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The aim of the present work is to develop the concept of complex interval\u2010valued q\u2010rung orthopair fuzzy set (CIVq\u2010ROFS) as a generalization of interval\u2010valued complex fuzzy set (IVCFS) and q\u2010rung orthopair fuzzy set (q\u2010ROFS), which can better express the time\u2010periodic problems and two\u2010dimensional information in a single set. In this article not only basic properties of CIVq\u2010ROFSs are discussed but also averaging aggregation operator (AAO) and geometric aggregation operator (GAO) with some desirable properties and operations on CIVq\u2010ROFSs are discussed. The proposed operations are the extension of the operations of IVq\u2010ROFS, q\u2010ROFS, interval\u2010valued Pythagorean fuzzy, Pythagorean fuzzy (PF), interval\u2010valued intuitionistic fuzzy, intuitionistic fuzzy, complex q\u2010ROFS, complex PF, and complex intuitionistic fuzzy theories. Further, the Analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) method are also examine based on CIVq\u2010ROFS to explore the reliability and proficiency of the work. Moreover, we discussed the advantages of CIVq\u2010ROFS and showed that the concepts of IVCFS and q\u2010ROFS are the special cases of CIVq\u2010ROFS. Moreover, the flexibility of proposed averaging aggregation operator and geometric aggregation operator in a multi\u2010attribute decision making (MADM) problem are also discussed. Finally, a comparative study of CIVq\u2010ROFSs with pre\u2010existing work is discussed in detail.<\/jats:p>","DOI":"10.1111\/exsy.12609","type":"journal-article","created":{"date-parts":[[2020,9,2]],"date-time":"2020-09-02T18:46:25Z","timestamp":1599072385000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":71,"title":["Algorithms for complex interval\u2010valued q\u2010rung orthopair fuzzy sets in decision making based on aggregation operators, <scp>AHP,<\/scp> and <scp>TOPSIS<\/scp>"],"prefix":"10.1111","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9099-8422","authenticated-orcid":false,"given":"Harish","family":"Garg","sequence":"first","affiliation":[{"name":"School of Mathematics, Thapar Institute of Engineering &amp; Technology Deemed University  Patiala Punjab India"}]},{"given":"Zeeshan","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics International Islamic University Islamabad  Islamabad Pakistan"}]},{"given":"Tahir","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics International Islamic University Islamabad  Islamabad Pakistan"}]}],"member":"311","published-online":{"date-parts":[[2020,8,27]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.4757515"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90205-4"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-33190-5_29"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2016.05.041"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00127-9"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(01)00110-6"},{"key":"e_1_2_10_9_1","unstructured":"Draeseke R. &Giles D. 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