{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T01:50:29Z","timestamp":1787017829870,"version":"build-2736575974"},"reference-count":48,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,11,29]],"date-time":"2020-11-29T00:00:00Z","timestamp":1606608000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Yulin University-Industry","award":["2019-75-2"],"award-info":[{"award-number":["2019-75-2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,11,29]]},"abstract":"<jats:p>\n                    As a generalization of Zhan\u2019s method (i.e., to increase the lower approximation and decrease the upper approximation), the present paper aims to define the family of complementary fuzzy\n                    <jats:inline-formula>\n                      <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\">\n                        <a:mi>\u03b2<\/a:mi>\n                      <\/a:math>\n                    <\/jats:inline-formula>\n                    -neighborhoods and thus three kinds of covering-based multigranulation (\n                    <jats:inline-formula>\n                      <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\">\n                        <c:mi mathvariant=\"normal\">\u2110<\/c:mi>\n                        <c:mo>,<\/c:mo>\n                        <c:mi mathvariant=\"script\">T<\/c:mi>\n                      <\/c:math>\n                    <\/jats:inline-formula>\n                    )-fuzzy rough sets models are established. Their axiomatic properties are investigated. Also, six kinds of covering-based variable precision multigranulation (\n                    <jats:inline-formula>\n                      <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\">\n                        <g:mi mathvariant=\"normal\">\u2110<\/g:mi>\n                        <g:mo>,<\/g:mo>\n                        <g:mi mathvariant=\"script\">T<\/g:mi>\n                      <\/g:math>\n                    <\/jats:inline-formula>\n                    )-fuzzy rough sets are defined and some of their properties are studied. Furthermore, the relationships among our given types are discussed. Finally, a decision-making algorithm is presented based on the proposed operations and illustrates with a numerical example to describe its performance.\n                  <\/jats:p>","DOI":"10.1155\/2020\/6661782","type":"journal-article","created":{"date-parts":[[2020,11,29]],"date-time":"2020-11-29T21:48:25Z","timestamp":1606686505000},"page":"1-20","source":"Crossref","is-referenced-by-count":15,"title":["Certain Types of Covering-Based Multigranulation (\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                      <a:mi mathvariant=\"normal\">\u2110<\/a:mi>\n                      <a:mo>,<\/a:mo>\n                      <a:mi mathvariant=\"script\">T<\/a:mi>\n                    <\/a:math>\n                    )-Fuzzy Rough Sets with Application to Decision-Making"],"prefix":"10.1155","volume":"2020","author":[{"given":"Jue","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Yulin University, Yulin 719000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9439-3404","authenticated-orcid":true,"given":"Mohammed","family":"Atef","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia 32511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shokry","family":"Nada","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia 32511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ashraf","family":"Nawar","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia 32511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"1","first-page":"375","article-title":"Fuzzy multiple attribute decision making: methods and applications","volume-title":"Lecture Notes in Economics and Mathematical Systems","author":"S. 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