{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T08:09:54Z","timestamp":1763366994631},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,5,10]],"date-time":"2012-05-10T00:00:00Z","timestamp":1336608000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2012,7]]},"DOI":"10.1007\/s10479-012-1147-9","type":"journal-article","created":{"date-parts":[[2012,5,9]],"date-time":"2012-05-09T07:50:43Z","timestamp":1336549843000},"page":"543-579","source":"Crossref","is-referenced-by-count":11,"title":["Maximization of the Choquet integral over a convex set and its application to resource allocation problems"],"prefix":"10.1007","volume":"196","author":[{"given":"Mikhail","family":"Timonin","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,5,10]]},"reference":[{"key":"1147_CR1","volume-title":"Lattice theory","author":"G. Birkhoff","year":"1967","unstructured":"Birkhoff, G. (1967). Lattice theory. Providence: Am. Math. Soc."},{"issue":"3","key":"1147_CR2","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/0165-4896(89)90056-5","volume":"17","author":"A. Chateauneuf","year":"1989","unstructured":"Chateauneuf, A., & Jaffray, J. (1989). Some characterizations of lower probabilities and other monotone capacities through the use of M\u00f6bius inversion. Mathematical Social Sciences, 17(3), 263\u2013283.","journal-title":"Mathematical Social Sciences"},{"issue":"4","key":"1147_CR3","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/0969-6016(94)90010-8","volume":"1","author":"C. Costa","year":"1994","unstructured":"Costa, C., & Vansnick, J. (1994). MACBETH\u2014an interactive path towards the construction of cardinal value functions. International Transactions in Operational Research, 1(4), 489\u2013500. issn:1475-3995.","journal-title":"International Transactions in Operational Research"},{"key":"1147_CR4","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8268-3","volume-title":"Nondifferentiable optimization","author":"V. Dem\u2019yanov","year":"1985","unstructured":"Dem\u2019yanov, V., Vasil\u2019ev, L., & Sasagawa, T. (1985). Nondifferentiable optimization. Berlin: Springer. isbn:0387909516.","ISBN":"http:\/\/id.crossref.org\/isbn\/0387909516"},{"issue":"2\u20133","key":"1147_CR5","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0888-613X(00)00039-6","volume":"24","author":"D. Denneberg","year":"2000","unstructured":"Denneberg, D. (2000). Totally monotone core and products of monotone measures. International Journal of Approximate Reasoning, 24(2\u20133), 273\u2013281. issn:0888-613X.","journal-title":"International Journal of Approximate Reasoning"},{"key":"1147_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-5287-7","volume-title":"Possibility theory: an approach to computerized processing of uncertainty","author":"D. Dubois","year":"1988","unstructured":"Dubois, D., Prade, H., & Harding, E. (1988). Possibility theory: an approach to computerized processing of uncertainty (vol.\u00a02). New York: Plenum Press."},{"key":"1147_CR7","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1145\/1390156.1390191","volume-title":"Proceedings of the 25th international conference on machine learning","author":"J. Duchi","year":"2008","unstructured":"Duchi, J., Shalev-Shwartz, S., Singer, Y., & Chandra, T. (2008). Efficient projections onto the l 1-ball for learning in high dimensions. In Proceedings of the 25th international conference on machine learning (pp. 272\u2013279). New York: ACM."},{"issue":"4","key":"1147_CR8","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1287\/opre.27.4.810","volume":"27","author":"J. Dyer","year":"1979","unstructured":"Dyer, J., & Sarin, R. (1979). Measurable multiattribute value functions. Operations Research, 27(4), 810\u2013822.","journal-title":"Operations Research"},{"key":"1147_CR9","series-title":"Lecture notes in economics and mathematical systems","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/978-3-642-19695-9_7","volume-title":"New state of MCDM in the 21st century","author":"H. Fouchal","year":"2011","unstructured":"Fouchal, H., Gandibleux, X., & LeHu\u00e9d\u00e9, F. (2011a). A lower bound of the Choquet integral integrated within martins\u2019 algorithm. In Y. Shi, S. Wang, G. Kou, & J. Wallenius (Eds.), Lecture notes in economics and mathematical systems: Vol.\u00a0648. New state of MCDM in the 21st century (pp. 79\u201389). Berlin: Springer."