{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T04:52:32Z","timestamp":1767847952782,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T00:00:00Z","timestamp":1581033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Humanity and Social Science Youth foundation of Ministry of Education","award":["19YJC630022"],"award-info":[{"award-number":["19YJC630022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the development of social media, the social relationships among group decision makers should be taken into consideration when addressing group decision making problems. As an extension of the fuzzy set, the Pythagorean fuzzy set has recently been applied to depict the uncertainty in practical group decision problems. The purpose of this paper is to propose a multi-criteria Pythagorean fuzzy group decision approach considering social relations. In this paper, the similarity degree and the paths between any two experts in a social network are combined to construct a connection strength matrix to detect the leader among all the experts. A leader-following consensus reaching algorithm is proposed to adjust the multi-criteria Pythagorean fuzzy decision making matrix. Moreover, a procedure for the multi-criteria Pythagorean fuzzy group decision approach based on social network analysis is proposed. We use an example to illustrate the feasibility and advantages of the proposed method.<\/jats:p>","DOI":"10.3390\/sym12020255","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T11:50:28Z","timestamp":1581076228000},"page":"255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Multi-Criteria Pythagorean Fuzzy Group Decision Approach Based on Social Network Analysis"],"prefix":"10.3390","volume":"12","author":[{"given":"Yanyan","family":"Wang","sequence":"first","affiliation":[{"name":"School of Economics and Management, Fuzhou University, Fuzhou 350108, China"},{"name":"Yanzhou Coal Mining Company Limited, Zoucheng City 273500, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junfeng","family":"Chu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Fuzhou University, Fuzhou 350108, China"},{"name":"Decision Sciences Institute, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yicong","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Fuzhou University, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1109\/TFUZZ.2013.2278989","article-title":"Pythagorean Membership Grades in Multicriteria Decision Making","volume":"1","author":"Yager","year":"2014","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1002\/int.21676","article-title":"Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets","volume":"1","author":"Zhang","year":"2014","journal-title":"Int. J. Intell. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"529","DOI":"10.3233\/IFS-162165","article-title":"A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem","volume":"1","author":"Garg","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.asoc.2015.12.020","article-title":"Pythagorean fuzzy TODIM approach to multi-criteria decision making","volume":"1","author":"Ren","year":"2016","journal-title":"Appl. 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Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1002\/int.21881","article-title":"A Novel Method for Multiattribute Decision Making with Interval-Valued Pythagorean Fuzzy Linguistic Information","volume":"1","author":"Du","year":"2017","journal-title":"Int. J. Intell. Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1007\/s10588-017-9242-8","article-title":"Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process","volume":"1","author":"Garg","year":"2017","journal-title":"Comput. Math. Organ. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1002\/int.21898","article-title":"A Novel Improved Accuracy Function for Interval Valued Pythagorean Fuzzy Sets and Its Applications in the Decision-Making Process","volume":"1","author":"Garg","year":"2017","journal-title":"Int. J. Intell. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.asoc.2017.06.034","article-title":"The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets","volume":"1","author":"Liang","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1002\/int.21879","article-title":"Projection Model for Fusing the Information of Pythagorean Fuzzy Multicriteria Group Decision Making Based on Geometric Bonferroni Mean","volume":"1","author":"Liang","year":"2017","journal-title":"Int. J. Intell. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1002\/int.21880","article-title":"Pythagorean Fuzzy Information Measures and Their Applications","volume":"1","author":"Peng","year":"2017","journal-title":"Int. J. Intell. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2119","DOI":"10.3233\/JIFS-162030","article-title":"Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making","volume":"1","author":"Wei","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.3233\/JIFS-16715","article-title":"Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making","volume":"1","author":"Wei","year":"2017","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1002\/int.21886","article-title":"Pythagorean Fuzzy Multiattribute Group Decision Making with Probabilistic Information and OWA Approach","volume":"1","author":"Zeng","year":"2017","journal-title":"Int. J. Intell. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1002\/int.21979","article-title":"Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process","volume":"1","author":"Garg","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"901","DOI":"10.3233\/JIFS-171636","article-title":"TODIM method for Pythagorean 2-tuple linguistic multiple attribute decision making","volume":"1","author":"Huang","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1002\/int.21946","article-title":"Pythagorean fuzzy power aggregation operators in multiple attribute decision making","volume":"1","author":"Wei","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1002\/int.21941","article-title":"Pythagorean Fuzzy LINMAP Method Based on the Entropy Theory for Railway Project Investment Decision Making","volume":"1","author":"Xue","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1002\/int.21953","article-title":"A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making","volume":"1","author":"Zeng","year":"2018","journal-title":"Int. J. Intell. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1002\/int.21686","article-title":"Social Network Decision Making with Linguistic Trustworthiness-Based Induced OWA Operators","volume":"1","author":"Perez","year":"2014","journal-title":"Int. J. Intell. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wasserman, S., and Faust, K. (1994). Social Network Analysis: Methods and Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511815478"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.knosys.2017.01.031","article-title":"A visual interaction consensus model for social network group decision making with trust propagation","volume":"1","author":"Wu","year":"2017","journal-title":"Knowl. -Based Syst."},{"key":"ref_25","first-page":"644","article-title":"A consensus support system model for group decision-making problems with multigranular linguistic preference relations","volume":"1","author":"Martinez","year":"2005","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.fss.2012.03.016","article-title":"A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures","volume":"1","author":"Wu","year":"2012","journal-title":"Fuzzy Sets Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/255\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:55:40Z","timestamp":1760172940000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/2\/255"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,7]]},"references-count":26,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["sym12020255"],"URL":"https:\/\/doi.org\/10.3390\/sym12020255","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,7]]}}}