A method for capturing the entire fuzzy non-dominated set of a fuzzy multi-criteria optimization problem

Fuzzy Sets and Systems - Tập 272 - Trang 1-29 - 2015
Debdas Ghosh1, Debjani Chakraborty2
1Department of Mathematics, Birla Institute of Technology & Science, Pilani-Hyderabad, Secunderabad, Telengana 500078, India
2Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, West Bengal, India

Tài liệu tham khảo

Arenas Parra, 1999, Solving the multiobjective possibilistic linear programming problem, Eur. J. Oper. Res., 117, 175, 10.1016/S0377-2217(98)00160-X Bellman, 1970, Decision making in a fuzzy environment, Manag. Sci., 17, B141, 10.1287/mnsc.17.4.B141 Benouaret, 2011, Top-k web service compositions using fuzzy dominance relationship, 144 Branke, 2004, Finding knees in multi-objective optimization, vol. 3242, 722 Bravo, 2009, Applying stochastic goal programming: a case study on water use planning, Eur. J. Oper. Res., 196, 1123, 10.1016/j.ejor.2008.04.034 Canto, 2008, Application of benders decomposition to power plant preventive maintenance scheduling, Eur. J. Oper. Res., 184, 759, 10.1016/j.ejor.2006.11.018 Carlsson, 1996, Fuzzy multiple criteria decision making: recent developments, Fuzzy Sets Syst., 78, 139, 10.1016/0165-0114(95)00165-4 Chakraborty, 2014, Analytical fuzzy plane geometry II, Fuzzy Sets Syst., 243, 84, 10.1016/j.fss.2013.06.016 Chang, 1997, A fuzzy multi-objective programming approach for optimal management of the reservoir watershed, Eur. J. Oper. Res., 99, 289, 10.1016/S0377-2217(96)00019-7 Das, 1999, On characterizing the “knee” of the Pareto curve based on normal-boundary intersection, Struct. Optim., 18, 107, 10.1007/s001580050111 Deb, 2011, Understanding knee points in bicriteria problems and their implications as preferred solution principles, Eng. Optim., 43, 1175, 10.1080/0305215X.2010.548863 Dias, 1988, The R & D project selection problem with fuzzy coefficients, Fuzzy Sets Syst., 26, 299, 10.1016/0165-0114(88)90125-X Durbach, 2012, Modeling uncertainty in multi-criteria decision analysis, Eur. J. Oper. Res., 223, 1, 10.1016/j.ejor.2012.04.038 Ehrgott, 2005, Multicriteria Optimization, vol. 491 Farina, 2004, A fuzzy definition of “optimality” for many-criteria optimization problems, IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum., 34, 315, 10.1109/TSMCA.2004.824873 Ganguly, 2013, Multi-objective particle swarm optimization based on fuzzy-pareto-dominance for possibilistic planning of electrical distribution systems incorporating distributed generation, Fuzzy Sets Syst., 213, 47, 10.1016/j.fss.2012.07.005 Ghosh, 2012, Analytical fuzzy plane geometry I, Fuzzy Sets Syst., 209, 66, 10.1016/j.fss.2012.02.011 Ghosh, 2013, Fuzzy ideal cone: a method to obtain complete fuzzy non-dominated set of fuzzy multi-criteria optimization problems with fuzzy parameters, 1 Ghosh, 2013, On fuzzy ideal cone method to capture entire fuzzy non-dominated set of fuzzy multi-criteria optimization problems with fuzzy parameters Ghosh, 2014, A direction based classical method to obtain complete pareto set of multi-criteria optimization problems, Opsearch Ghosh, 2014, A new method to obtain fuzzy pareto set of fuzzy multi-criteria optimization problems, J. Intell. Fuzzy Syst., 26, 1223, 10.3233/IFS-130808 Ghosh, 2015, Analytical fuzzy plane geometry III, Fuzzy Sets Syst. Inuiguchi, 1992, Solution concepts for fuzzy multiple objective programming problems, Jpn. J. Fuzzy Theory Syst., 4, 97 Inuiguchi, 1996, Possible and necessary efficiency in possibilistic multiobjective linear programming problems and possible efficiency test, Fuzzy Sets Syst., 78, 231, 10.1016/0165-0114(95)00169-7 Jiménez, 2007, Linear programming