{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T03:41:54Z","timestamp":1777520514379,"version":"3.51.4"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"17","license":[{"start":{"date-parts":[[2018,7,31]],"date-time":"2018-07-31T00:00:00Z","timestamp":1532995200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s00500-018-3416-2","type":"journal-article","created":{"date-parts":[[2018,7,31]],"date-time":"2018-07-31T04:41:02Z","timestamp":1533012062000},"page":"7843-7852","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Intuitionistic fuzzy inverse 1-median location problem on tree networks with value at risk objective"],"prefix":"10.1007","volume":"23","author":[{"given":"Akram","family":"Soltanpour","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fahimeh","family":"Baroughi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Behrooz","family":"Alizadeh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,7,31]]},"reference":[{"key":"3416_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"KT Atanassov","year":"1986","unstructured":"Atanassov KT (1986) Intutionistic fuzzy sets. Fuzzy Sets Syst 20:87\u201396","journal-title":"Fuzzy Sets Syst"},{"key":"3416_CR2","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/s00186-011-0346-5","volume":"73","author":"F Baroughi","year":"2011","unstructured":"Baroughi F, Burkard RE, Gassner E (2011) Inverse \n                              $$p$$\n                              \n                                 \n                                 \n                                    p\n                                 \n                              \n                              \n                           -median problems with variable edge lengths. Math Methods Oper Res 73:263\u2013280","journal-title":"Math Methods Oper Res"},{"key":"3416_CR3","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/j.disopt.2004.03.003","volume":"1","author":"RE Burkard","year":"2004","unstructured":"Burkard RE, Pleschiutschnig C, Zhan J (2004) Inverse median problems. Discrete Optim 1:23\u201339","journal-title":"Discrete Optim"},{"key":"3416_CR4","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1016\/j.disopt.2006.11.008","volume":"5","author":"RE Burkard","year":"2008","unstructured":"Burkard RE, Pleschiutschnig C, Zhan J (2008) The inverse 1-median problem on a cycle. Discrete Optim 5:242\u2013253","journal-title":"Discrete Optim"},{"issue":"6","key":"3416_CR5","doi-asserted-by":"publisher","first-page":"1116","DOI":"10.1016\/j.ins.2010.11.024","volume":"181","author":"G Beliakov","year":"2011","unstructured":"Beliakov G, Bustince H, Goswami DP et al (2011) On averaging operators for Atanassov\u2019s intuitionistic fuzzy sets. Inf Sci 181(6):1116\u20131124","journal-title":"Inf Sci"},{"key":"3416_CR6","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/S0377-2217(98)00330-0","volume":"116","author":"MJ Canos","year":"1999","unstructured":"Canos MJ, Ivorra C, Liern V (1999) An exact algorithm for the fuzzy \n                              $$p$$\n                              \n                                 \n                                 \n                                    p\n                                 \n                              \n                              \n                           -median problem. Eur J Oper Res 116:80\u201386","journal-title":"Eur J Oper Res"},{"key":"3416_CR7","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1016\/S0377-2217(99)00500-7","volume":"130","author":"MJ Canos","year":"2001","unstructured":"Canos MJ, Ivorra C, Liern V (2001) The fuzzy \n                              $$p$$\n                              \n                                 \n                                 \n                                    p\n                                 \n                              \n                              \n                           -median problem: a global analysis of the solutions. Eur J Oper Res 130:430\u2013436","journal-title":"Eur J Oper Res"},{"key":"3416_CR8","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/j.ejor.2007.08.011","volume":"191","author":"MJ Canos","year":"2008","unstructured":"Canos MJ, Ivorra C, Liern V (2008) Marginal analysis for the fuzzy \n                              $$p$$\n                              \n                                 \n                                 \n                                    p\n                                 \n                              \n                              \n                           -median problem. Eur J Oper Res 191:264\u2013271","journal-title":"Eur J Oper Res"},{"issue":"3","key":"3416_CR9","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1016\/S0165-0114(98)00191-2","volume":"114","author":"SK De","year":"2000","unstructured":"De SK, Biswas R, Roy AR (2000) Some operations on intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):477\u2013484","journal-title":"Fuzzy Sets Syst"},{"key":"3416_CR10","doi-asserted-by":"publisher","first-page":"1219","DOI":"10.1007\/s00170-012-4400-0","volume":"66","author":"K Devi","year":"2013","unstructured":"Devi K, Yadav SP (2013) A multicriteria intuitionistic fuzzy group decision making for plant location selection with ELECTRE method. Int J Adv Manuf Technol 66:1219\u20131229","journal-title":"Int J Adv Manuf Technol"},{"key":"3416_CR11","first-page":"3447","volume":"4","author":"AN Gani","year":"2010","unstructured":"Gani AN, Jabarulla MM (2010) On searching intuitionistic fuzzy shortest path in a network. Appl Math Sci 4:3447\u20133454","journal-title":"Appl Math Sci"},{"key":"3416_CR12","doi-asserted-by":"publisher","first-page":"1241","DOI":"10.1016\/j.endm.2010.05.157","volume":"36","author":"M Galavii","year":"2010","unstructured":"Galavii M (2010) The inverse 1-median problem on a tree and on a path. Electron Notes Disrete Math 36:1241\u20131248","journal-title":"Electron Notes Disrete Math"},{"key":"3416_CR13","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s10898-011-9742-x","volume":"54","author":"X Guan","year":"2012","unstructured":"Guan X, Zhang B (2012) Inverse 1-median problem on trees under weighted Hamming distance. J Glob Optim 54:75\u201382","journal-title":"J Glob Optim"},{"key":"3416_CR14","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1287\/trsc.5.2.212","volume":"5","author":"AJ Goldman","year":"1971","unstructured":"Goldman AJ (1971) Optimal center location in simple networks. Transp Sci 5:212\u2013221","journal-title":"Transp Sci"},{"key":"3416_CR15","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/978-3-642-14355-7_16","volume":"6124","author":"X Guan","year":"2010","unstructured":"Guan X, Zhang B (2010) Inverse 1-median problem on trees under weighted \n                              $$ {l}_{\\infty }$$\n                              \n                                 \n                                 \n                                    \n                                       l\n                                       \u221e\n                                    \n                                 \n                              \n                              \n                            norm. Lect Notes Comput Sci 6124:150\u2013160","journal-title":"Lect Notes Comput Sci"},{"key":"3416_CR16","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/j.disopt.2012.05.001","volume":"9","author":"J Hatzl","year":"2012","unstructured":"Hatzl J (2012) 2-Balanced flows and the inverse 1-median problem in the Chebyshev space. Discrete Optim 9:137\u2013148","journal-title":"Discrete Optim"},{"key":"3416_CR17","first-page":"1","volume":"1860","author":"T Kumar","year":"2017","unstructured":"Kumar T, Bajaj RK, Kaushik R (2017) Expected value based ranking of intuitionistic fuzzy variables. AIP Conf Proc 1860:1\u201312","journal-title":"AIP Conf Proc"},{"key":"3416_CR18","first-page":"97","volume":"12","author":"D Kutangila-Mayoya","year":"2005","unstructured":"Kutangila-Mayoya D, Verdegay JL (2005) \n                              $$p$$\n                              \n                                 \n                                 \n                                    p\n                                 \n                              \n                              \n                           -median problems in a fuzzy environment. Mathw Soft Comput 12:97\u2013106","journal-title":"Mathw Soft Comput"},{"key":"3416_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-39987-2","volume-title":"Uncertainty theory: an introduction to its axiomatic foundations","author":"B Liu","year":"2004","unstructured":"Liu B (2004) Uncertainty theory: an introduction to its axiomatic foundations. Springer, Berlin"},{"key":"3416_CR20","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1016\/S0165-0114(03)00091-5","volume":"142","author":"Moreno Perez. J. A","year":"2004","unstructured":"Perez. J. A