Abstract
In this paper a fuzzifying approach is proposed to cope with vagueness appearing in the objecdtives and the constraints of linear as well as of a class of nonlinear stochastic programming problems. An interactive procedure has also been proposed to assist the decision maker in obtaining satisficing solutions of stochastic programming problems using this approach.
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References
BRACKEN, J. AND MCCORMIC, G. R “Selected applications of nonlinear programming”, John Wiley & Sons. New York (1968).
CHAKRABORTY D., RAO, J.R. And TIWARI R.N. “Interactive decision making in mixed (fuzzy and stochastic) environment”, Opsearch, 31, 89–107, (1994).
DELGALO, D., KACPRZYK, J., VERDEGAY, J.L. AND VILA, M.A. (Eds) Tuzzy optimization: Recent advances”, Physica Verlag. Germany, (1994).
GOICOECHEA, A., HANSEN, D.R. AND DUCKSTEIN, L. “Multiobjective decision making wsith engineering and business applications”, John Wiley & Sons, New York, (1982).
INUGUCHI, M. AND SAKAWA, M. “A possibilistic linear program is equivalent to a stochastic linear program in a special case”, Tuzzy Sets and Systems, 76, 309–317, (1995).
MOHAN, C. and NGUYEN, H.T “A controlled random search technique for global optimization incorporating simulated annealing concept”, submitted for publication in The Journal of Global Optimization (1996a).
MOHAN, C. AND NGUYEN, H.T. “A controlled random search technique incorporated simulated annealing concept for solving integer and mixed integer global optimization problems”, submitted for publication in Computational Optimization and Applications (1996 b).
MOHAN C. AND SHANKER, K. “A control random search technique for global optimization using quadratic approximation”, Asia-Pacific Journal of Operational Research, 11, 93–101, (1994).
NGUYEN, H.T. “Some global optimization techniques and their use in solving optimization problems in crisp and fuzzy environments”, Ph.D. Thesis submitted in Department of Mathematics, University of Roorkee, India, (1996).
PRICE, W.L. “Global optimization by controlled random search”, Journal of Optimization: Theory and Applications, 40, 333–348, (1983).
ROMMELFANGER, H. “Tulfal — An interactive method for solving multiobjective fuzzy linear programming problems”, in Slowinski, R. AND Teghem, J. (Eds.) “Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty”. Kluwer Academic Publisher, Dordrecht, Holland, 279–299, (1990).
ROUBENS, M. AND TEGHEM, J. “Comparison of methodologies for fuzzy and stochastic multiobjective programming”, Fuzzy Sets and Systems, 42, 119–132, (1991).
SAKAWA, M. “Fuzzy sets and interactive multiobjective optimization”, Plenum Press, New York, (1993).
SLOWINSKI, R. AND TEGHEM, J. (Eds.) “Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty”, Lluwer Academic Publishers, Dordrecht, Holland, (1990).
STANCU-MINASIAN, I.M. “Stochastic programming with multiple objective functions”, D. Reidel, Dordrecht, Holland, (1984).
STANCU-MINASIAN, I.M. “Overview of different approaches for solving stochastic programming problems with multiple objective functions”, In Slowinski, T. AND Teghem, J. (Eds.) “Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty”, Kluwer Academic Publisher, Dordrecht, Holland, 103–116, (1990).
ZADEH, L.A. “Fuzzy sets”, Information and Control, 8, 338–353, (1965).
ZIMMERMANN, H.J. “Fuzzy set, decision making and expert systems”, Kluwer Academic Publisher, Dordrecht, Holland, (1987).
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Mohan, C., Nguyen, H.T. A Fuzzifying Approach to Stochastic Programming. OPSEARCH 34, 73–96 (1997). https://doi.org/10.1007/BF03398512
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DOI: https://doi.org/10.1007/BF03398512