{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T12:44:31Z","timestamp":1778503471091,"version":"3.51.4"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,5,21]],"date-time":"2022-05-21T00:00:00Z","timestamp":1653091200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,5,21]],"date-time":"2022-05-21T00:00:00Z","timestamp":1653091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11401469"],"award-info":[{"award-number":["11401469"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Fuzzy Optim Decis Making"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s10700-022-09391-2","type":"journal-article","created":{"date-parts":[[2022,5,21]],"date-time":"2022-05-21T06:02:37Z","timestamp":1653112957000},"page":"247-265","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Optimality conditions for nonlinear optimization problems with interval-valued objective function in admissible orders"],"prefix":"10.1007","volume":"22","author":[{"given":"Lifeng","family":"Li","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,21]]},"reference":[{"key":"9391_CR1","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s10898-019-00841-7","volume":"77","author":"M Arana-Jim\u00e9nez","year":"2020","unstructured":"Arana-Jim\u00e9nez, M., & S\u00e1nchez-Gil, C. (2020). On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers. Journal of Global Optimization, 77, 27\u201352.","journal-title":"Journal of Global Optimization"},{"key":"9391_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69512-4","volume-title":"Differential inclusions","author":"JP Aubin","year":"1984","unstructured":"Aubin, J. P., & Cellina, A. (1984). Differential inclusions. New York: Springer."},{"key":"9391_CR3","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s00186-012-0399-0","volume":"76","author":"AK Bhurjee","year":"2012","unstructured":"Bhurjee, A. K., & Panda, G. (2012). Efficient solution of interval optimization problem. Mathematical Methods of Operations Research, 76, 273\u2013288.","journal-title":"Mathematical Methods of Operations Research"},{"key":"9391_CR4","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.fss.2012.07.015","volume":"220","author":"H Bustince","year":"2013","unstructured":"Bustince, H., Fernandez, J., Koles\u00e1rov\u00e1, A., & Mesiar, R. (2013). Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets and Systems, 220, 69\u201377.","journal-title":"Fuzzy Sets and Systems"},{"key":"9391_CR5","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/s10700-013-9156-y","volume":"12","author":"Y Chalco-Cano","year":"2013","unstructured":"Chalco-Cano, Y., Lodwick, W. A., & Rufian-Lizana, A. (2013). Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative. Fuzzy Optimization and Decision Making, 12, 305\u2013322.","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"9391_CR6","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.compstruc.2015.11.006","volume":"164","author":"J Cheng","year":"2016","unstructured":"Cheng, J., Liu, Z., Wu, Z., et al. (2016). Direct optimization of uncertain structures based on degree of interval constraint violation. Computers & Structures, 164, 83\u201394.","journal-title":"Computers & Structures"},{"key":"9391_CR7","doi-asserted-by":"publisher","first-page":"3183","DOI":"10.1016\/j.apm.2013.03.014","volume":"39","author":"R Ezzati","year":"2015","unstructured":"Ezzati, R., Khorram, E., & Enayati, R. (2015). A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem. Applied Mathematical Modelling, 39, 3183\u20133193.","journal-title":"Applied Mathematical Modelling"},{"key":"9391_CR8","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/j.apm.2018.12.025","volume":"69","author":"C Fu","year":"2019","unstructured":"Fu, C., Liu, Y., & Xiao, Z. (2019). Interval differential evolution with dimension- reduction interval analysis method for uncertain optimization problems. Applied Mathematical Modelling, 69, 441\u2013452.","journal-title":"Applied Mathematical Modelling"},{"key":"9391_CR9","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/j.neucom.2013.04.052","volume":"137","author":"DW Gong","year":"2014","unstructured":"Gong, D. W., Ji, X. F., Sun, J., & Sun, X. Y. (2014). Interactive evolutionary algorithms with decision-makers preferences for solving interval multi-objective optimization problems. Neurocomputing, 137, 241\u2013251.","journal-title":"Neurocomputing"},{"key":"9391_CR10","doi-asserted-by":"publisher","first-page":"108300","DOI":"10.1016\/j.ymssp.2021.108300","volume":"165","author":"HB Huang","year":"2022","unstructured":"Huang, H. B., Huang, X. R., Ding, W. P., et al. (2022). Uncertainty optimization of pure electric vehicle interior tire\/road noise comfort based on data-driven. Mechanical Systems and Signal Processing, 165, 108300.","journal-title":"Mechanical Systems and Signal Processing"},{"key":"9391_CR11","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/0377-2217(90)90375-L","volume":"48","author":"H Ishibuchi","year":"1990","unstructured":"Ishibuchi, H., & Tanaka, H. (1990). Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research, 48, 219\u2013225.","journal-title":"European Journal of Operational Research"},{"key":"9391_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2007.03.031","volume":"188","author":"C Jiang","year":"2008","unstructured":"Jiang, C., Han, X., Liu, G. R., & Liu, G. P. (2008). A nonlinear interval number programming method for uncertain optimization problems. European Journal of Operational Research, 188, 1\u201313.","journal-title":"European Journal of Operational Research"},{"key":"9391_CR13","doi-asserted-by":"publisher","first-page":"882","DOI":"10.1002\/mma.6796","volume":"44","author":"T Jin","year":"2021","unstructured":"Jin, T., Xia, H. X., & Chen, H. (2021a). Optimal control problem of the uncertain second-order circuit based on first hitting criteria. Mathematical Methods in the Applied Sciences, 44, 882\u2013900.","journal-title":"Mathematical Methods in the Applied Sciences"},{"key":"9391_CR14","doi-asserted-by":"publisher","first-page":"5955","DOI":"10.1007\/s00034-021-01761-2","volume":"40","author":"T Jin","year":"2021","unstructured":"Jin, T., Xia, H. X., Deng, W., et al. (2021b). Uncertain fractional-order multi-objective optimization based on reliability analysis and application to fractional-order circuit with caputo type. Circuits, Systems, and Signal Processing, 40, 5955\u20135982.","journal-title":"Circuits, Systems, and Signal Processing"},{"key":"9391_CR15","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1007\/s00158-018-2106-0","volume":"59","author":"A Kaveh","year":"2019","unstructured":"Kaveh, A., Dadras, A., & Geran Malek, N. (2019). Robust design optimization of laminated plates under uncertain bounded buckling loads. Structural and Multidisciplinary Optimization, 59, 877\u2013891.","journal-title":"Structural and Multidisciplinary Optimization"},{"key":"9391_CR16","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1016\/j.apm.2010.07.037","volume":"35","author":"A Kumar","year":"2011","unstructured":"Kumar, A., Kaur, J., & Singh, P. (2011). A new method for solving fully fuzzy linear programming problems. Applied Mathematical Modelling, 35, 817\u2013823.","journal-title":"Applied Mathematical Modelling"},{"key":"9391_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ins.2019.02.012","volume":"486","author":"DC Li","year":"2019","unstructured":"Li, D. C., Leung, Y., & Wu, W. Z. (2019). Multiobjective interval linear programming in admissible-order vector space. Information Sciences, 486, 1\u201319.","journal-title":"Information Sciences"},{"key":"9391_CR18","volume-title":"Interval methods for systems of equations","author":"A Neumaier","year":"1990","unstructured":"Neumaier, A. (1990). Interval methods for systems of equations. Cambridge: Cambridge University Press."},{"key":"9391_CR19","doi-asserted-by":"publisher","first-page":"106634","DOI":"10.1016\/j.cie.2020.106634","volume":"147","author":"MS Rahman","year":"2020","unstructured":"Rahman, M. S., Shaikh, A. A., & Bhunia, A. K. (2020). Necessary and sufficient optimality conditions for non-linear unconstrained and constrained optimization problem with interval valued objective function. Computers & Industrial Engineering, 147, 106634.","journal-title":"Computers & Industrial Engineering"},{"key":"9391_CR20","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.compstruc.2014.11.006","volume":"149","author":"R Santoro","year":"2015","unstructured":"Santoro, R., Muscolino, G., & Elishakoff, I. (2015). Optimization and anti-optimization solution of combined parameterized and improved interval analyses for structures with uncertainties. Computers & Structures, 149, 31\u201342.","journal-title":"Computers & Structures"},{"key":"9391_CR21","doi-asserted-by":"publisher","first-page":"1311","DOI":"10.1016\/j.na.2008.12.005","volume":"71","author":"L Stefanini","year":"2009","unstructured":"Stefanini, L. (2009). Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Analysis: Theory, Methods & Applications, 71, 1311\u20131328.","journal-title":"Nonlinear Analysis: Theory, Methods & Applications"},{"key":"9391_CR24","doi-asserted-by":"publisher","first-page":"113065","DOI":"10.1016\/j.cma.2020.113065","volume":"366","author":"LQ Wang","year":"2020","unstructured":"Wang, L. Q., Chen, Z. T., Yang, G. L., et al. (2020). An interval uncertain optimization method using back-propagation neural network differentiation. Computer Methods in Applied Mechanics and Engineering, 366, 113065.","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"9391_CR22","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.ejor.2005.09.007","volume":"176","author":"HC Wu","year":"2007","unstructured":"Wu, H. C. (2007). The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function. European Journal of Operational Research, 176, 46\u201359.","journal-title":"European Journal of Operational Research"},{"key":"9391_CR23","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s10700-018-9299-y","volume":"18","author":"HC Wu","year":"2019","unstructured":"Wu, H. C. (2019). Applying the concept of null set to solve the fuzzy optimization problems. Fuzzy Optimization and Decision Making, 18, 279\u2013314.","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"9391_CR25","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1080\/03081070600574353","volume":"35","author":"ZS Xu","year":"2006","unstructured":"Xu, Z. S., & Yager, R. R. (2006). Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems, 35, 417\u2013433.","journal-title":"International Journal of General Systems"}],"container-title":["Fuzzy Optimization and Decision Making"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10700-022-09391-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10700-022-09391-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10700-022-09391-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,27]],"date-time":"2023-04-27T02:38:29Z","timestamp":1682563109000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10700-022-09391-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,21]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["9391"],"URL":"https:\/\/doi.org\/10.1007\/s10700-022-09391-2","relation":{},"ISSN":["1568-4539","1573-2908"],"issn-type":[{"value":"1568-4539","type":"print"},{"value":"1573-2908","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,21]]},"assertion":[{"value":"24 April 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 May 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}