{"title":"模糊度量空间及其拓扑性质","authors":"M. Masriani, Q. Aini, Syamsul Bahri","doi":"10.29303/emj.v4i2.95","DOIUrl":null,"url":null,"abstract":"The fuzzy set theory is mathematics that applies fuzziness characteristics, so that gives the truth value at interval [0,1]. It is different from the crisp set that gives a truth value of 0 if it is not a member and 1 if it is a member. The theory of fuzzy sets has been developed continuously by scientists. One of the developments of the fuzzy set is the fuzzy metric space which the definition was introduced by George and Veeramani. Based on the analysis results, it is found that every metric space X if and only if X is fuzzy metric space. As a result, the topological properties of the metric space still apply to the fuzzy metric space","PeriodicalId":281429,"journal":{"name":"EIGEN MATHEMATICS JOURNAL","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fuzzy Metric Space and Its Topological Properties\",\"authors\":\"M. Masriani, Q. Aini, Syamsul Bahri\",\"doi\":\"10.29303/emj.v4i2.95\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The fuzzy set theory is mathematics that applies fuzziness characteristics, so that gives the truth value at interval [0,1]. It is different from the crisp set that gives a truth value of 0 if it is not a member and 1 if it is a member. The theory of fuzzy sets has been developed continuously by scientists. One of the developments of the fuzzy set is the fuzzy metric space which the definition was introduced by George and Veeramani. Based on the analysis results, it is found that every metric space X if and only if X is fuzzy metric space. As a result, the topological properties of the metric space still apply to the fuzzy metric space\",\"PeriodicalId\":281429,\"journal\":{\"name\":\"EIGEN MATHEMATICS JOURNAL\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-01-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EIGEN MATHEMATICS JOURNAL\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29303/emj.v4i2.95\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EIGEN MATHEMATICS JOURNAL","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29303/emj.v4i2.95","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The fuzzy set theory is mathematics that applies fuzziness characteristics, so that gives the truth value at interval [0,1]. It is different from the crisp set that gives a truth value of 0 if it is not a member and 1 if it is a member. The theory of fuzzy sets has been developed continuously by scientists. One of the developments of the fuzzy set is the fuzzy metric space which the definition was introduced by George and Veeramani. Based on the analysis results, it is found that every metric space X if and only if X is fuzzy metric space. As a result, the topological properties of the metric space still apply to the fuzzy metric space
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