{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T15:39:10Z","timestamp":1769701150296,"version":"3.49.0"},"reference-count":36,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,7,2]]},"abstract":"<jats:p>\u00a0Both fuzzy set and rough set are important mathematical tools to describe incomplete and uncertain information, and they are highly complementary to each other. What is more, most fuzzy rough sets are obtained by combining Zadeh fuzzy sets and Pawlak rough sets. There are few reports about the combination of axiomatic fuzzy sets and Pawlak rough sets. For this reason, we propose the axiomatic fuzzy rough sets (namely rough set model with respect to the axiomatic fuzzy set) establishing on fuzzy membership space. In this paper, we first present a similarity description method based on vague partitions. Then the concept of similarity operator is proposed to describe uncertainty in the fuzzy approximation space. Finally, some characterizations concerning upper and lower approximation operators are shown, including basic properties. Furthermore, we give a algorithm to verify the effectiveness and efficiency of the model.<\/jats:p>","DOI":"10.3233\/jifs-223643","type":"journal-article","created":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T16:57:44Z","timestamp":1683651464000},"page":"1423-1436","source":"Crossref","is-referenced-by-count":3,"title":["Rough set model based on axiomatic fuzzy set"],"prefix":"10.1177","volume":"45","author":[{"given":"Siyu","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, PR, China"}]},{"given":"Keyun","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, PR, China"}]},{"given":"Xiaodong","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, PR, China"}]},{"given":"Chao","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southwest Jiaotong University, Chengdu, PR, China"}]}],"member":"179","reference":[{"issue":"3","key":"10.3233\/JIFS-223643_ref1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Information and Control"},{"key":"10.3233\/JIFS-223643_ref2","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/j.ins.2020.08.076","article-title":"Interval type-2 fuzzy setsimproved by simulated annealing for locating the electric chargingstations","volume":"547","author":"Trk","year":"2021","journal-title":"Information Sciences"},{"issue":"1","key":"10.3233\/JIFS-223643_ref3","doi-asserted-by":"crossref","first-page":"122","DOI":"10.12677\/ORF.2021.111015","article-title":"Pattern recognition method of Euclidean closeness based on type 2 intuitionistic fuzzy sets","volume":"11","author":"Yin","year":"2021","journal-title":"Operations Research and Fuzziness"},{"issue":"4","key":"10.3233\/JIFS-223643_ref4","first-page":"406","article-title":"Type-2 fuzzy set based rough fuzzyc-means clustering algorithm","volume":"35","author":"Bao","year":"2020","journal-title":"Journal of Chengdu University ofInformation Technology"},{"issue":"2","key":"10.3233\/JIFS-223643_ref5","first-page":"292","article-title":"Technology innovation risk evaluation based on interval value intuitionistic fuzzy sets","volume":"26","author":"Tian","year":"2020","journal-title":"Journal of Shanghai University (Natural Science Edition)"},{"issue":"6","key":"10.3233\/JIFS-223643_ref6","doi-asserted-by":"crossref","first-page":"1777","DOI":"10.1007\/s00500-017-2855-5","article-title":"Redefinition of the concept of fuzzy set basedon vague partition from the perspective of axiomatization","volume":"22","author":"Pan","year":"2018","journal-title":"Soft Computing"},{"issue":"6","key":"10.3233\/JIFS-223643_ref7","doi-asserted-by":"crossref","first-page":"2079","DOI":"10.1007\/s00500-018-3061-9","article-title":"Correction to: redefinition of the concept offuzzy set based on vague partition from the perspective ofaxiomatization","volume":"22","author":"Pan","year":"2018","journal-title":"Soft Computing"},{"issue":"5","key":"10.3233\/JIFS-223643_ref8","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough set","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int. 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