{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:25:39Z","timestamp":1777703139032,"version":"3.51.4"},"reference-count":40,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T00:00:00Z","timestamp":1557360000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2019,6,11]]},"abstract":"<jats:p>\u00a0Pythagorean cubic fuzzy set, is an extension of the interval valued Pythagorean fuzzy set which relax the condition of the square sum of its membership and non-membership degree is less than or equal to one to supremum square sum of its membership and non-membership functions is less than one. Based on this information and by combining the idea of the confidence levels of each Pythagorean cubic fuzzy number, the proposed study investigated a new averaging and geometric operators, namely confidence Pythagorean cubic fuzzy weighted and geometric operators along with their order are presented. Some of their desired properties related to the new defined operators have been investigated. Under the given information, a multi criteria decision making process has been proposed with a numerical example for showing the effectiveness and validity of it.<\/jats:p>","DOI":"10.3233\/jifs-181516","type":"journal-article","created":{"date-parts":[[2019,5,10]],"date-time":"2019-05-10T10:43:02Z","timestamp":1557484982000},"page":"5669-5683","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":16,"title":["Pythagorean cubic fuzzy aggregation information based on confidence levels and its application to multi-criteria decision making process"],"prefix":"10.1177","volume":"36","author":[{"given":"Faisal","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hazara University Mansehra, KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saleem","family":"Abdullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University Mardan, KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tariq","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Electronics Engineering, University of Engineering and Technology Taxila Sub Campus, Chakwal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Shakeel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University Mansehra, KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Rahim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University Mansehra, KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noor","family":"ul Amin","sequence":"additional","affiliation":[{"name":"Department of Information Technology, Hazara University, Mansehra, KP, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,5,9]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-016-0538-7"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-015-0081-9"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2016.08.017"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-015-0432-8"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21860"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2015.10.040"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21809"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-162165"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21827"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1186\/s40064-016-2591-9"},{"key":"e_1_3_1_13_2","first-page":"13","article-title":"Entropy based multi-criteria decision making method under fuzzy environment and unknown attribute weights","volume":"6","author":"Garg H.","year":"2015","unstructured":"H.Garg N.Agarwal and A.Tripathi, Entropy based multi-criteria decision making method under fuzzy environment and unknown attribute weights, Glob J Technol Optim 6 (2015), 13\u201320.","journal-title":"Glob J Technol Optim"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1615\/Int.J.UncertaintyQuantification.2016018441"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1615\/Int.J.UncertaintyQuantification.2016018603"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10588-017-9242-8"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2015.03.003"},{"key":"e_1_3_1_18_2","author":"Khan F.","year":"2018","unstructured":"F.Khan, M.S.A.Khan, M.Shehzad and S.Abdullah, Pythagorean cubic fuzzy aggregation operators and their application to multi-criteria decision making problems, (2018). 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