{"title":"Fuzzy rough sets in Šostak sense","authors":"Ismail Ibedou, S. E. Abbas","doi":"10.1007/s11766-022-4100-y","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we defined the fuzzy operator Φ<sub>λ</sub> in a fuzzy ideal approximation space (<i>X, R</i>, <span>\\({\\cal I}\\)</span>) associated with a fuzzy rough set λ in <i>Š</i>ostak sense. Associated with Φ<sub>λ</sub>, there are fuzzy ideal interior and closure operators int<span>\n <sup>λ</sup><sub>Φ</sub>\n \n </span> and cl<span>\n <sup>λ</sup><sub>Φ</sub>\n \n </span>, respectively. <i>r</i>-fuzzy separation axioms, <i>r</i>-fuzzy connectedness and <i>r</i>-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in <i>r</i>-fuzzy approximation spaces. There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces. Lastly, using a fuzzy grill, we will get the same results given during the context.</p></div>","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":"37 4","pages":"563 - 582"},"PeriodicalIF":1.0000,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-022-4100-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we defined the fuzzy operator Φλ in a fuzzy ideal approximation space (X, R, \({\cal I}\)) associated with a fuzzy rough set λ in Šostak sense. Associated with Φλ, there are fuzzy ideal interior and closure operators intλΦ and clλΦ, respectively. r-fuzzy separation axioms, r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces. There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces. Lastly, using a fuzzy grill, we will get the same results given during the context.
期刊介绍：
Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects.
The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry.
Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.
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