{"title":"模糊距离与模糊范数","authors":"Masamichi Kon","doi":"10.15807/JORSJ.60.66","DOIUrl":null,"url":null,"abstract":"We consider fuzzy sets on a metric, vector, or normed space. It is not assumed that the fuzzy sets have compact supports. In the present paper, a fuzzy distance and a fuzzy norm are proposed in order to measure the difference between two fuzzy sets, and their fundamental properties are investigated. Their definitions are based on Zadeh’s extension principle. Although they are different from the classical ones based on the Hausdorff metric, they are suitable for data containing uncertainty or vagueness. The obtained results can be expected to be useful for analyzing such data when the data are represented as fuzzy sets.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"66-77"},"PeriodicalIF":0.0000,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.66","citationCount":"0","resultStr":"{\"title\":\"FUZZY DISTANCE AND FUZZY NORM\",\"authors\":\"Masamichi Kon\",\"doi\":\"10.15807/JORSJ.60.66\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider fuzzy sets on a metric, vector, or normed space. It is not assumed that the fuzzy sets have compact supports. In the present paper, a fuzzy distance and a fuzzy norm are proposed in order to measure the difference between two fuzzy sets, and their fundamental properties are investigated. Their definitions are based on Zadeh’s extension principle. Although they are different from the classical ones based on the Hausdorff metric, they are suitable for data containing uncertainty or vagueness. The obtained results can be expected to be useful for analyzing such data when the data are represented as fuzzy sets.\",\"PeriodicalId\":51107,\"journal\":{\"name\":\"Journal of the Operations Research Society of Japan\",\"volume\":\"60 1\",\"pages\":\"66-77\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-04-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.15807/JORSJ.60.66\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Operations Research Society of Japan\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15807/JORSJ.60.66\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Decision Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Operations Research Society of Japan","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15807/JORSJ.60.66","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Decision Sciences","Score":null,"Total":0}
We consider fuzzy sets on a metric, vector, or normed space. It is not assumed that the fuzzy sets have compact supports. In the present paper, a fuzzy distance and a fuzzy norm are proposed in order to measure the difference between two fuzzy sets, and their fundamental properties are investigated. Their definitions are based on Zadeh’s extension principle. Although they are different from the classical ones based on the Hausdorff metric, they are suitable for data containing uncertainty or vagueness. The obtained results can be expected to be useful for analyzing such data when the data are represented as fuzzy sets.
期刊介绍：
The journal publishes original work and quality reviews in the field of operations research and management science to OR practitioners and researchers in two substantive categories: operations research methods; applications and practices of operations research in industry, public sector, and all areas of science and engineering.
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