},{"key":"1147_CR10","volume-title":"2011 IEEE symposium on computational intelligence in multicriteria decision-making","author":"H. Fouchal","year":"2011","unstructured":"Fouchal, H., Gandibleux, X., & LeHu\u00e9d\u00e9, F. (2011b). Preferred solutions computed with a label setting algorithm based on Choquet integral for multi-objective shortest paths. In 2011 IEEE symposium on computational intelligence in multicriteria decision-making."},{"issue":"7","key":"1147_CR11","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1287\/mnsc.30.7.890","volume":"30","author":"G. Fox","year":"1984","unstructured":"Fox, G., Baker, N., & Bryant, J. (1984). Economic models for R and D project selection in the presence of project interactions. Management Science, 30(7), 890\u2013902. issn:0025-1909.","journal-title":"Management Science"},{"key":"1147_CR12","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/978-3-642-04045-0_30","volume-title":"Multiple criteria decision making for sustainable energy and transportation systems","author":"L. Galand","year":"2010","unstructured":"Galand, L., Perny, P., & Spanjaard, O. (2010a). A branch and bound algorithm for Choquet optimization in multicriteria problems. In Multiple criteria decision making for sustainable energy and transportation systems (pp. 355\u2013365)."},{"issue":"2","key":"1147_CR13","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.ejor.2009.10.015","volume":"204","author":"L. Galand","year":"2010","unstructured":"Galand, L., Perny, P., & Spanjaard, O. (2010b). Choquet-based optimisation in multiobjective shortest path and spanning tree problems. European Journal of Operational Research, 204(2), 303\u2013315. issn:0377-2217.","journal-title":"European Journal of Operational Research"},{"issue":"4","key":"1147_CR14","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1145\/581271.581274","volume":"5","author":"L. Gordon","year":"2002","unstructured":"Gordon, L., & Loeb, M. (2002). The economics of information security investment. ACM Transactions on Information and System Security, 5(4), 438\u2013457. issn:1094-9224.","journal-title":"ACM Transactions on Information and System Security"},{"issue":"2","key":"1147_CR15","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/S0165-0114(97)00168-1","volume":"92","author":"M. Grabisch","year":"1997","unstructured":"Grabisch, M. (1997). k-Order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems, 92(2), 167\u2013189. issn:0165-0114.","journal-title":"Fuzzy Sets and Systems"},{"issue":"1","key":"1147_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10288-007-0064-2","volume":"6","author":"M. Grabisch","year":"2008","unstructured":"Grabisch, M., & Labreuche, C. (2008). A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR: A Quarterly Journal of Operations Research, 6(1), 1\u201344. issn:1619-4500.","journal-title":"4OR: A Quarterly Journal of Operations Research"},{"issue":"1","key":"1147_CR17","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/S0377-2217(02)00354-5","volume":"148","author":"M. Grabisch","year":"2003","unstructured":"Grabisch, M., Labreuche, C., & Vansnick, J. (2003). On the extension of pseudo-boolean functions for the aggregation of interacting criteria. European Journal of Operational Research, 148(1), 28\u201347.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"1147_CR18","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1016\/j.ejor.2007.02.025","volume":"186","author":"M. Grabisch","year":"2008","unstructured":"Grabisch, M., Kojadinovic, I., & Meyer, P. (2008). A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: applications of the Kappalab R package. European Journal of Operational Research, 186(2), 766\u2013785. issn:0377-2217.","journal-title":"European Journal of Operational Research"},{"key":"1147_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-85823-9","volume-title":"Boolean methods in operations research and related areas","author":"P. Hammer","year":"1968","unstructured":"Hammer, P., & Rudeanu, S. (1968). Boolean methods in operations research and related areas. Berlin: Springer."