{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T03:15:09Z","timestamp":1770434109156,"version":"3.49.0"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2010,10,24]],"date-time":"2010-10-24T00:00:00Z","timestamp":1287878400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Oper Res Int J"],"published-print":{"date-parts":[[2012,11]]},"DOI":"10.1007\/s12351-010-0090-2","type":"journal-article","created":{"date-parts":[[2010,10,23]],"date-time":"2010-10-23T02:16:21Z","timestamp":1287800181000},"page":"271-286","source":"Crossref","is-referenced-by-count":11,"title":["Stackelberg solutions for fuzzy random bilevel linear programming through level sets and probability maximization"],"prefix":"10.1007","volume":"12","author":[{"given":"Masatoshi","family":"Sakawa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hideki","family":"Katagiri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takeshi","family":"Matsui","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,10,24]]},"reference":[{"issue":"2","key":"90_CR1","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1016\/j.ins.2007.03.029","volume":"178","author":"EE Ammar","year":"2008","unstructured":"Ammar EE (2008) On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem. Inf Sci 178(2):468\u2013484","journal-title":"Inf Sci"},{"issue":"1","key":"90_CR2","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/S0377-2217(98)00336-1","volume":"119","author":"MA Amouzegar","year":"1999","unstructured":"Amouzegar MA, Moshirvaziri K (1999) Determining optimal pollution control policies: an application of bilevel programming. Eur J Oper Res 119(1):100\u2013120","journal-title":"Eur J Oper Res"},{"issue":"1","key":"90_CR3","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0305-0548(82)90007-7","volume":"9","author":"JF Bard","year":"1982","unstructured":"Bard JF, Falk JE (1982) An explicit solution to the multi-level programming problem. Comput Oper Res 9(1):77\u2013100","journal-title":"Comput Oper Res"},{"issue":"2","key":"90_CR4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1137\/0911017","volume":"11","author":"JF Bard","year":"1990","unstructured":"Bard JF, Moore JT (1990) A branch and bound algorithm for the bilevel programming problem. SIAM J Sci Stat Comput 11(2):281\u2013292","journal-title":"SIAM J Sci Stat Comput"},{"issue":"8","key":"90_CR5","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1287\/mnsc.30.8.1004","volume":"30","author":"WF Bialas","year":"1984","unstructured":"Bialas WF, Karwan MH (1984) Two-level linear programming. Manag Sci 30(8):1004\u20131020","journal-title":"Manag Sci"},{"key":"90_CR6","volume-title":"Introduction to Stochastic Programming","author":"JR Birge","year":"1997","unstructured":"Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, London"},{"issue":"1","key":"90_CR7","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/S0377-2217(02)00648-3","volume":"152","author":"HI Calvete","year":"2004","unstructured":"Calvete HI, Gale C (2004) A note on bilevel linear fractional programming problem. Eur J Oper Res 152(1):296\u2013299","journal-title":"Eur J Oper Res"},{"issue":"3\u20134","key":"90_CR8","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1002\/nav.3800090303","volume":"9","author":"A Charnes","year":"1962","unstructured":"Charnes A, Cooper WW (1962) Programming with linear fractional functionals. Nav Res Logist Q 9(3\u20134):181\u2013186","journal-title":"Nav Res Logist Q"},{"issue":"1","key":"90_CR9","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1287\/opre.11.1.18","volume":"11","author":"A Charnes","year":"1963","unstructured":"Charnes A, Cooper WW (1963) Deterministic equivalents for optimizing and satisficing under chance constraints. Oper Res 11(1):18\u201339","journal-title":"Oper Res"},{"issue":"3","key":"90_CR10","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s10589-005-4612-4","volume":"30","author":"B Colson","year":"2005","unstructured":"Colson B, Marcotte P, Savard G (2005) A trust-region method for nonlinear bilevel programming: algorithm and computational experience. Comput Optim Appl 30(3):211\u2013227","journal-title":"Comput Optim Appl"},{"issue":"2","key":"90_CR11","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1023\/A:1017571111854","volume":"110","author":"S Dempe","year":"2001","unstructured":"Dempe S, Bard JF (2001) Bundle trust-region algorithm for bilinear bilevel programming. J Optim Theory Appl 110(2):265\u2013268","journal-title":"J Optim Theory Appl"},{"issue":"4","key":"90_CR12","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1007\/s10898-006-9100-6","volume":"38","author":"NP Faisca","year":"2007","unstructured":"Faisca NP, Dua V, Rustem B, Saraiva PM, Pistikopoulos EN (2007) Parametric global optimisation for bilevel programming. J