for building interpretable fuzzy models by adopting suitable forms of fuzzy sets as linguistic values based on their characteristic charts.","PeriodicalId":6478,"journal":{"name":"2015 IEEE Seventh International Conference on Intelligent Computing and Information Systems (ICICIS)","volume":"41 1","pages":"21-26"},"PeriodicalIF":0.0000,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 IEEE Seventh International Conference on Intelligent Computing and Information Systems (ICICIS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/INTELCIS.2015.7397257","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
This paper provides general analytical formulas for similarity and distinguishabilty measures of fuzzy sets of Cauchy type membership functions. A generalized analytical formula between similarity and possibility measures has also been obtained. A comparison with the case of Gaussian fuzzy sets ensures interesting monotonic characteristic charts for Cauchy type fuzzy sets compared with those of Gaussian fuzzy sets. This result represents a significant guide for building interpretable fuzzy models by adopting suitable forms of fuzzy sets as linguistic values based on their characteristic charts.
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