},{"key":"1147_CR20","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139174084","volume-title":"Decisions with multiple objectives: preferences and value tradeoffs","author":"R. Keeney","year":"1993","unstructured":"Keeney, R., & Raiffa, H. (1993). Decisions with multiple objectives: preferences and value tradeoffs. Cambridge: Cambridge University Press. isbn:0521438837.","ISBN":"http:\/\/id.crossref.org\/isbn\/0521438837"},{"key":"1147_CR21","isbn-type":"print","volume-title":"Combinatorial optimization: theory and algorithms","author":"B. Korte","year":"2008","unstructured":"Korte, B., & Vygen, J. (2008). Combinatorial optimization: theory and algorithms. Berlin: Springer. isbn:3540718435.","ISBN":"http:\/\/id.crossref.org\/isbn\/3540718435"},{"key":"1147_CR22","volume-title":"Foundation of measurement. Vol. 1. Additive and polynomial representations","author":"D. Krantz","year":"1971","unstructured":"Krantz, D., Luce, R., Suppers, P., & Tversky, A. (1971). Foundation of measurement. Vol. 1. Additive and polynomial representations. San Diego: Academic Press."},{"key":"1147_CR23","first-page":"609","volume-title":"10th int. conf. on information processing and management of uncertainty in knowledge-based systems (IPMU 2004)","author":"C. Labreuche","year":"2004","unstructured":"Labreuche, C. (2004). Determination of the criteria to be improved first in order to improve as much as possible the overall evaluation. In 10th int. conf. on information processing and management of uncertainty in knowledge-based systems (IPMU 2004) (pp. 609\u2013616)."},{"issue":"1","key":"1147_CR24","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/S0165-0114(02)00429-3","volume":"137","author":"C. Labreuche","year":"2003","unstructured":"Labreuche, C., & Grabisch, M. (2003). The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets and Systems, 137(1), 11\u201326. issn:0165-0114.","journal-title":"Fuzzy Sets and Systems"},{"issue":"4","key":"1147_CR25","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s10732-006-8075-2","volume":"12","author":"F. Hu\u00e9d\u00e9 Le","year":"2006","unstructured":"Le Hu\u00e9d\u00e9, F., Grabisch, M., Labreuche, C., & Sav\u00e9ant, P. (2006a). Integration and propagation of a multi-criteria decision making model in constraint programming. Journal of Heuristics, 12(4), 329\u2013346. issn:1381-1231.","journal-title":"Journal of Heuristics"},{"key":"1147_CR26","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s10479-006-0064-1","volume":"147","author":"F. Hu\u00e9d\u00e9 Le","year":"2006","unstructured":"Le Hu\u00e9d\u00e9, F., Grabisch, M., Labreuche, C., & Sav\u00e9ant, P. (2006b). MCS\u2014a new algorithm for multicriteria optimisation in constraint programming. Annals of Operations Research, 147, 143\u2013174.","journal-title":"Annals of Operations Research"},{"key":"1147_CR27","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/978-3-642-68874-4_10","volume-title":"Mathematical programming: the state of the art","author":"L. Lov\u00e1sz","year":"1983","unstructured":"Lov\u00e1sz, L. (1983). Submodular functions and convexity. In Mathematical programming: the state of the art (pp. 235\u2013257)."},{"key":"1147_CR28","volume-title":"Proceedings of CP\u201906 workshop on preferences and soft constraints","author":"M. D. Moffitt","year":"2006","unstructured":"Moffitt, M. D., Peintner, B., & Yorke-smith, N. (2006). Multi-criteria optimization of temporal preferences. In Proceedings of CP\u201906 workshop on preferences and soft constraints."},{"key":"1147_CR29","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-8853-9","volume-title":"Introductory lectures on convex optimization: a basic course","author":"Y. Nesterov","year":"2004","unstructured":"Nesterov, Y. (2004). Introductory lectures on convex optimization: a basic course. Netherlands: Springer. isbn:1402075537.","ISBN":"http:\/\/id.crossref.org\/isbn\/1402075537"},{"issue":"6","key":"1147_CR30","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1016\/j.ijar.2009.02.010","volume":"50","author":"W. Ogryczak","year":"2009","unstructured":"Ogryczak, W., & \u015aliwi\u0144ski, T. (2009). On efficient WOWA optimization for decision support under risk. International Journal of Approximate Reasoning, 50(6), 915\u2013928. issn:0888-613X.","journal-title":"International Journal of Approximate Reasoning"},{"issue":"5","key":"1147_CR31","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1287\/mnsc.18.5.64","volume":"18","author":"G. Owen","year":"1972","unstructured":"Owen, G. (1972). Multilinear extensions of games. Management Science, 18(5), 64\u201379. issn:0025-1909.","journal-title":"Management Science"},{"key":"1147_CR32","volume-title":"Introduction to optimization (Vvedenie v optimizatsiyu)","author":"B. Polyak","year":"1983","unstructured":"Polyak, B. (1983). Introduction to optimization (Vvedenie v optimizatsiyu). Moskva: Nauka."