{"title":"Fuzzifying pseudo-metric topologies on the fuzzy real line","authors":"F. Shi̇","doi":"10.15672/hujms.1209995","DOIUrl":null,"url":null,"abstract":"In this paper, three natural fuzzifying topologies are presented on the fuzzy real line. Then the notion of fuzzifying pseudo-quasi-metrics is introduced. It is proved that the three fuzzifying topologies can be induced respectively by three fuzzifying pseudo-quasi-metrics. Our definition of fuzzifying pseudo-metric is slightly different from that of KM-fuzzy metric. A fuzzifying pseudo-metrics can be regarded as a weak form of a KM fuzzy metric.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"11 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1209995","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, three natural fuzzifying topologies are presented on the fuzzy real line. Then the notion of fuzzifying pseudo-quasi-metrics is introduced. It is proved that the three fuzzifying topologies can be induced respectively by three fuzzifying pseudo-quasi-metrics. Our definition of fuzzifying pseudo-metric is slightly different from that of KM-fuzzy metric. A fuzzifying pseudo-metrics can be regarded as a weak form of a KM fuzzy metric.
期刊介绍：
Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics.
We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.
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