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Syst."],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Pythagorean fuzzy sets (briefly, PFSs) were created as an upgrade to intuitionistic fuzzy sets (briefly, IFSs) which helped to address some problems that IFSs couldn\u2019t solve. The definition of q-rung orthopair fuzzy sets (briefly, q-ROFS) is then declared to generalize and solve PFS and IFS failures. Using the concept of PF <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-neighborhood, Zhan et al. defined the description of the covering through the Pythagorean fuzzy rough set (briefly, CPFRS). Hussain et al. also developed the concept of q-ROF <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-neighborhood to build the concept of covering through q-rung orthopair fuzzy rough sets (Cq-ROFRS). To enhance the results in Zhan et al.\u2019s and Hussain et al.\u2019s method and in a related context, the concept of PF complementary <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-neighborhood is constructed. Hence, using PF <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-neighborhood and PF complementary <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-neighborhood, three novel kinds of CPFRS are investigated and the related characteristics are analyzed. The interrelationships between Zhan et al.\u2019s approach and our approaches are also discussed. Besides, the concept of q-ROF complementary <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-neighborhood is examined. Three new Cq-ROFRS models are differentiated using the principles of q-ROF <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-neighborhood and q-ROF complementary <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-neighborhood. As a result, the related properties and relationships between these various models and Hussain et al.\u2019s model are established. Because of these correlations, we may consider our approach to be a generalization of Zhan et al.\u2019s and Hussain et al\u2019s approaches. Finally, we developed applications to solve MADM problems using CPFRS and Cq-ROFRS, as well as variances of the two methods using numerical examples are presented.<\/jats:p>","DOI":"10.1007\/s40747-021-00622-4","type":"journal-article","created":{"date-parts":[[2022,2,2]],"date-time":"2022-02-02T03:02:41Z","timestamp":1643770961000},"page":"2349-2370","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Cq-ROFRS: covering q-rung orthopair fuzzy rough sets and its application to multi-attribute decision-making process"],"prefix":"10.1007","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9099-8422","authenticated-orcid":false,"given":"Harish","family":"Garg","sequence":"first","affiliation":[]},{"given":"Mohammed","family":"Atef","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,2]]},"reference":[{"issue":"5","key":"622_CR1","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/BF01001956","volume":"11","author":"Z Pawlak","year":"1982","unstructured":"Pawlak Z (1982) Rough sets. 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