{"title":"基于水平集测度的全称积分的概念","authors":"E. Klement, R. Mesiar, E. Pap","doi":"10.1109/SISY.2009.5291184","DOIUrl":null,"url":null,"abstract":"For functions with values in the nonnegative real numbers, universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures, including as special cases Choquet and Sugeno integrals. For a fixed pseudo-multiplication on the nonnegative real numbers, the smallest and the greatest universal integrals are given. Finally, another construction method for obtaining universal integrals is introduced.","PeriodicalId":378688,"journal":{"name":"2009 7th International Symposium on Intelligent Systems and Informatics","volume":"27 6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"A concept of universal integral based on measures of level sets\",\"authors\":\"E. Klement, R. Mesiar, E. Pap\",\"doi\":\"10.1109/SISY.2009.5291184\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For functions with values in the nonnegative real numbers, universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures, including as special cases Choquet and Sugeno integrals. For a fixed pseudo-multiplication on the nonnegative real numbers, the smallest and the greatest universal integrals are given. Finally, another construction method for obtaining universal integrals is introduced.\",\"PeriodicalId\":378688,\"journal\":{\"name\":\"2009 7th International Symposium on Intelligent Systems and Informatics\",\"volume\":\"27 6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-10-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 7th International Symposium on Intelligent Systems and Informatics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SISY.2009.5291184\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 7th International Symposium on Intelligent Systems and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SISY.2009.5291184","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A concept of universal integral based on measures of level sets
For functions with values in the nonnegative real numbers, universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures, including as special cases Choquet and Sugeno integrals. For a fixed pseudo-multiplication on the nonnegative real numbers, the smallest and the greatest universal integrals are given. Finally, another construction method for obtaining universal integrals is introduced.
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