{"title":"广义测度综述","authors":"E. Klement, S. Weber","doi":"10.1109/FUZZY.1992.258773","DOIUrl":null,"url":null,"abstract":"The authors present a unified approach to several concepts on generalized measures with various domains and ranges, which are: sigma -additive measures; probability measures of fuzzy events; fuzzy probability measures; fuzzy-valued fuzzy measures; ( sigma -) perpendicular to -decomposable measures; measures of fuzzy sets; and perpendicular to '-decomposable measures, where perpendicular to ' is the extension of an Archimedean t-conorm on (0,M) to D/sub M/ via the extension principle. All these measures are handled in a unified way. The main emphasis is on integral representations of such measures if they are defined on a collection of fuzzy sets.<<ETX>>","PeriodicalId":222263,"journal":{"name":"[1992 Proceedings] IEEE International Conference on Fuzzy Systems","volume":"48 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A survey on generalized measures\",\"authors\":\"E. Klement, S. Weber\",\"doi\":\"10.1109/FUZZY.1992.258773\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The authors present a unified approach to several concepts on generalized measures with various domains and ranges, which are: sigma -additive measures; probability measures of fuzzy events; fuzzy probability measures; fuzzy-valued fuzzy measures; ( sigma -) perpendicular to -decomposable measures; measures of fuzzy sets; and perpendicular to '-decomposable measures, where perpendicular to ' is the extension of an Archimedean t-conorm on (0,M) to D/sub M/ via the extension principle. All these measures are handled in a unified way. The main emphasis is on integral representations of such measures if they are defined on a collection of fuzzy sets.<<ETX>>\",\"PeriodicalId\":222263,\"journal\":{\"name\":\"[1992 Proceedings] IEEE International Conference on Fuzzy Systems\",\"volume\":\"48 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-03-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"[1992 Proceedings] IEEE International Conference on Fuzzy Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FUZZY.1992.258773\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1992 Proceedings] IEEE International Conference on Fuzzy Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FUZZY.1992.258773","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The authors present a unified approach to several concepts on generalized measures with various domains and ranges, which are: sigma -additive measures; probability measures of fuzzy events; fuzzy probability measures; fuzzy-valued fuzzy measures; ( sigma -) perpendicular to -decomposable measures; measures of fuzzy sets; and perpendicular to '-decomposable measures, where perpendicular to ' is the extension of an Archimedean t-conorm on (0,M) to D/sub M/ via the extension principle. All these measures are handled in a unified way. The main emphasis is on integral representations of such measures if they are defined on a collection of fuzzy sets.<>
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