Moreno, Marcos Moreno Vega J, Verdegay JL (2004) Fuzzy location problems on networks. Fuzzy Sets Syst 142:393\u2013405","journal-title":"Fuzzy Sets Syst"},{"key":"3416_CR21","doi-asserted-by":"publisher","first-page":"944","DOI":"10.1007\/s10957-015-0829-2","volume":"168","author":"KT Nguyen","year":"2016","unstructured":"Nguyen KT (2016) Inverse 1-median problem on block graphs with variable vertex weights. J Optim Theory Appl 168:944\u2013957","journal-title":"J Optim Theory Appl"},{"key":"3416_CR22","doi-asserted-by":"publisher","first-page":"513","DOI":"10.7494\/OpMath.2016.36.4.513","volume":"36","author":"KT Nguyen","year":"2016","unstructured":"Nguyen KT, Chi NTL (2016) A model for the inverse 1-median problem on trees under uncertain costs. Opusc Math 36:513\u2013523","journal-title":"Opusc Math"},{"key":"3416_CR23","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s12543-011-0067-8","volume":"3","author":"J Peng","year":"2011","unstructured":"Peng J (2011) Credibilistic value and average value at risk in fuzzy risk analysis. Fuzzy Inf Eng 3:69\u201379","journal-title":"Fuzzy Inf Eng"},{"key":"3416_CR24","doi-asserted-by":"publisher","first-page":"9033","DOI":"10.1016\/j.eswa.2015.07.065","volume":"42","author":"Z Pei","year":"2015","unstructured":"Pei Z (2015) Intuitionistic fuzzy variables: concepts and applications in decision making. Expert Syst Appl 42:9033\u20139045","journal-title":"Expert Syst Appl"},{"key":"3416_CR25","first-page":"595","volume":"64","author":"AR Sepasian","year":"2015","unstructured":"Sepasian AR, Rahbarnia F (2015) An \n                              $$O(n \\log n)$$\n                              \n                                 \n                                 \n                                    \n                                       O\n                                       (\n                                       n\n                                       log\n                                       n\n                                       )\n                                    \n                                 \n                              \n                              \n                            algorithm for the inverse 1-median problem on trees with variable vertex weights and edge reductions. Optimization 64:595\u2013602","journal-title":"Optimization"},{"key":"3416_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2016\/7590492","volume":"2016","author":"F Taleshian","year":"2016","unstructured":"Taleshian F, Fathali J (2016) A mathematical model for fuzzy \n                              $$p$$\n                              \n                                 \n                                 \n                                    p\n                                 \n                              \n                              \n                           -median problem with fuzzy weights and variables. Adv Oper Res 2016:1\u201313","journal-title":"Adv Oper Res"},{"issue":"6","key":"3416_CR27","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","volume":"15","author":"Z Xu","year":"2007","unstructured":"Xu Z (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179\u20131187","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"3416_CR28","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8:338\u2013353","journal-title":"Inf Control"},{"key":"3416_CR29","doi-asserted-by":"publisher","first-page":"71","DOI":"10.3233\/IFS-151712","volume":"30","author":"J Zhou","year":"2015","unstructured":"Zhou J, Yang F, Wang K (2015) Fuzzy arithmetic on L\u2013R fuzzy numbers with applications to fuzzy programming. J Intell Fuzzy Syst 30:71\u201387","journal-title":"J Intell Fuzzy Syst"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-018-3416-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-018-3416-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-018-3416-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,30]],"date-time":"2019-07-30T19:09:43Z","timestamp":1564513783000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-018-3416-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,31]]},"references-count":29,"journal-issue":{"issue":"17","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["3416"],"URL":"https:\/\/doi.org\/10.1007\/s00500-018-3416-2","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,31]]},"assertion":[{"value":"31 July 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}