Abstract
Uncertain variables are used to describe the phenomenon where uncertainty appears in a complex system. For modeling the multi-objective decision-making problems with uncertain parameters, a class of uncertain optimization is suggested for the decision systems in Liu and Chen (2013), http://orsc.edu.cn/online/131020 which is called the uncertain multi-objective programming. In order to solve the proposed uncertain multi-objective programming, an interactive uncertain satisficing approach involving the decision-maker’s flexible demands is proposed in this paper. It makes an improvement in contrast to the noninteractive methods. Finally, a numerical example about the capital budget problem is given to illustrate the effectiveness of the proposed model and the relevant solving approach.
Similar content being viewed by others
References
Aiello, G., Scalia, G. L., & Enea, M. (2013). A non-dominated ranking multi objective genetic algorithm and electre method for unequal area facility layout problems. Expert Systems with Applications, 40(12), 4812–4819.
Baril, C., Yacout, S., & Clément, B. (2012). An interactive multi-objective algorithm for decentralized decision making in product design. Optimization and Engineering, 12(1), 121–150.
Deep, K., Singh, K. P., Kansal, M. L., & Mohan, C. (2011). An interactive method using genetic algorithm for multi-objective optimization problems modeled in fuzzy environment. Expert Systems with Applications, 38(3), 1659–1667.
Gass, S., & Saaty, T. (1955). The computational algorithm for the parametric objective function. Naval Research Logistics Quarterly, 2(1–2), 39–45.
Haimes, Y. Y., & Chankong, V. (1979). Kuhn-tucker multipliers as trade-offs in multiobjective decision-making analysis. Automatica, 15(1), 59–72.
Haimes, Y. Y., Lasdon, L. S., & Wismer, D. A. (1971). On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Transactions on Systems, Man, and Cybernetics, 1(3), 296–297.
Huang, H. Z., Gu, Y. K., & Du, X. (2006). An interactive fuzzy multi-objective optimization method for engineering design. Engineering Applications of Artificial Intelligence, 19(5), 451–460.
Liang, T. F. (2006). Distribution planning decisions using interactive fuzzy multi-objective linear programming. Fuzzy Sets and Systems, 157(10), 1303–1316.
Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.
Liu, B. (2009a). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Liu, B. (2009b). 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. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications, 1, 1.
Liu, B. (2014). Uncertain random graph and uncertain random network. Journal of Uncertain Systems, 8(2), 3–12.
Liu, B., & Chen, X. W. (2013). Uncertain multiobjective programming and uncertain goal programming. http://orsc.edu.cn/online/131020
Liu, Y. H., & Ha, M. H. (2010). Expected value of function of uncertain variables. Journal of Uncertain Systems, 4(3), 181–186.
Niknam, T., Meymand, H. Z., & Mojarrad, H. D. (2011). An efficient algorithm for multi-objective optimal operation management of distribution network considering fuel cell power plants. Energy, 36(1), 119–132.
Peng, J., & Yao, K. (2011). A new option pricing model for stocks in uncertainty markets. International Journal of Operations Research, 8(2), 18–26.
Sakawa, M., & Yano, H. (1986). Interactive fuzzy decision making for multiobjective nonlinear programming using augmented minimax problems. Fuzzy Sets and Systems, 20(1), 31–43.
Sheng, Y. H., & Gao, J. (2014). Chance distribution of the maximum flow of uncertain random network. Journal of Uncertainty Analysis and Applications, 2, 15.
Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets and Systems, 159(2), 193–214.
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.
Xu, J., & Zhao, L. (2010). A multi-objective decision-making model with fuzzy rough coefficients and its application to the inventory problem. Information Sciences, 180(5), 679–696.
Yang, X., & Gao, J. (2013). Uncertain differential games with application to capitalism. Journal of Uncertainty Analysis and Applications, 1, 17.
Yang, X., & Gao, J. (2014). Uncertain core for coalitional game with uncertain payoffs. Journal of Uncertain Systems, 8(1), 13–21.
Yao, K., & Li, X. (2012). Uncertain alternating renewal process and its application. IEEE Transactions on Fuzzy Systems, 20(6), 1154–1160.
Yao, K. (2013a). Extreme values and integral of solution of uncertain differential equation. Journal of Uncertainty Analysis and Applications, 1, 2.
Yao, K. (2013b). A type of uncertain differential equations with analytic solution. Journal of Uncertainty Analysis and Applications, 1, 8.
Zadeh, L. A. (1963). Optimality and non-scalar-valued performance criteria. IEEE Transactions on Automatic Control, 8(1), 59–60.
Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1(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., Chen, L., & Wang, K. (2013). Path optimality conditions for minimum spanning tree problem with uncertain edge weights. http://orsc.edu.cn/online/131223
Zhou, J., Yang, F., & Wang, K. (2014). Multi-objective optimization in uncertain random environments. Fuzzy Optimization and Decision Making. doi:10.1007/s10700-014-9183-3.
Acknowledgments
This work was supported by Grants from the National Social Science Foundation of China (No. 13CGL057), the National Natural Science Foundation of China (No. 71272177), and the Innovation Program of Shanghai Municipal Education Commission (No. 13ZS065).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhong, S., Chen, Y., Zhou, J. et al. An interactive satisficing approach for multi-objective optimization with uncertain parameters. J Intell Manuf 28, 535–547 (2017). https://doi.org/10.1007/s10845-014-0998-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10845-014-0998-0