Glob Optim 38(4):609\u2013623","journal-title":"J Glob Optim"},{"issue":"2","key":"90_CR13","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/s10589-007-9066-4","volume":"39","author":"M Fampa","year":"2008","unstructured":"Fampa M, Barroso LA, Candal D, Simonetti L (2008) Bilevel optimization applied to strategic pricing in competitive electricity markets. Comput Optim Appl 39(2):121\u2013142","journal-title":"Comput Optim Appl"},{"issue":"19","key":"90_CR14","doi-asserted-by":"crossref","first-page":"2546","DOI":"10.1016\/j.fss.2006.05.002","volume":"157","author":"MA Gil","year":"2006","unstructured":"Gil MA, Lopez-Diaz M, Ralescu DA (2006) Overview on the development of fuzzy random variables. Fuzzy Sets Syst 157(19):2546\u20132557","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"90_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1011268113791","volume":"20","author":"ZH G\u00fcm\u00fcs","year":"2001","unstructured":"G\u00fcm\u00fcs ZH, Floudas CA (2001) Global optimization of nonlinear bilevel programming problems. J Glob Optim 20(1):1\u201331","journal-title":"J Glob Optim"},{"issue":"5","key":"90_CR16","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.1137\/0913069","volume":"13","author":"P Hansen","year":"1992","unstructured":"Hansen P, Jaumard B, Savard G (1992) New branch-and-bound rules for linear bilevel programming. SIAM J Sci Stat Comput 13(5):1194\u20131217","journal-title":"SIAM J Sci Stat Comput"},{"issue":"1","key":"90_CR17","first-page":"59","volume":"12","author":"H Katagiri","year":"2004","unstructured":"Katagiri H, Ishii H, Sakawa M (2004a) On fuzzy random linear knapsack problems. Cent Eur J Oper Res 12(1):59\u201370","journal-title":"Cent Eur J Oper Res"},{"issue":"1","key":"90_CR18","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/S0377-2217(02)00523-4","volume":"152","author":"H Katagiri","year":"2004","unstructured":"Katagiri H, Sakawa M, Ishii H (2004b) Fuzzy random bottleneck spanning tree problems using possibility and necessity measures. Eur J Oper Res 152(1):88\u201395","journal-title":"Eur J Oper Res"},{"issue":"3\u20134","key":"90_CR19","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/j.mcm.2003.08.007","volume":"40","author":"H Katagiri","year":"2004","unstructured":"Katagiri H, Sakawa M, Kato K, Nishizaki I (2004c) A fuzzy random multiobjective 0\u20131 programming based on the expectation optimization model using possibility and necessity measures. Math Comput Model 40(3\u20134):411\u2013421","journal-title":"Math Comput Model"},{"issue":"D(8","key":"90_CR20","doi-asserted-by":"crossref","first-page":"1912","DOI":"10.1093\/ietisy\/e88-d.8.1912","volume":"88","author":"H Katagiri","year":"2005","unstructured":"Katagiri H, Mermri EB, Sakawa M, Kato K, Nishizaki I (2005a) A possibilistic and stochastic programming approach to fuzzy random MST problems. IEICE Trans Inf Syst E88-D(8):1912\u20131919","journal-title":"IEICE Trans Inf Syst E"},{"issue":"2","key":"90_CR21","first-page":"361","volume":"61","author":"H Katagiri","year":"2005","unstructured":"Katagiri H, Sakawa M, Ishii H (2005b) A study on fuzzy random portfolio selection problems using possibility and necessity measures. Sci Math Jpn 61(2):361\u2013369","journal-title":"Sci Math Jpn"},{"issue":"1","key":"90_CR22","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1080\/01969720500320817","volume":"37","author":"H Katagiri","year":"2006","unstructured":"Katagiri H, Sakawa M, Nishizaki I (2006) Interactive decision making using possibility and necessity measures for a fuzzy random multiobjective 0\u20131 programming problem. Cybern Syst 37(1):59\u201374","journal-title":"Cybern Syst"},{"issue":"2","key":"90_CR23","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.ejor.2007.02.050","volume":"188","author":"H Katagiri","year":"2008","unstructured":"Katagiri H, Sakawa M, Kato K, Nishizaki I (2008) Interactive multiobjective fuzzy random linear programming: maximization of possibility and probability. Eur J Oper Res 188(2):530\u2013539","journal-title":"Eur J Oper Res"},{"issue":"1\u20132","key":"90_CR24","doi-asserted-by":"crossref","first-page":"181","DOI":"10.2307\/1910956","volume":"31","author":"S Kataoka","year":"1963","unstructured":"Kataoka S (1963) A stochastic programming model. Econometorica 31(1\u20132):181\u2013196","journal-title":"Econometorica"},{"key":"90_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-3943-1","volume-title":"Statistics with Vague Data","author":"R Kruse","year":"1987","unstructured":"Kruse R, Meyer KD (1987) Statistics with vague data. D. Riedel Publishing Company, Dordrecht"},{"issue":"1","key":"90_CR26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0020-0255(78)90019-1","volume":"15","author":"H Kwakernaak","year":"1978","unstructured":"Kwakernaak