Abstract
Uncertain random variables are used to describe the phenomenon of simultaneous appearance of both uncertainty and randomness in a complex system. For modeling multi-objective decision-making problems with uncertain random parameters, a class of uncertain random optimization is suggested for decision systems in this paper, called the uncertain random multi-objective programming. For solving the uncertain random programming, some notions of the Pareto solutions and the compromise solutions as well as two compromise models are defined. Subsequently, some properties of these models are investigated, and then two equivalent deterministic mathematical programming models under some particular conditions are presented. Some numerical examples are also given for illustration.
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References
Abdelaziz, F. B., Aouni, B., & Fayedh, R. E. (2007). Multi-objective stochastic programming for portfolio selection. European Journal of Operational Research, 177(3), 1811–1823.
Badri, M. A., Mortagy, A. K., & Alsayed, C. A. (1998). A multi-objective model for locating fire stations. European Journal of Operational Research, 110(2), 243–260.
Beale, E. M. L. (1955). On minimizing a convex function subject to linear inequalities. Journal of the Royal Statistical Society, Series B, 17, 173–184.
Charnes, A., & Cooper, W. W. (1959). Chance-constrained programming. Management Science, 6, 73–80.
Dantzig, G. B. (1955). Linear programming under uncertainty. Management Science, 1, 197–206.
Gao, Y. (2012). Uncertain inference control for balancing inverted pendulum. Fuzzy Optimization and Decision Making, 11(4), 481–492.
Ke, H. (2012). Uncertain random multilevel programming with application to product control problem. http://orsc.edu.cn/online/121027.
Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.
Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Liu, B. (2009). Theory and practice of uncertain programming (2nd ed.). Berlin: Springer.
Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.
Liu, B. (2012). Why is there a need for uncertainty theory? Journal of Uncertain Systems, 6(1), 3–10.
Liu, B., & Chen, X.W. (2013). Uncertain multiobjective programming and uncertain goal programming. http://orsc.edu.cn/online/131020.
Liu, B., & Yao, K. (2012). Uncertain multilevel programming: Algorithm and applications. http://orsc.edu.cn/online/120114.
Liu, Y. H. (2013). Uncertain random variables: A mixture of uncertainty and randomness. Soft Computing, 17(4), 625–634.
Liu, Y. H. (2013). Uncertain random programming with applications. Fuzzy Optimization and Decision Making, 12(2), 153–169.
Nijkamp, P., & Rietveld, P. (1976). Multi-objective programming models: New ways in regional decision-making. Regional Science and Urban Economics, 6(3), 253–274.
Qin, Z. (2013). Uncertain random goal programming. http://orsc.edu.cn/online/130323.
Shapiro, A., & Philpott, A. (2007). A tutorial on stochastic programming, Manuscript. http://www2.isye.gatech.edu/~ashapiro/publications.html.
Tzeng, G. H., Cheng, H. J., & Huang, T. D. (2007). Multi-objective optimal planning for designing relief delivery systems. Transportation Research Part E: Logistics and Transportation Review, 43(6), 673–686.
Weber, C. A., & Ellram, L. M. (1993). Supplier selection using multi-objective programming: A decision support system approach. International Journal of Physical Distribution & Logistics Management, 23, 3–14.
Wu, D. D., Zhang, Y., Wu, D., & Olson, D. L. (2010). Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach. European Journal of Operational Research, 200(3), 774–787.
Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.
Zhang, X., Wang, Q., & Zhou, J. (2013). Two uncertain programming models for inverse minimum spanning tree problem. Industrial Engineering and Management Systems, 12(1), 9–15.
Zhou, J., Li, Z., & Wang, K. (2013). A multi-objective model for locating fire stations under uncertainty. Advances in Information Sciences and Service Sciences, 5(7), 1184–1191.
Acknowledgments
This work was supported in part by grants from the Ministry of Education Funded Project for Humanities and Social Sciences Research (No. 12JDXF005), the Innovation Program of Shanghai Municipal Education Commission (No. 13ZS065), and the National Social Science Foundation of China (No. 13CGL057).
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Zhou, J., Yang, F. & Wang, K. Multi-objective optimization in uncertain random environments. Fuzzy Optim Decis Making 13, 397–413 (2014). https://doi.org/10.1007/s10700-014-9183-3
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DOI: https://doi.org/10.1007/s10700-014-9183-3