with fuzzy parameters: an interactive method resolution, Eur. J. Oper. Res., 177, 1599, 10.1016/j.ejor.2005.10.002 Jiménez, 2009, Pareto-optimal solutions in fuzzy multi-objective linear programming, Fuzzy Sets Syst., 160, 2714, 10.1016/j.fss.2008.12.005 Kahraman, 2008 Köppen, 2004, A fuzzy scheme for the ranking of multivariate data and its application, 140 Köppen, 2005, Fuzzy-pareto-dominance and its application in evolutionary multi-objective optimization, 399 Kundu, 2011, Multi-objective optimization with artificial weed colonies, Inf. Sci., 181, 2441, 10.1016/j.ins.2010.09.026 Lai, 1994, Fuzzy Multiple Objective Decision Making: Methods and Applications, vol. 404 Luhandjula, 1987, Multiple objective programming problems with possibilistic coefficients, Fuzzy Sets Syst., 21, 135, 10.1016/0165-0114(87)90159-X Luhandjula, 2014, An approach for solving a fuzzy multiobjective programming problem, Eur. J. Oper. Res., 232, 249, 10.1016/j.ejor.2013.05.040 Maeda, 2008, On characterization of fuzzy vectors and its applications to fuzzy mathematical programming problems, Fuzzy Sets Syst., 159, 3333, 10.1016/j.fss.2008.02.004 Marler, 2004, Survey of multi-objective optimization methods for engineering, Struct. Multidiscip. Optim., 26, 369, 10.1007/s00158-003-0368-6 Nasir, 2012, An improved multi-objective optimization algorithm based on fuzzy dominance for risk minimization in biometric sensor network, 399 Orlovsky, 1978, Decision-making with a fuzzy preference relation, Fuzzy Sets Syst., 1, 155, 10.1016/0165-0114(78)90001-5 Osman, 1993, Stability of multiobjective nonlinear programming problems with fuzzy parameters, Math. Comput. Simul., 35, 321, 10.1016/0378-4754(93)90062-Y Pascoletti, 1984, Scalarizing vector optimization problems, J. Optim. Theory Appl., 42, 499, 10.1007/BF00934564 Peng, 2005, Fuzzy dominance based on credibility distributions, vol. 3613, 295 Rachmawati, 2006, A multi-objective evolutionary algorithm with weighted-sum niching for convergence on knee regions, 749 Ramík, 2007, Optimal solutions in optimization problem with objective function depending on fuzzy parameters, Fuzzy Sets Syst., 158, 1873, 10.1016/j.fss.2007.04.003 Sahoo, 2012, Fuzzy-pareto-dominance driven possibilistic model based planning of electrical distribution systems using multi-objective particle swarm optimization, Expert Syst. Appl., 39, 881, 10.1016/j.eswa.2011.07.086 Sakawa, 1991, Feasibility and pareto optimality for multiobjective nonlinear programming problems with fuzzy parameters, Fuzzy Sets Syst., 43, 1, 10.1016/0165-0114(91)90017-K Sengupta, 2011, An improved multi-objective algorithm based on decomposition with fuzzy dominance for deployment of wireless sensor networks, vol. 7076, 688 Serafinska, 2012, A multi-objective optimization approach with a view to robustness improvement, 483 Silva, 2011, The use of possibility theory in the definition of fuzzy pareto-optimality, Fuzzy Optim. Decis. Mak., 10, 11, 10.1007/s10700-010-9092-z Słowiński, 1986, A multicriteria fuzzy linear programming method for water supply system development planning, Fuzzy Sets Syst., 19, 217, 10.1016/0165-0114(86)90052-7 Słowiński, 1990 Smaling, 2005 Smaling, 2004, Fuzzy pareto frontiers in multidisciplinary system architecture analysis, 1 Takeda, 1980, Multiple criteria decision problems with fuzzy domination structures, Fuzzy Sets Syst., 3, 123, 10.1016/0165-0114(80)90050-0 Trautmann, 2009, Pareto-dominance in noisy environments, 3119 Triantis, 2003, Fuzzy pair-wise dominance and fuzzy indices: an evaluation of productive performance, Eur. J. Oper. Res., 144, 412, 10.1016/S0377-2217(02)00141-8 Wang, 2009, Mathematics of Fuzziness – Basic Issues, vol. 245