H (1978) Fuzzy random variables-I. Definitions and theorems. Inf Sci 15(1):1\u201329","journal-title":"Inf Sci"},{"issue":"5","key":"90_CR27","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1109\/91.963757","volume":"9","author":"B Liu","year":"2001","unstructured":"Liu B (2001) Fuzzy random chance-constrained programming. IEEE Trans Fuzzy Syst 9(5):713\u2013720","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"90_CR28","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/91.963758","volume":"9","author":"B Liu","year":"2001","unstructured":"Liu B (2001) Fuzzy random dependent-chance programming. IEEE Trans Fuzzy Syst 9(5):721\u2013726","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"2","key":"90_CR29","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1023\/A:1023447217758","volume":"2","author":"YK Liu","year":"2003","unstructured":"Liu YK, Liu B (2003) Fuzzy random variables: a scalar expected value operator. Fuzzy Optim Decis Mak 2(2):143\u2013160","journal-title":"Fuzzy Optim Decis Mak"},{"issue":"3","key":"90_CR30","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0165-0114(95)00043-7","volume":"77","author":"MK Luhandjula","year":"1996","unstructured":"Luhandjula MK (1996) Fuzziness and randomness in an optimization framework. Fuzzy Sets Syst 77(3):291\u2013297","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"90_CR31","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1016\/j.ejor.2005.07.019","volume":"174","author":"MK Luhandjula","year":"2006","unstructured":"Luhandjula MK (2006) Fuzzy stochastic linear programming: survey and future research directions. Eur J Oper Res 174(3):1353\u20131367","journal-title":"Eur J Oper Res"},{"issue":"1","key":"90_CR32","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0165-0114(95)00240-5","volume":"81","author":"MK Luhandjula","year":"1996","unstructured":"Luhandjula MK, Gupta MM (1996) On fuzzy stochastic optimization. Fuzzy Sets Syst 81(1):47\u201355","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"90_CR33","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BF00121268","volume":"8","author":"MG Nicholls","year":"1996","unstructured":"Nicholls MG (1996) The applications of non-linear bi-level programming to the aluminium industry. J Glob Optim 8(3):245\u2013261","journal-title":"J Glob Optim"},{"issue":"1","key":"90_CR34","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1023\/A:1021729618112","volume":"103","author":"I Nishizaki","year":"1999","unstructured":"Nishizaki I, Sakawa M (1999) Stackelberg solutions to multiobjective two-level linear programming problems. J Optim Theory Appl 103(1):161\u2013182","journal-title":"J Optim Theory Appl"},{"issue":"2","key":"90_CR35","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1080\/019697200124892","volume":"31","author":"I Nishizaki","year":"2000","unstructured":"Nishizaki I, Sakawa M (2000) Computational methods through genetic algorithms for obtaining Stackelberg solutions to two-level mixed zero-one programming problems. Cybern Syst 31(2):203\u2013221","journal-title":"Cybern Syst"},{"issue":"3","key":"90_CR36","first-page":"281","volume":"11","author":"I Nishizaki","year":"2003","unstructured":"Nishizaki I, Sakawa M, Katagiri H (2003) Stackelberg solutions to multiobjective two-level linear programming problems with random variable coefficients. Cent Eur J Oper Res 11(3):281\u2013296","journal-title":"Cent Eur J Oper Res"},{"issue":"2","key":"90_CR37","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/0022-247X(86)90093-4","volume":"114","author":"ML Puri","year":"1996","unstructured":"Puri ML, Ralescu DA (1996) Fuzzy random variables. J Math Anal Appl 114(2):409\u2013422","journal-title":"J Math Anal Appl"},{"issue":"1","key":"90_CR38","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0165-0114(94)90245-3","volume":"65","author":"Z Qiao","year":"1994","unstructured":"Qiao Z, Zhang Y, Wang GY (1994) On fuzzy random linear programming. Fuzzy Sets Syst 65(1):31\u201349","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"90_CR39","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1016\/j.amc.2006.10.032","volume":"188","author":"E Roghanian","year":"2007","unstructured":"Roghanian E, Sadjadi SJ, Aryanezhad MB (2007) A probabilistic bi-level linear multi-objective programming problem to supply chain planning. Appl Math Comput 188(1):786\u2013800","journal-title":"Appl Math Comput"},{"issue":"17","key":"90_CR40","doi-asserted-by":"crossref","first-page":"1892","DOI":"10.1016\/j.fss.2007.04.005","volume":"156","author":"H Rommelfanger","year":"2007","unstructured":"Rommelfanger H (2007) A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values. Fuzzy Sets Syst 156(17):1892\u20131904","journal-title":"Fuzzy Sets