{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T18:35:46Z","timestamp":1770748546451,"version":"3.50.0"},"reference-count":42,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2015,7,29]],"date-time":"2015-07-29T00:00:00Z","timestamp":1438128000000},"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":[[2015,7,29]]},"abstract":"<jats:p>On the basis of Frank operators, the operational rules of intuitionistic fuzzy numbers are redefined, then the intuitionistic fuzzy Frank power average operator (IFFPA), intuitionistic fuzzy Frank power weighted average operator (IFFPWA) and intuitionistic fuzzy Frank power ordered weighted average operator (IFFPOWA) are proposed by combining Frank operations and power aggregation operators. At the same time, some desirable properties of these operators, such as idempotency, commutativity and boundedness, are studied, and some special cases are analyzed. Furthermore, with respect to multiple attribute group decision making (MAGDM) problems in which attribute values take the form of the intuitionistic fuzzy numbers, two group decision making methods based on IFFPWA and IFFPOWA operators are developed. Finally, an illustrative example is given to verify the proposed methods and to demonstrate their practicality and effectiveness.<\/jats:p>","DOI":"10.3233\/ifs-151699","type":"journal-article","created":{"date-parts":[[2015,11,10]],"date-time":"2015-11-10T11:37:42Z","timestamp":1447155462000},"page":"2235-2246","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":80,"title":["Multiple attribute group decision making methods based on intuitionisticfuzzy frank power aggregation operators"],"prefix":"10.1177","volume":"29","author":[{"given":"Xin","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering,\rShandong University of Finance and Economics, Jinan, China"}]},{"given":"Peide","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering,\rShandong University of Finance and Economics, Jinan, China"}]},{"given":"Yumei","family":"Wang","sequence":"additional","affiliation":[{"name":"Dongfang College, Shandong University of Finance and Economics, Jinan, China"}]}],"member":"179","published-online":{"date-parts":[[2015,9,9]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90215-7"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90331-X"},{"key":"e_1_3_2_5_2","doi-asserted-by":"crossref","unstructured":"Atanassov KT 1999 Intuitionistic Fuzzy Sets Springer Heidelberg","DOI":"10.1007\/978-3-7908-1870-3"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90205-4"},{"key":"e_1_3_2_7_2","unstructured":"Beliakov G Pradera A Calvo T 2007 Aggregation Functions: A Guide for Practitioners Springer Heidelberg Berlin New York"},{"key":"e_1_3_2_8_2","first-page":"867","article-title":"A fuzzy number interval arithmetic based fuzzy MCDM algorithm","volume":"4","author":"Chu TC","year":"2002","unstructured":"Chu TC 2002 A fuzzy number interval arithmetic based fuzzy MCDM algorithm International Journal of Fuzzy Systems 4 867 872","journal-title":"International Journal of Fuzzy Systems"},{"key":"e_1_3_2_9_2","first-page":"19","article-title":"A generalization of operators on intuitionistic fuzzy sets using triangular norms and conforms","volume":"8","author":"Deschrijver G","year":"2002","unstructured":"Deschrijver G, Kerre EE 2002 A generalization of operators on intuitionistic fuzzy sets using triangular norms and conforms Notes on Intuition Fuzzy Sets 8 19 27","journal-title":"Notes on Intuition Fuzzy Sets"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.4550080303"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02189866"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.11.088"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2013.2248736"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.04.014"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1080\/18756891.2013.862357"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.12.133"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141142"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2013.12.010"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2013.12.009"},{"key":"e_1_3_2_20_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/923213","article-title":"Frank aggregation operators for triangular interval type-2 fuzzy set and its application to multiple attribute group decision making","volume":"2014","author":"Qin JD","year":"2014","unstructured":"Qin JD, Liu XW 2014 Frank aggregation operators for triangular interval type-2 fuzzy set and its application to multiple attribute group decision making Journal of Applied Mathematics 2014 1 24","journal-title":"Journal of Applied Mathematics"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.microrel.2006.01.007"},{"key":"e_1_3_2_22_2","first-page":"773","article-title":"Method of intuitionistic trapezoidal fuzzy number for multi-attribute group decision","volume":"25","author":"Wan SP","year":"2010","unstructured":"Wan SP, Dong JY 2010 Method of intuitionistic trapezoidal fuzzy number for multi-attribute group decision Control and Decision 25 773 776","journal-title":"Control and Decision"},{"key":"e_1_3_2_23_2","first-page":"1253","article-title":"Multi-criteria interval intuitionistic fuzzy decision-making approach with incomplete certain information","volume":"21","author":"Wang JQ","year":"2006","unstructured":"Wang JQ 2006 Multi-criteria interval intuitionistic fuzzy decision-making approach with incomplete certain information Control and Decision 21 1253 1256 1263","journal-title":"Control and Decision"},{"key":"e_1_3_2_24_2","first-page":"601","article-title":"Overview on fuzzy multi-criteria decision-making approach","volume":"23","author":"Wang JQ","year":"2008","unstructured":"Wang JQ 2008 Overview on fuzzy multi-criteria decision-making approach Control and Decision 23 601 606","journal-title":"Control and Decision"},{"key":"e_1_3_2_25_2","first-page":"8","article-title":"The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics","volume":"3","author":"Wang JQ","year":"2009","unstructured":"Wang JQ, Li JJ 2009 The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics Science & Technology Information 3 8 9","journal-title":"Science & Technology Information"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.130"},{"issue":"5","key":"e_1_3_2_27_2","first-page":"1141","article-title":"Research on flexible probability logic operator based on frank T\/S norms","volume":"37","author":"Wang WS","year":"2009","unstructured":"Wang WS, He HC 2009 Research on flexible probability logic operator based on frank T\/S norms Chinese Journal of Electronics 37 5 1141 1145","journal-title":"Chinese Journal of Electronics"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2009.08.009"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2012.02.004"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2011.12.002"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488507004686"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2006.890678"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2010.04.010"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081070600574353"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2009.2036907"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.1109\/21.87068"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.1109\/3468.983429"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21538"},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_41_2","doi-asserted-by":"publisher","DOI":"10.3846\/tede.2010.18"},{"key":"e_1_3_2_42_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.20386"},{"key":"e_1_3_2_43_2","doi-asserted-by":"publisher","DOI":"10.2298\/CSIS130109046S"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151699","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/IFS-151699","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151699","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T08:24:44Z","timestamp":1770711884000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-151699"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,29]]},"references-count":42,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,7,29]]}},"alternative-id":["10.3233\/IFS-151699"],"URL":"https:\/\/doi.org\/10.3233\/ifs-151699","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,29]]}}}