},{"issue":"1","key":"1147_CR33","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/S0021-9800(68)80087-0","volume":"4","author":"R. Read","year":"1968","unstructured":"Read, R. (1968). An introduction to chromatic polynomials. Journal of Combinatorial Theory, 4(1), 52\u201371.","journal-title":"Journal of Combinatorial Theory"},{"issue":"1","key":"1147_CR34","doi-asserted-by":"crossref","first-page":"32","DOI":"10.2307\/2296028","volume":"30","author":"S. Reiter","year":"1963","unstructured":"Reiter, S. (1963). Choosing an investment program among interdependent projects. Review of Economic Studies, 30(1), 32\u201336. issn:0034-6527.","journal-title":"Review of Economic Studies"},{"issue":"11","key":"1147_CR35","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1287\/mnsc.12.11.829","volume":"12","author":"S. Reiter","year":"1966","unstructured":"Reiter, S., & Rice, D. (1966). Discrete optimizing solution procedures for linear and nonlinear integer programming problems. Management Science, 12(11), 829\u2013850. issn:0025-1909.","journal-title":"Management Science"},{"key":"1147_CR36","isbn-type":"print","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/FUZZY.2007.4295596","volume-title":"IEEE international conference on fuzzy systems, 2007. FUZZ-IEEE 2007","author":"S. Sahraoui","year":"2007","unstructured":"Sahraoui, S., Montmain, J., Berrah, L., & Mauris, G. (2007). User-friendly optimal improvement of an overall industrial performance based on a fuzzy Choquet integral aggregation. In IEEE international conference on fuzzy systems, 2007. FUZZ-IEEE 2007 (pp.\u00a01\u20136). New York: IEEE Press. isbn:1424412099.","ISBN":"http:\/\/id.crossref.org\/isbn\/1424412099"},{"issue":"2","key":"1147_CR37","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1016\/0377-2217(94)00257-6","volume":"89","author":"R. Santhanam","year":"1996","unstructured":"Santhanam, R., & Kyparisis, G. (1996). A decision model for interdependent information system project selection. European Journal of Operational Research, 89(2), 380\u2013399. issn:0377-2217.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"1147_CR38","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1090\/S0002-9939-1986-0835875-8","volume":"97","author":"D. Schmeidler","year":"1986","unstructured":"Schmeidler, D. (1986). Integral representation without additivity. Proceedings of the American Mathematical Society, 97(2), 255\u2013261. issn:0002-9939.","journal-title":"Proceedings of the American Mathematical Society"},{"key":"1147_CR39","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-6015-6","volume-title":"Nondifferentiable optimization and polynomial problems","author":"N. Shor","year":"1998","unstructured":"Shor, N. (1998). Nondifferentiable optimization and polynomial problems. Norwell: Kluwer Academic. isbn:0792349970.","ISBN":"http:\/\/id.crossref.org\/isbn\/0792349970"},{"issue":"2","key":"1147_CR40","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0012-365X(73)90108-8","volume":"5","author":"R. Stanley","year":"1973","unstructured":"Stanley, R. (1973). Acyclic orientations of graphs. Discrete Mathematics, 5(2), 171\u2013178.","journal-title":"Discrete Mathematics"},{"key":"1147_CR41","unstructured":"Timonin, M. (2011). Python procedures for the Choquet integral optimization. http:\/\/code.google.com\/p\/choquet-robust-optimization , June."},{"key":"1147_CR42","isbn-type":"print","volume-title":"Optimization methods (Metody optimizatsii)","author":"F. Vasilyev","year":"2002","unstructured":"Vasilyev, F. (2002). Optimization methods (Metody optimizatsii). Moscow: Faktorial Press. isbn:5886880569.","ISBN":"http:\/\/id.crossref.org\/isbn\/5886880569"},{"issue":"7","key":"1147_CR43","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1287\/mnsc.12.7.485","volume":"12","author":"H. Weingartner","year":"1966","unstructured":"Weingartner, H. (1966). Capital budgeting of interrelated projects: survey and synthesis. Management Science, 12(7), 485\u2013516. issn:0025-1909.","journal-title":"Management Science"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-012-1147-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-012-1147-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-012-1147-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T12:19:17Z","timestamp":1561724357000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-012-1147-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5,10]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["1147"],"URL":"https:\/\/doi.org\/10.1007\/s10479-012-1147-9","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,5,10]]}}}