A novel solving method for multi-objective decision making problems under fuzzy conditions
Subject Areas : Operation ResearchAlireza Alinezhad 1 , Abolfazl Kazemi 2 , Mojgan Khorasani 3
1 - Associate Professor, Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin branch, Islamic Azad University, Qazvin, Iran.
2 - Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3 - Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Keywords: goal programming, Multiple Objective Optimization, Relative Importance, Satisfying Optimization,
Abstract :
This paper proposes a satisfying optimization method for fuzzy multiple objective optimization problem. Actually, the presented method realizes the trade-off between optimization and fuzzy importance requirement. Generally, the main aim of the presented approach is to make the more important objective achieving the higher desirable satisfying degree. In practice, vagueness and imprecision of the goals, constraints and parameters in this problem make the decision-making complicated for decision makers who have to deal with the parameters to make the optimized decision. Hence, the reformulated optimization models based on goal programming is proposed for different fuzzy relations and fuzzy importance. In fact, decision makers can select the appropriate alternative considering their determinations from variety of solutions using parameter λ. Applying the proposed model, not only the satisfying results of all the objectives can be acquired, but also the fuzzy importance requirement can be simultaneously actualized. In addition, a numerical example is provided to illustrate how the model is applied. Finally, the conclusions and recommendations are presented.
Aköz, O., & Petrovic, D. (2007). A fuzzy goal programming method with imprecise goal hierarchy. European journal of operational research, 181(3), 1427-1433.
Alikhani, R., & Azar, A. (2013). A combined goal programming model for gas resources allocation under uncertainty. Advances in Fuzzy Sets and Systems, 15(1), 17.
Alikhani, R., & Azar, A. (2015). A hybrid fuzzy satisfying optimization model for sustainable gas resources allocation. Journal of Cleaner Production, 107, 353-365.
Alinezhad, A. (2016). An Integrated DEA and Data Mining Approach for Performance Assessment. Iranian Journal of Optimization, 8(2), 59-69.
Alinezhad, A., & Taherinezhad, A. (2020). Control Chart Recognition Patterns Using Fuzzy Rule-Based System. Iranian Journal of Optimization, 12(2), 149-160.
Amini, A., & Alinezhad, A. (2016). A combined evaluation method to rank alternatives based on VIKOR and DEA with belief structure under uncertainty. Iranian Journal of Optimization, 8(2), 111-122.
Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), B-141.
Biuki, M., Kazemi, A., & Alinezhad, A. (2020). An integrated location-routing-inventory model for sustainable design of a perishable products supply chain network. Journal of Cleaner Production, 260, 120842.
Chankong, V., & Haimes, Y. Y. (1983). Multiobjective decision making: theory and methodology. Courier Dover Publications.
Charnes, A., & Cooper, W. W. (1961). Management Models and Industrial Applications of Linear Programming, Vol. 1. John Wiley, New York.
Chen, L. H., & Tsai, F. C. (2001). Fuzzy goal programming with different importance and priorities. European journal of operational research, 133(3), 548-556.
Cai, Y. P., Huang, G. H., Tan, Q., & Yang, Z. F. (2009). Planning of community-scale renewable energy management systems in a mixed stochastic and fuzzy environment. Renewable energy, 34(7), 1833-1847.
Çakır, E., & Ulukan, H. Z. (2019, July). Fuzzy multi-objective decision making approach for nuclear power plant installation. In International Conference on Intelligent and Fuzzy Systems (pp. 1258-1265). Springer, Cham.
Daim, T. U., Kayakutlu, G., & Cowan, K. (2010). Developing Oregon’s renewable energy portfolio using fuzzy goal programming model. Computers & Industrial Engineering, 59(4), 786-793.
Goodrich, M. A., Stirling, W. C., & Frost, R. L. (1998). A theory of satisficing decisions and control. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 28(6), 763-779.
Hannan, E. L. (1981). Linear programming with multiple fuzzy goals. Fuzzy sets and systems, 6(3), 235-248.
Hu, C., & Li, S. (2006). Enhanced interactive satisfying optimization approach to multiple objective optimization with preemptive priorities. International Journal of Information Technology & Decision Making, 5(01), 47-63.
Ijiri, Y. (1965). Management goals and accounting for control (Vol. 3). North Holland Publishing Company.
Jinturkar, A. M., & Deshmukh, S. S. (2011). A fuzzy mixed integer goal programming approach for cooking and heating energy planning in rural India. Expert Systems with Applications, 38(9), 11377-11381.
Kaya, T., & Kahraman, C. (2011). Multicriteria decision making in energy planning using a modified fuzzy TOPSIS methodology. Expert Systems with Applications, 38(6), 6577-6585.
