{"title":"k -代数的区间值直觉模糊理想","authors":"M. Akram, K. H. Dar, B. Meng, K. Shum","doi":"10.5555/1503527.1503529","DOIUrl":null,"url":null,"abstract":"The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-algebras and investigate some interesting properties. We characterize Artinian and Noetherian K-algebras by considering IIFIs of a K-algebra K: Characterization theorems of fully invariant and characteristic IIFIs are also discussed.","PeriodicalId":112268,"journal":{"name":"WSEAS Transactions on Mathematics archive","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Interval-valued intuitionistic fuzzy ideals of K-algebras\",\"authors\":\"M. Akram, K. H. Dar, B. Meng, K. Shum\",\"doi\":\"10.5555/1503527.1503529\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-algebras and investigate some interesting properties. We characterize Artinian and Noetherian K-algebras by considering IIFIs of a K-algebra K: Characterization theorems of fully invariant and characteristic IIFIs are also discussed.\",\"PeriodicalId\":112268,\"journal\":{\"name\":\"WSEAS Transactions on Mathematics archive\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS Transactions on Mathematics archive\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5555/1503527.1503529\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Mathematics archive","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5555/1503527.1503529","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Interval-valued intuitionistic fuzzy ideals of K-algebras
The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-algebras and investigate some interesting properties. We characterize Artinian and Noetherian K-algebras by considering IIFIs of a K-algebra K: Characterization theorems of fully invariant and characteristic IIFIs are also discussed.
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