{"title":"Aggregation Operators and the Lipschitzian Condition","authors":"J. Jacas, J. Recasens","doi":"10.1109/FUZZY.2007.4295514","DOIUrl":null,"url":null,"abstract":"Lipschitzian and kernel aggregation operators with respect to the natural T-indistinguishability operator Et and their powers are studied. A t-norm T is proved to be E T -Lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T.","PeriodicalId":236515,"journal":{"name":"2007 IEEE International Fuzzy Systems Conference","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2007 IEEE International Fuzzy Systems Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FUZZY.2007.4295514","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Lipschitzian and kernel aggregation operators with respect to the natural T-indistinguishability operator Et and their powers are studied. A t-norm T is proved to be E T -Lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T.
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