{"title":"Sugeno积分的扩展Chebyshev型不等式","authors":"H. Román-Flores, A. Flores-Franulic, H. Agahi","doi":"10.1109/NAFIPS.2010.5548189","DOIUrl":null,"url":null,"abstract":"An extended Chebyshev type inequality for the Sugeno integral on abstract spaces is studied. More precisely, necessary and sufficient conditions under which the inequality, ∫<inf>A</inf>Φ(f ⋆ g)dµ ≥ (∫<inf>A</inf>Φ(f)dµ) ⋆ (∫<inf>A</inf> Φ(g)dµ) or its reverse hold for an arbitrary fuzzy measure-based type Sugeno integral µ and a binary operation ⋆: [0, ∞)<sup>2</sup> → [0, ∞) and a nonnegative function Φ : [0, ∞) → [0, ∞), are given.","PeriodicalId":394892,"journal":{"name":"2010 Annual Meeting of the North American Fuzzy Information Processing Society","volume":"427 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Extended Chebyshev type inequality for Sugeno integral\",\"authors\":\"H. Román-Flores, A. Flores-Franulic, H. Agahi\",\"doi\":\"10.1109/NAFIPS.2010.5548189\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An extended Chebyshev type inequality for the Sugeno integral on abstract spaces is studied. More precisely, necessary and sufficient conditions under which the inequality, ∫<inf>A</inf>Φ(f ⋆ g)dµ ≥ (∫<inf>A</inf>Φ(f)dµ) ⋆ (∫<inf>A</inf> Φ(g)dµ) or its reverse hold for an arbitrary fuzzy measure-based type Sugeno integral µ and a binary operation ⋆: [0, ∞)<sup>2</sup> → [0, ∞) and a nonnegative function Φ : [0, ∞) → [0, ∞), are given.\",\"PeriodicalId\":394892,\"journal\":{\"name\":\"2010 Annual Meeting of the North American Fuzzy Information Processing Society\",\"volume\":\"427 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-07-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 Annual Meeting of the North American Fuzzy Information Processing Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/NAFIPS.2010.5548189\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 Annual Meeting of the North American Fuzzy Information Processing Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/NAFIPS.2010.5548189","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Extended Chebyshev type inequality for Sugeno integral
An extended Chebyshev type inequality for the Sugeno integral on abstract spaces is studied. More precisely, necessary and sufficient conditions under which the inequality, ∫AΦ(f ⋆ g)dµ ≥ (∫AΦ(f)dµ) ⋆ (∫A Φ(g)dµ) or its reverse hold for an arbitrary fuzzy measure-based type Sugeno integral µ and a binary operation ⋆: [0, ∞)2 → [0, ∞) and a nonnegative function Φ : [0, ∞) → [0, ∞), are given.
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