Syst"},{"key":"90_CR41","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-1633-4","volume-title":"Fuzzy Sets and Interactive Multiobjective Optimization","author":"M Sakawa","year":"1993","unstructured":"Sakawa M (1993) Fuzzy sets and interactive multiobjective optimization. Plenum Press, New York"},{"key":"90_CR42","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7908-1851-2","volume-title":"Large Scale Interactive Fuzzy Multiobjective Programming","author":"M Sakawa","year":"2000","unstructured":"Sakawa M (2000) Large scaleinteractive fuzzy multiobjective programming. Physica-Verlag, Heidelberg"},{"key":"90_CR43","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-1519-7","volume-title":"Genetic Algorithms and Fuzzy Multiobjective Optimization","author":"M Sakawa","year":"2001","unstructured":"Sakawa M (2001) Genetic algorithms and fuzzy multiobjective optimization. Kluwer Academic Publishers, Boston"},{"key":"90_CR44","doi-asserted-by":"crossref","unstructured":"Sakawa M, Kato K (2008) Interactive fuzzy multi-objective stochastic linear programming. In: Fuzzy multi-criteria decision making\u2014theory and applications with recent developments. Springer, New York, pp 375\u2013408","DOI":"10.1007\/978-0-387-76813-7_15"},{"key":"90_CR45","volume-title":"Cooperative and Noncooperative Multi-Level Programming","author":"M Sakawa","year":"2009","unstructured":"Sakawa M, Nishizaki I (2009) Cooperative and noncooperative multi-level programming. Springer, New York"},{"key":"90_CR46","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-6305-1","volume-title":"Nondifferentiable and Two-Level Mathematical Programming","author":"K Shimizu","year":"1997","unstructured":"Shimizu K, Ishizuka Y, Bard JF (1997) Nondifferentiable and two-level mathematical programming. Kluwer Academic Publishers, Boston"},{"issue":"5","key":"90_CR47","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/BF00935665","volume":"11","author":"M Simaan","year":"1973","unstructured":"Simaan M, Cruz JB Jr. (1973) On the Stackelberg strategy in nonzero-sum games. J Optim Theory Appl 11(5):533\u2013555","journal-title":"J Optim Theory Appl"},{"key":"90_CR48","volume-title":"Stochastic Programming with Multiple Objective Functions","author":"IM Stancu-Minasian","year":"1984","unstructured":"Stancu-Minasian IM (1984) Stochastic programming with multiple objective functions. D. Reidel Publishing Company, Dordrecht"},{"key":"90_CR49","doi-asserted-by":"crossref","unstructured":"Stancu-Minasian IM (1990) Overview of different approaches for solving stochastic programming problems with multiple objective functions. In: Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty. Kluwer Academic Publishers, Dordrecht\/Boston\/London, pp 71\u2013101","DOI":"10.1007\/978-94-009-2111-5_5"},{"key":"90_CR50","volume-title":"Fractional Programming","author":"IM Stancu-Minasian","year":"1992","unstructured":"Stancu-Minasian IM (1992) Fractional programming. Kluwer Academic Publishers, Dordrecht\/Boston\/London"},{"issue":"3","key":"90_CR51","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/0165-0114(93)90025-D","volume":"57","author":"GY Wang","year":"1993","unstructured":"Wang GY, Qiao Z (1993) Linear programming with fuzzy random variable coefficients. Fuzzy Sets Syst 57(3):295\u2013311","journal-title":"Fuzzy Sets Syst"},{"issue":"4","key":"90_CR52","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/BF01096412","volume":"3","author":"DJ White","year":"1993","unstructured":"White DJ, Anandalingam G (1993) A penalty function approach for solving bi-level linear programs. J Glob Optim 3(4):397\u2013419","journal-title":"J Glob Optim"},{"issue":"14","key":"90_CR53","doi-asserted-by":"crossref","first-page":"2899","DOI":"10.1016\/j.ins.2008.03.003","volume":"178","author":"J Xu","year":"2008","unstructured":"Xu J, Liu Y (2008) Multi-objective decision making model under fuzzy random environment and its application to inventory problems. Inf Sci 178(14):2899\u20132914","journal-title":"Inf Sci"}],"container-title":["Operational Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-010-0090-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12351-010-0090-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-010-0090-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,3]],"date-time":"2023-06-03T23:45:57Z","timestamp":1685835957000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12351-010-0090-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,24]]},"references-count":53,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,11]]}},"alternative-id":["90"],"URL":"https:\/\/doi.org\/10.1007\/s12351-010-0090-2","relation":{},"ISSN":["1109-2858","1866-1505"],"issn-type":[{"value":"1109-2858","type":"print"},{"value":"1866-1505","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,24]]}}}