{"title":"Type-2 Fuzzy Logic: Theory and Applications","authors":"O. Castillo, P. Melin, J. Kacprzyk, W. Pedrycz","doi":"10.1109/GrC.2007.118","DOIUrl":null,"url":null,"abstract":"Type-2 fuzzy sets are used for modeling uncertainty and imprecision in a better way. These type-2 fuzzy sets were originally presented by Zadeh in 1975 and are essentially \"fuzzy fuzzy\" sets where the fuzzy degree of membership is a type-1 fuzzy set. The new concepts were introduced by Mendel and Liang allowing the characterization of a type-2 fuzzy set with a superior membership function and an inferior membership function; these two functions can be represented each one by a type-1 fuzzy set membership function. The interval between these two functions represents the footprint of uncertainty (FOU), which is used to characterize a type-2 fuzzy set.","PeriodicalId":259430,"journal":{"name":"2007 IEEE International Conference on Granular Computing (GRC 2007)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"596","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2007 IEEE International Conference on Granular Computing (GRC 2007)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/GrC.2007.118","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 596
Abstract
Type-2 fuzzy sets are used for modeling uncertainty and imprecision in a better way. These type-2 fuzzy sets were originally presented by Zadeh in 1975 and are essentially "fuzzy fuzzy" sets where the fuzzy degree of membership is a type-1 fuzzy set. The new concepts were introduced by Mendel and Liang allowing the characterization of a type-2 fuzzy set with a superior membership function and an inferior membership function; these two functions can be represented each one by a type-1 fuzzy set membership function. The interval between these two functions represents the footprint of uncertainty (FOU), which is used to characterize a type-2 fuzzy set.
二类模糊集可以更好地对不确定性和不精确性进行建模。这些2型模糊集最初由Zadeh在1975年提出，本质上是“模糊模糊”集，其中模糊隶属度是1型模糊集。Mendel和Liang引入了新的概念，允许具有一个上隶属函数和一个下隶属函数的2型模糊集的刻划;这两个函数可以分别用1型模糊集隶属函数表示。这两个函数之间的间隔表示不确定性的足迹(footprint of uncertainty, FOU)， FOU用于描述2型模糊集。
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