{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T19:50:54Z","timestamp":1740167454931,"version":"3.37.3"},"reference-count":42,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06n07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advs. Complex Syst."],"published-print":{"date-parts":[[2018,9]]},"abstract":"<jats:p> Given a system where the real-valued states of the agents are aggregated by a function to a real-valued state of the entire system, we are interested in the influence or importance of different agents for that function. This generalizes the notion of power indices for binary voting systems to decisions over interval policy spaces and has applications in economics, engineering, security analysis, and other disciplines. Here, we study the question of importance in systems with interval decisions. Based on the classical Shapley\u2013Shubik and Penrose\u2013Banzhaf index, from binary voting, we motivate and analyze two importance measures. Additionally, we present some results for parametric classes of aggregation functions. <\/jats:p>","DOI":"10.1142\/s0219525918500248","type":"journal-article","created":{"date-parts":[[2018,11,26]],"date-time":"2018-11-26T22:23:42Z","timestamp":1543271022000},"page":"1850024","source":"Crossref","is-referenced-by-count":4,"title":["IMPORTANCE IN SYSTEMS WITH INTERVAL DECISIONS"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4597-2041","authenticated-orcid":false,"given":"SASCHA","family":"KURZ","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Bayreuth, Universit\u00e4tsstr. 30, 95440 Bayreuth, Germany"}]}],"member":"219","published-online":{"date-parts":[[2019,1,9]]},"reference":[{"key":"S0219525918500248BIB001","doi-asserted-by":"publisher","DOI":"10.1108\/09590551211230232"},{"key":"S0219525918500248BIB002","first-page":"317","volume":"19","author":"Banzhaf J. F.","year":"1964","journal-title":"Rutgers Law Rev."},{"key":"S0219525918500248BIB003","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1040.0247"},{"key":"S0219525918500248BIB004","doi-asserted-by":"publisher","DOI":"10.1111\/j.1538-4632.1976.tb00549.x"},{"key":"S0219525918500248BIB005","doi-asserted-by":"publisher","DOI":"10.1111\/j.1539-6924.1999.tb00399.x"},{"volume-title":"The Handbook of Research Synthesis and Meta-Analysis","year":"2009","author":"Cooper H.","key":"S0219525918500248BIB006"},{"key":"S0219525918500248BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2017.06.004"},{"key":"S0219525918500248BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.enpol.2010.11.045"},{"key":"S0219525918500248BIB009","first-page":"539","volume":"22","author":"Dragan I. C.","year":"2005","journal-title":"Int. J. Pure Appl. Math."},{"key":"S0219525918500248BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01780630"},{"key":"S0219525918500248BIB011","doi-asserted-by":"publisher","DOI":"10.1287\/moor.4.2.99"},{"key":"S0219525918500248BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s00182-015-0490-x"},{"key":"S0219525918500248BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/BF00118651"},{"key":"S0219525918500248BIB014","doi-asserted-by":"publisher","DOI":"10.4337\/9781840647761"},{"key":"S0219525918500248BIB015","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2002.800893"},{"key":"S0219525918500248BIB016","doi-asserted-by":"publisher","DOI":"10.1038\/075509e0"},{"key":"S0219525918500248BIB017","doi-asserted-by":"publisher","DOI":"10.1038\/075450a0"},{"key":"S0219525918500248BIB018","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177013825"},{"key":"S0219525918500248BIB019","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139644150"},{"key":"S0219525918500248BIB020","volume":"5","author":"Hegselmann R.","year":"2002","journal-title":"J. Artif. Soc. Social Simul."},{"key":"S0219525918500248BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s10614-005-6296-3"},{"key":"S0219525918500248BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/BF00115658"},{"key":"S0219525918500248BIB023","doi-asserted-by":"publisher","DOI":"10.1007\/s00182-006-0011-z"},{"key":"S0219525918500248BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-4896(97)00028-0"},{"key":"S0219525918500248BIB025","doi-asserted-by":"publisher","DOI":"10.1086\/670380"},{"key":"S0219525918500248BIB027","doi-asserted-by":"publisher","DOI":"10.1007\/BF01415753"},{"key":"S0219525918500248BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-012-1108-3"},{"key":"S0219525918500248BIB029","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2011.587008"},{"key":"S0219525918500248BIB030","doi-asserted-by":"publisher","DOI":"10.3390\/economies2010045"},{"key":"S0219525918500248BIB031","doi-asserted-by":"publisher","DOI":"10.1086\/693039"},{"key":"S0219525918500248BIB032","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1008636108"},{"key":"S0219525918500248BIB033","doi-asserted-by":"publisher","DOI":"10.1007\/s00355-006-0186-z"},{"key":"S0219525918500248BIB034","doi-asserted-by":"publisher","DOI":"10.1016\/j.mathsocsci.2017.05.003"},{"key":"S0219525918500248BIB035","doi-asserted-by":"publisher","DOI":"10.1093\/restud\/rds026"},{"key":"S0219525918500248BIB036","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718485"},{"key":"S0219525918500248BIB037","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.18.5.64"},{"key":"S0219525918500248BIB038","doi-asserted-by":"publisher","DOI":"10.2307\/2981392"},{"key":"S0219525918500248BIB039","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2010.10.002"},{"key":"S0219525918500248BIB040","doi-asserted-by":"publisher","DOI":"10.1007\/BF00292733"},{"key":"S0219525918500248BIB041","doi-asserted-by":"publisher","DOI":"10.2307\/1951053"},{"key":"S0219525918500248BIB042","series-title":"Economies, Societies and Nations","volume-title":"The Wisdom of Crowds: Why the Many are Smarter than the Few and How Collective Wisdom Shapes Business","volume":"296","author":"Surowiecki J.","year":"2005"},{"key":"S0219525918500248BIB043","volume-title":"Theory of Games and Economic Behavior","author":"von Neumann J.","year":"1953","edition":"3"}],"container-title":["Advances in Complex Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219525918500248","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T12:28:06Z","timestamp":1565180886000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219525918500248"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9]]},"references-count":42,"journal-issue":{"issue":"06n07","published-online":{"date-parts":[[2019,1,9]]},"published-print":{"date-parts":[[2018,9]]}},"alternative-id":["10.1142\/S0219525918500248"],"URL":"https:\/\/doi.org\/10.1142\/s0219525918500248","relation":{},"ISSN":["0219-5259","1793-6802"],"issn-type":[{"type":"print","value":"0219-5259"},{"type":"electronic","value":"1793-6802"}],"subject":[],"published":{"date-parts":[[2018,9]]}}}