{"title":"一般2型模糊集的构造","authors":"D. Hu, T. Lin, Qiang Fan","doi":"10.1109/GrC.2013.6740396","DOIUrl":null,"url":null,"abstract":"Focus on constructing of general type-2 fuzzy set, the essence of type-n fuzzy sets are discovered. We first proved the consistency between interval estimation and nested sets representation theorem of type-1 fuzzy sets, which guarantees the rationality of our methods in this paper. Then, based on the fact that a type-1 fuzzy set can be constructed by a collection of intervals, an algorithm for constructing general type-2 fuzzy sets based on the collections of interval type-2 fuzzy sets was proposed. Furthermore, a new concept, interval type-2 fuzzy sets with uncertain bounds, was defined. And the ways for constructing general type-2 fuzzy sets by give interval type-2 fuzzy sets with uncertain bounds and constructing interval type-2 fuzzy sets with uncertain bounds by given general type-2 fuzzy sets were proposed. Finally, from the viewpoint of uncertain bounds, the essence of type-n fuzzy sets was discussed.","PeriodicalId":415445,"journal":{"name":"2013 IEEE International Conference on Granular Computing (GrC)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The construction of general type-2 fuzzy sets\",\"authors\":\"D. Hu, T. Lin, Qiang Fan\",\"doi\":\"10.1109/GrC.2013.6740396\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Focus on constructing of general type-2 fuzzy set, the essence of type-n fuzzy sets are discovered. We first proved the consistency between interval estimation and nested sets representation theorem of type-1 fuzzy sets, which guarantees the rationality of our methods in this paper. Then, based on the fact that a type-1 fuzzy set can be constructed by a collection of intervals, an algorithm for constructing general type-2 fuzzy sets based on the collections of interval type-2 fuzzy sets was proposed. Furthermore, a new concept, interval type-2 fuzzy sets with uncertain bounds, was defined. And the ways for constructing general type-2 fuzzy sets by give interval type-2 fuzzy sets with uncertain bounds and constructing interval type-2 fuzzy sets with uncertain bounds by given general type-2 fuzzy sets were proposed. Finally, from the viewpoint of uncertain bounds, the essence of type-n fuzzy sets was discussed.\",\"PeriodicalId\":415445,\"journal\":{\"name\":\"2013 IEEE International Conference on Granular Computing (GrC)\",\"volume\":\"49 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2013 IEEE International Conference on Granular Computing (GrC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/GrC.2013.6740396\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2013 IEEE International Conference on Granular Computing (GrC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/GrC.2013.6740396","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Focus on constructing of general type-2 fuzzy set, the essence of type-n fuzzy sets are discovered. We first proved the consistency between interval estimation and nested sets representation theorem of type-1 fuzzy sets, which guarantees the rationality of our methods in this paper. Then, based on the fact that a type-1 fuzzy set can be constructed by a collection of intervals, an algorithm for constructing general type-2 fuzzy sets based on the collections of interval type-2 fuzzy sets was proposed. Furthermore, a new concept, interval type-2 fuzzy sets with uncertain bounds, was defined. And the ways for constructing general type-2 fuzzy sets by give interval type-2 fuzzy sets with uncertain bounds and constructing interval type-2 fuzzy sets with uncertain bounds by given general type-2 fuzzy sets were proposed. Finally, from the viewpoint of uncertain bounds, the essence of type-n fuzzy sets was discussed.
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