Kahraman, C., Kaya, İ., & Cebi, S. (2009). A comparative analysis for multiattribute selection among renewable energy alternatives using fuzzy axiomatic design and fuzzy analytic hierarchy process. Energy, 34(10), 1603-1616.
Kaya, T., & Kahraman, C. (2010). Multicriteria renewable energy planning using an integrated fuzzy VIKOR & AHP methodology: The case of Istanbul. Energy, 35(6), 2517-2527.
Lai, Y. J., & Hwang, C. L. (1994). Fuzzy multiple objective decision making. In Fuzzy multiple objective decision making (pp. 139-262). Springer, Berlin, Heidelberg.
Li, Y. F., Li, Y. P., Huang, G. H., & Chen, X. (2010). Energy and environmental systems planning under uncertainty—an inexact fuzzy-stochastic programming approach. Applied Energy, 87(10), 3189-3211.
Li, S., Yang, Y., & Teng, C. (2004). Fuzzy goal programming with multiple priorities via generalized varying-domain optimization method. IEEE Transactions on Fuzzy Systems, 12(5), 596-605.
Lin, C. C. (2004). A weighted max–min mod for fuzzy goal programming. Fuzzy sets and systems, 142(3), 407-420.
Liu, B.(2002). Theory and practice of uncertain programming (Vol. 239). Berlin: Springer.
Majidi, M., Nojavan, S., Esfetanaj, N. N., Najafi-Ghalelou, A., & Zare, K. (2017). A multi-objective model for optimal operation of a battery/PV/fuel cell/grid hybrid energy system using weighted sum technique and fuzzy satisfying approach considering responsible load management. Solar Energy, 144, 79-89.
Mavrotas, G., Diakoulaki, D., Florios, K., & Georgiou, P. (2008). A mathematical programming framework for energy planning in services’ sector buildings under uncertainty in load demand: The case of a hospital in Athens. Energy policy, 36(7), 2415-2429.
Narasimhan, R. (1980). Goal programming in a fuzzy environment. Decision sciences, 11(2), 325-336.
Nouri, A., Khodaei, H., Darvishan, A., Sharifian, S., & Ghadimi, N. (2018). RETRACTED: Optimal performance of fuel cell-CHP-battery based micro-grid under real-time energy management: An epsilon constraint method and fuzzy satisfying approach.
Pal, B. B., & Moitra, B. N. (2003). A goal programming procedure for solving problems with multiple fuzzy goals using dynamic programming. European Journal of Operational Research, 144(3), 480-491.
Sakawa, M., Kato, K., & Katagiri, H. (2004). An interactive fuzzy satisficing method for multiobjective linear programming problems with random variable coefficients through a probability maximization model. Fuzzy sets and systems, 146(2), 205-220.
Sakawa, M., Yano, H., & Yumine, T. (1987). An interactive fuzzy satisficing method for multiobjective linear-programming problems and its application. IEEE Transactions on Systems, Man, and Cybernetics, 17(4), 654-661.
Sarrafha, K., Kazemi, A., & Alinezhad, A. (2014). A multi-objective evolutionary approach for integrated production-distribution planning problem in a supply chain network. Journal of Optimization in Industrial Engineering, 7(14), 89-102.
Steuer, R. E. (1986). Multiple criteria optimization. Theory, computation and applications.
Su, T. S., & Wu, C. C. (2020). A fuzzy multi-objective decision system for recoverable remanufacturing planning. Journal of Information and Optimization Sciences, 42(1), 135-154.
Tabrizi, N., Babaei, E., & Mehdinejad, M. (2016). An interactive fuzzy satisfying method based on particle swarm optimization for multi-objective function in reactive power market. Iranian Journal of Electrical and Electronic Engineering, 12(1), 65-72.
Tanaka, H., Okuda, T., & Asai, K. (1974). Fuzzy mathematical programming. Transactions of the society of instrument and control engineers, 9(5), 607-613.
Tiwari, R. N., Dharmar, S., & Rao, J. R. (1986). Priority structure in fuzzy goal programming. Fuzzy sets and systems, 19(3), 251-259.
Tiwari, R. N., Dharmar, S., & Rao, J. (1987). Fuzzy goal programming—an additive model. Fuzzy sets and systems, 24(1), 27-34.
Yang, J. B. (2000). Minimax reference point approach and its application for multiobjective optimisation. European Journal of Operational Research, 126(3), 541-556.
Yang, J. B., & Sen, P. (1996). Preference modelling by estimating local utility functions for multiobjective optimization. European Journal of Operational Research, 95(1), 115-138.
Yu, P.L. (1985). ‘Multi-criteria Decision Making: Concepts, Techniques, and Extensions’, Plenum, New York.
Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), 45-55.