{"title":"半线性空间中具有sup *组合的模糊关系方程组的最小解","authors":"L. Nosková, I. Perfilieva","doi":"10.1109/FUZZY.2007.4295592","DOIUrl":null,"url":null,"abstract":"The problem of solvability of a system of fuzzy relation equations with sup-* composition is considered in semilinear vector spaces. Based on the fact that a complete set of solutions is determined by minimal solutions, we focused on characterization of them. At first, sets of all minimal solutions of a single equation have been described under different assumptions on an underlying algebra. Dependently on the ordering of the support set, either necessary or sufficient conditions, or criteria of being a minimal solution have been obtained. Then minimal solutions of a system are build from minimal solutions of single equations.","PeriodicalId":236515,"journal":{"name":"2007 IEEE International Fuzzy Systems Conference","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"System of fuzzy relation equations with sup-* composition in semi-linear spaces: minimal solutions\",\"authors\":\"L. Nosková, I. Perfilieva\",\"doi\":\"10.1109/FUZZY.2007.4295592\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problem of solvability of a system of fuzzy relation equations with sup-* composition is considered in semilinear vector spaces. Based on the fact that a complete set of solutions is determined by minimal solutions, we focused on characterization of them. At first, sets of all minimal solutions of a single equation have been described under different assumptions on an underlying algebra. Dependently on the ordering of the support set, either necessary or sufficient conditions, or criteria of being a minimal solution have been obtained. Then minimal solutions of a system are build from minimal solutions of single equations.\",\"PeriodicalId\":236515,\"journal\":{\"name\":\"2007 IEEE International Fuzzy Systems Conference\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-08-27\",\"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.2007.4295592\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2007 IEEE International Fuzzy Systems Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FUZZY.2007.4295592","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
System of fuzzy relation equations with sup-* composition in semi-linear spaces: minimal solutions
The problem of solvability of a system of fuzzy relation equations with sup-* composition is considered in semilinear vector spaces. Based on the fact that a complete set of solutions is determined by minimal solutions, we focused on characterization of them. At first, sets of all minimal solutions of a single equation have been described under different assumptions on an underlying algebra. Dependently on the ordering of the support set, either necessary or sufficient conditions, or criteria of being a minimal solution have been obtained. Then minimal solutions of a system are build from minimal solutions of single equations.
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