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An interactive satisficing method for solving multiobjective mixed fuzzy-stochastic programming problems. (English) Zbl 1002.90109
Summary: In this paper an interactive satisficing method (named PRELIME) is proposed for solving mixed fuzzy-stochastic multiobjective programming problems. The proposed method can be used to solve linear as well as a class of nonlinear multiobjective problems in mixed fuzzy-stochastic environment wherein various kinds of uncertainties related to fuzziness and/or randomness are present. In this method a fuzzifying approach has been proposed which treats the stochastic objectives on the basis of extended E-model and the stochastic constraints as fuzzified chance constraints. As a result of this the stochastic objectives as well as the stochastic constraints are treated in a fuzzy environment providing an opportunity to the decision maker to trade-off fuzzy as well as stochastic objectives and constraints during the interactive process of search for a satisficing solution. The use of the method has been illustrated on some test examples taken from literature.

MSC:
90C70Fuzzy programming
Software:
FULPAL
WorldCat.org
Full Text: DOI
References:
[1] Chakraborty, D.; Rao, J. R.; Tiwari, R. N.: Interactive decision making in mixed (fuzzy and stochastic) environment. Opsearch 31, 89-107 (1994) · Zbl 0815.90101
[2] D. Delgalo, J. Kacprzyk, J.L. Verdegay, M.A. Vila (Eds.), Fuzzy optimization: Recent advances, Physica Verlag, Germany, 1994.
[3] M. Fedrizzi, J. Kacprzyk, M. Roubens (Eds.), Interactive fuzzy optimization, Lecture Notes in Economics and Mathematical Systems, vol. 368, 1991. · Zbl 0754.00004
[4] Goicoechea, A.; Hansen, D. R.; Duckstein, L.: Multiobjective decision making with engineering and business applications. (1982) · Zbl 0584.90045
[5] Inuiguchi, M.; Sakawa, M.: A possibilistic linear program is equivalent to a stochastic linear program in a special case. Fuzzy sets and systems 76, 309-317 (1995) · Zbl 0856.90131
[6] (a) C. Mohan, H.T. Nguyen, A fuzzifying approach to stochastic programming, Opsearch 34 (1997) 73--96. (b) C. Mohan, H.T. Nguyen, Reference direction interactive method for solving multiobjective fuzzy programming problems, European J. Oper. Res. 107 (1998) 599--613. · Zbl 0904.90124
[7] C. Mohan, H.T. Nguyen, A controlled random search technique incorporating simulated annealing concept for solving integer and mixed integer global optimization problems, Comput. Optim. Appl. (1997), accepted for publication. · Zbl 0970.90053
[8] Mohan, C.; Shanker, K.: A controlled random search technique for global optimization using quadratic approximation. Asia-Pacific J. Oper. res. 11, 93-101 (1994) · Zbl 0807.90104
[9] Nguyen, H. T.: Some global optimization techniques and their use in solving optimization problems in crisp and fuzzy environments, ph.d. Thesis. (1996)
[10] Price, W. L.: Global optimization by controlled random search. J. optim. Theory appl. 40, 333-348 (1983) · Zbl 0494.90063
[11] Rommelfanger, H.: FULPAL -- an interactive method for solving multiobjective fuzzy linear programming problems. Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, 279-299 (1990) · Zbl 0734.90120
[12] Rommelfanger, H.: Stochastic programming with vague data. Ann. univ. Sci. Budapest, sect. Comput. 12, 213-221 (1991) · Zbl 0885.90118
[13] Roubens, M.; Teghem, J.: Comparison of methodologies for fuzzy and stochastic multiobjective programming. Fuzzy sets and systems 42, 119-132 (1991) · Zbl 0744.90102
[14] Sakawa, M.: Fuzzy sets and interactive multiobjective optimization. (1993) · Zbl 0842.90070
[15] Sakawa, M.; Yano, H.: An interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. Fuzzy sets and systems 30, 221-238 (1989) · Zbl 0676.90078
[16] Slowinski, R.: Flipan interactive method for multiobjective linear programming with fuzzy parameters. Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, 249-262 (1990)
[17] Slowinski, R.; Teghem, J.: Comparison study of STRANGE and FLIP. Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, 365-396 (1990) · Zbl 0724.00033
[18] R. Slowinski, J. Teghem (Eds.), Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming Under Uncertainty, Kluwer Academic Publishers, Dordrecht, 1990. · Zbl 0724.00033
[19] Stancu-Minasian, I. M.: Stochastic programming with multiple objective functions. (1984) · Zbl 0554.90069
[20] Teghem, J.: STRANGE -- an interactive method for multiobjective stochastic linear programming and STRANGE-MONIX -- its extension to integer variables. Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty, 103-116 (1990)
[21] Zimmermann, H. J.: Fuzzy set, decision making and expert systems. (1987)