{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T11:46:30Z","timestamp":1769773590881,"version":"3.49.0"},"reference-count":27,"publisher":"SAGE Publications","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,11,4]]},"abstract":"<jats:p>Algebraic and Einstein are two different types of norms which are the special cases of the Hamacher norm. These norms are used for evaluating or constructing three different types of aggregation operators, such as averaging\/geometric, Einstein averaging\/geometric, and Hamacher averaging\/geometric aggregation operators. Moreover, complex Atanassov intuitionistic fuzzy (CA-IF) information is a very famous and dominant technique or tool which is used for depicting unreliable and awkward information. In this manuscript, we present the Hamacher operational laws for CA-IF values. Furthermore, we derive the power aggregation operators (PAOs) for CA-IF values, called CA-IF power Hamacher averaging (CA-IFPHA), CA-IF power Hamacher ordered averaging (CA-IFPHOA), CA-IF power Hamacher geometric (CA-IFPHG), and CA-IF power Hamacher ordered geometric (CA-IFPHOG) operators. Some dominant and valuable properties are also stated. Moreover, the multi-attribute decision-making (MADM) methods are developed based on the invented operators for CA-IF information and the detailed decision steps are given. Many prevailing operators are selected as special cases of the invented theory. Finally, the derived technique will offer many choices to the expert to evaluate the best alternatives during comparative analysis.<\/jats:p>","DOI":"10.3233\/jifs-230323","type":"journal-article","created":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T11:41:47Z","timestamp":1695382907000},"page":"8383-8403","source":"Crossref","is-referenced-by-count":2,"title":["Power aggregation operators based on hamacher t-norm and t-conorm for complex intuitionistic fuzzy information and their application in decision-making problems"],"prefix":"10.1177","volume":"45","author":[{"given":"Hao","family":"Dong","sequence":"first","affiliation":[{"name":"School of Business Administration, Shandong Women\u2019s University, Shandong, Jinan, China"}]},{"given":"Zeeshan","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan"}]},{"given":"Tahir","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan"}]},{"given":"Peide","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Business Administration, Shandong Women\u2019s University, Shandong, Jinan, China"},{"name":"Shandong Key Laboratory of New Smart Media, Jinan Shandong, China"}]}],"member":"179","reference":[{"issue":"3","key":"10.3233\/JIFS-230323_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"},{"issue":"1","key":"10.3233\/JIFS-230323_ref2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy sets and systems"},{"issue":"2","key":"10.3233\/JIFS-230323_ref3","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1109\/91.995119","article-title":"Complex fuzzy sets","volume":"10","author":"Ramot","year":"2002","journal-title":"IEEE Transactions on Fuzzy Systems"},{"issue":"18","key":"10.3233\/JIFS-230323_ref5","doi-asserted-by":"crossref","first-page":"9011","DOI":"10.1007\/s00500-022-07254-x","article-title":"Fuzzy superior mandelbrot sets","volume":"26","author":"Mahmood","year":"2022","journal-title":"Soft Computing"},{"issue":"12","key":"10.3233\/JIFS-230323_ref6","doi-asserted-by":"crossref","first-page":"715","DOI":"10.3390\/axioms11120715","article-title":"TOPSIS method based on hamacher choquet-integral aggregation operators for atanassov-intuitionistic fuzzy sets and their applications in decision-making","volume":"11","author":"Mahmood","year":"2022","journal-title":"Axioms"},{"key":"10.3233\/JIFS-230323_ref7","doi-asserted-by":"crossref","first-page":"116242","DOI":"10.1016\/j.eswa.2021.116242","article-title":"Choquet integral-based intuitionistic fuzzy arithmetic aggregation operators in multi-criteria decision-making.","volume":"191","author":"Jia","year":"2022","journal-title":"Expert Systems with Applications"},{"issue":"3","key":"10.3233\/JIFS-230323_ref8","doi-asserted-by":"crossref","first-page":"3351","DOI":"10.3233\/JIFS-191718","article-title":"The distance measures and cross-entropy based on complex fuzzy sets and their application in decision making","volume":"39","author":"Liu","year":"2020","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"10","key":"10.3233\/JIFS-230323_ref9","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1002\/int.22127","article-title":"Some results on information measures for complex intuitionistic fuzzy sets","volume":"34","author":"Garg","year":"2019","journal-title":"International Journal of Intelligent Systems"},{"issue":"16","key":"10.3233\/JIFS-230323_ref10","doi-asserted-by":"crossref","first-page":"1922","DOI":"10.3390\/math9161922","article-title":"Another view of complex intuitionistic fuzzy soft sets based on prioritized aggregation operators and their applications to multiattribute decision making","volume":"9","author":"Ali","year":"2021","journal-title":"Mathematics"},{"issue":"1","key":"10.3233\/JIFS-230323_ref11","doi-asserted-by":"crossref","first-page":"33","DOI":"10.18576\/isl\/090105","article-title":"Needs and importance of reliability prediction: An industrial perspective","volume":"9","author":"Sahu","year":"2020","journal-title":"Information Sciences Letters"},{"key":"10.3233\/JIFS-230323_ref12","doi-asserted-by":"crossref","unstructured":"Attaallah A. , Alsuhabi H. , Shukla S. , Kumar R. , Gupta B.K. and Khan R.A. , Analyzing the big data security through a unified decision-making approach. 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