{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T18:37:42Z","timestamp":1761763062934,"version":"3.37.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2018,7,18]],"date-time":"2018-07-18T00:00:00Z","timestamp":1531872000000},"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":[[2019,5]]},"DOI":"10.1007\/s00500-018-3401-9","type":"journal-article","created":{"date-parts":[[2018,7,18]],"date-time":"2018-07-18T21:18:01Z","timestamp":1531948681000},"page":"2887-2898","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Sparse analytic hierarchy process: an experimental analysis"],"prefix":"10.1007","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7257-4079","authenticated-orcid":false,"given":"Gabriele","family":"Oliva","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roberto","family":"Setola","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Scala","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paolo","family":"Dell\u2019Olmo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,7,18]]},"reference":[{"issue":"10","key":"3401_CR1","doi-asserted-by":"publisher","first-page":"P10012","DOI":"10.1088\/1742-5468\/2005\/10\/P10012","volume":"2005","author":"D Achlioptas","year":"2005","unstructured":"Achlioptas D, Molloy M, Moore C, Van Bussel F (2005) Rapid mixing for lattice colourings with fewer colours. J Stat Mech Theory Exp 2005(10):P10012","journal-title":"J Stat Mech Theory Exp"},{"issue":"1","key":"3401_CR2","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/0022-2496(83)90028-7","volume":"27","author":"J Acz\u00e9l","year":"1983","unstructured":"Acz\u00e9l J, Saaty TL (1983) Procedures for synthesizing ratio judgements. J Math Psychol 27(1):93\u2013102","journal-title":"J Math Psychol"},{"key":"3401_CR3","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.future.2013.06.030","volume":"30","author":"C Alcaraz","year":"2014","unstructured":"Alcaraz C, Lopez J (2014) WASAM: A dynamic wide-area situational awareness model for critical domains in smart grids. Future Gener Comput Syst 30:146\u2013154","journal-title":"Future Gener Comput Syst"},{"issue":"2","key":"3401_CR4","first-page":"57","volume":"32","author":"J Barzilai","year":"1994","unstructured":"Barzilai J, Golany B (1994) Ahp rank reversal, normalization and aggregation rules. Inf Syst Oper Res 32(2):57\u201364","journal-title":"Inf Syst Oper Res"},{"issue":"3","key":"3401_CR5","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/0167-6377(87)90026-5","volume":"6","author":"J Barzilai","year":"1987","unstructured":"Barzilai J, Cook WD, Golany B (1987) Consistent weights for judgements matrices of the relative importance of alternatives. Oper Res Lett 6(3):131\u2013134","journal-title":"Oper Res Lett"},{"issue":"1","key":"3401_CR6","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1007\/s12597-013-0134-5","volume":"51","author":"I Beg","year":"2014","unstructured":"Beg I, Rashid T (2014) Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS. Opsearch 51(1):98\u2013129","journal-title":"Opsearch"},{"issue":"2","key":"3401_CR7","doi-asserted-by":"publisher","first-page":"e0118093","DOI":"10.1371\/journal.pone.0118093","volume":"10","author":"A Bessi","year":"2015","unstructured":"Bessi A, Coletto M, Davidescu GA, Scala A, Caldarelli G, Quattrociocchi W (2015) Science vs conspiracy: collective narratives in the age of misinformation. PLoS ONE 10(2):e0118093","journal-title":"PLoS ONE"},{"key":"3401_CR8","unstructured":"Boz\u00f3ki S, Tsyganok V (2017) The logarithmic least squares optimality of the geometric mean of weight vectors calculated from all spanning trees for (in) complete pairwise comparison matrices. arXiv preprint \n                    arXiv:1701.04265"},{"issue":"3","key":"3401_CR9","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1016\/S0377-2217(96)00250-0","volume":"102","author":"FJ Carmone","year":"1997","unstructured":"Carmone FJ, Kara A, Zanakis SH (1997) A monte carlo investigation of incomplete pairwise comparison matrices in AHP. Eur J Oper Res 102(3):538\u2013553","journal-title":"Eur J Oper Res"},{"issue":"1","key":"3401_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0165-0114(97)00377-1","volume":"114","author":"C-T Chen","year":"2000","unstructured":"Chen C-T (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 114(1):1\u20139","journal-title":"Fuzzy Sets Syst"},{"key":"3401_CR11","unstructured":"Chen S-J, Hwang C-L, Hwang FP (2011) Fuzzy multiple attribute decision making (methods and applications). Lecture notes in economics and mathematical systems"},{"issue":"3\u20135","key":"3401_CR12","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/0270-0255(87)90489-1","volume":"9","author":"GB Crawford","year":"1987","unstructured":"Crawford GB (1987) The geometric mean procedure for estimating the scale of a judgement matrix. Math Model 9(3\u20135):327\u2013334","journal-title":"Math Model"},{"issue":"1","key":"3401_CR13","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1002\/bs.3830030104","volume":"3","author":"JM Davis","year":"1958","unstructured":"Davis JM (1958) The transitivity of preferences. Behav Sci 3(1):26\u201333","journal-title":"Behav Sci"},{"issue":"1","key":"3401_CR14","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1177\/0272989X8900900108","volume":"9","author":"JG Dolan","year":"1989","unstructured":"Dolan JG, Isselhardt BJ, Cappuccio JD (1989) The analytic hierarchy process in medical decision making: a tutorial. Med Decis Mak 9(1):40\u201350","journal-title":"Med Decis Mak"},{"issue":"3","key":"3401_CR15","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1287\/mnsc.36.3.249","volume":"36","author":"JS Dyer","year":"1990","unstructured":"Dyer JS (1990) Remarks on the analytic hierarchy process. Manag Sci 36(3):249\u2013258","journal-title":"Manag Sci"},{"key":"3401_CR16","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/j.laa.2014.04.018","volume":"454","author":"M Dyer","year":"2014","unstructured":"Dyer M, Greenhill C, Ullrich M (2014) Structure and eigenvalues of heat-bath markov chains. Linear Algebra Appl 454:57\u201371","journal-title":"Linear Algebra Appl"},{"issue":"2","key":"3401_CR17","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1016\/S0377-2217(03)00154-1","volume":"153","author":"MT Escobar","year":"2004","unstructured":"Escobar MT, Aguar\u00f3n J, Moreno-Jim\u00e9nez JM (2004) A note on AHP group consistency for the row geometric mean priorization procedure. Eur J Oper Res 153(2):318\u2013322","journal-title":"Eur J Oper Res"},{"issue":"9","key":"3401_CR18","doi-asserted-by":"publisher","first-page":"1465","DOI":"10.1109\/TAC.2004.834433","volume":"49","author":"AJ Fax","year":"2004","unstructured":"Fax AJ, Murray RM (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49(9):1465\u20131476","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"3401_CR19","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.ejor.2006.09.065","volume":"183","author":"M Fedrizzi","year":"2007","unstructured":"Fedrizzi M, Giove S (2007) Incomplete pairwise comparison and consistency optimization. Eur J Oper Res 183(1):303\u2013313","journal-title":"Eur J Oper Res"},{"key":"3401_CR20","first-page":"295","volume-title":"Multi criteria decision making and the analytic hierarchy process","author":"EH Forman","year":"1990","unstructured":"Forman EH (1990) Multi criteria decision making and the analytic hierarchy process. Springer, Berlin, pp 295\u2013318"},{"key":"3401_CR21","doi-asserted-by":"publisher","DOI":"10.1201\/b14835","volume-title":"Markov chain Monte Carlo in practice","author":"WR Gilks","year":"1995","unstructured":"Gilks WR, Richardson S, Spiegelhalter D (1995) Markov chain Monte Carlo in practice. CRC Press, London"},{"key":"3401_CR22","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511613586","volume-title":"Finite Markov chains and algorithmic applications","author":"O H\u00e4ggstr\u00f6m","year":"2002","unstructured":"H\u00e4ggstr\u00f6m O (2002) Finite Markov chains and algorithmic applications, vol 52. Cambridge University Press, Cambridge"},{"issue":"3\u20135","key":"3401_CR23","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1016\/0270-0255(87)90492-1","volume":"9","author":"PT Harker","year":"1987","unstructured":"Harker PT (1987a) Alternative modes of questioning in the analytic hierarchy process. Math Model 9(3\u20135):353\u2013360","journal-title":"Math Model"},{"issue":"11","key":"3401_CR24","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1016\/0270-0255(87)90503-3","volume":"9","author":"PT Harker","year":"1987","unstructured":"Harker PT (1987b) Incomplete pairwise comparisons in the analytic hierarchy process. Math Model 9(11):837\u2013848","journal-title":"Math Model"},{"issue":"1","key":"3401_CR25","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","volume":"57","author":"KW Hastings","year":"1970","unstructured":"Hastings KW (1970) Monte carlo sampling methods using markov chains and their applications. Biometrika 57(1):97\u2013109","journal-title":"Biometrika"},{"key":"3401_CR26","volume-title":"The use of the analytic hierarchy process in health care decision making","author":"JM Hummel","year":"2009","unstructured":"Hummel JM, IJzermann MJ (2009) The use of the analytic hierarchy process in health care decision making. University of Twente, Enschede"},{"issue":"1\/2","key":"3401_CR27","doi-asserted-by":"publisher","first-page":"81","DOI":"10.2307\/2332226","volume":"30","author":"MG Kendall","year":"1938","unstructured":"Kendall MG (1938) A new measure of rank correlation. Biometrika 30(1\/2):81\u201393","journal-title":"Biometrika"},{"issue":"1","key":"3401_CR28","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.seps.2005.10.006","volume":"42","author":"L Liang","year":"2008","unstructured":"Liang L, Wang G, Hua Z, Zhang B (2008) Mapping verbal responses to numerical scales in the analytic hierarchy process. Socio-Econ Plan Sci 42(1):46\u201355","journal-title":"Socio-Econ Plan Sci"},{"issue":"1","key":"3401_CR29","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1016\/j.ejor.2007.05.001","volume":"189","author":"MJ Liberatore","year":"2008","unstructured":"Liberatore MJ, Nydick RL (2008) The analytic hierarchy process in medical and health care decision making: a literature review. Eur J Oper Res 189(1):194\u2013207","journal-title":"Eur J Oper Res"},{"key":"3401_CR30","volume-title":"The delphi method","author":"HA Linstone","year":"1975","unstructured":"Linstone HA, Turoff M et al (1975) The delphi method. Addison-Wesley, Reading"},{"key":"3401_CR31","doi-asserted-by":"crossref","unstructured":"Menci M, Oliva G, Papi M, Setola R, Scala A (2018) A suite of distributed methodologies to solve the sparse analytic hierarchy process problem. In: 2018th European control conference","DOI":"10.23919\/ECC.2018.8550604"},{"issue":"6","key":"3401_CR32","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1063\/1.1699114","volume":"21","author":"N Metropolis","year":"1953","unstructured":"Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087\u20131092","journal-title":"J Chem Phys"},{"issue":"1","key":"3401_CR33","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1109\/JPROC.2006.887293","volume":"95","author":"R Olfati-Saber","year":"2007","unstructured":"Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215\u2013233","journal-title":"Proc IEEE"},{"key":"3401_CR34","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/j.automatica.2017.07.051","volume":"85","author":"G Oliva","year":"2017","unstructured":"Oliva G, Setola R, Scala A (2017) Sparse and distributed analytic hierarchy process. Automatica 85:211\u2013220","journal-title":"Automatica"},{"key":"3401_CR35","doi-asserted-by":"crossref","unstructured":"Rubio JE, Alcaraz C, Lopez J (2017) Preventing advanced persistent threats in complex control networks. In: European symposium on research in computer security. Springer, pp 402\u2013418","DOI":"10.1007\/978-3-319-66399-9_22"},{"issue":"3","key":"3401_CR36","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1016\/0022-2496(77)90033-5","volume":"15","author":"TL Saaty","year":"1977","unstructured":"Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15(3):234\u2013281","journal-title":"J Math Psychol"},{"issue":"3","key":"3401_CR37","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1287\/mnsc.36.3.259","volume":"36","author":"TL Saaty","year":"1990","unstructured":"Saaty TL (1990) An exposition of the AHP in reply to the paper \u201cremarks on the analytic hierarchy process\u201d. Manag Sci 36(3):259\u2013268","journal-title":"Manag Sci"},{"issue":"3","key":"3401_CR38","doi-asserted-by":"publisher","first-page":"404","DOI":"10.15807\/jorsj.41.404","volume":"41","author":"S Shiraishi","year":"1998","unstructured":"Shiraishi S, Obata T, Daigo M (1998) Properties of a positive reciprocal matrix and their application to AHP. J Oper Res Soc Jpn 41(3):404\u2013414","journal-title":"J Oper Res Soc Jpn"},{"key":"3401_CR39","doi-asserted-by":"publisher","DOI":"10.1515\/9781400844807","volume-title":"Heavenly mathematics: the forgotten art of spherical trigonometry","author":"G Brummelen Van","year":"2012","unstructured":"Van Brummelen G (2012) Heavenly mathematics: the forgotten art of spherical trigonometry. Princeton University Press, Princeton"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-018-3401-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-018-3401-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-018-3401-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,17]],"date-time":"2019-07-17T19:12:04Z","timestamp":1563390724000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-018-3401-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,18]]},"references-count":39,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["3401"],"URL":"https:\/\/doi.org\/10.1007\/s00500-018-3401-9","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2018,7,18]]},"assertion":[{"value":"18 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":"All authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and\/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Informed consent was obtained from all individual participants included in the study.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}