A New Approach to Fuzzy Constraints in Linear Programming
In the article it is described a new proposal of the transformation of fuzzy constraints in linear programming problem with fuzzy coefficients for hard constraints using triparametric approach. As regards constraint coefficients, it is assumed that they are flat fuzzy numbers on the L-R representation. The method is a trial of generalization of possibilistic approach based on the Zadeh’s extension principle so that the nature of interpretation of fuzzy inequality can be graduated from the most optimistic to the most pessimistic interpretation. The proposed parameters of feasibility enable the person who decides to differentiate preferences in relation to particular constraints.
KeywordsMembership Function Fuzzy Number Linear Programming Problem Fuzzy Optimization Fuzzy Linear Programming
Unable to display preview. Download preview PDF.
- 5.Dubois D. (1987) Linear programming with fuzzy data. In: Bezdek J.C. (ed) Analysis of Fuzzy Information 3. CRC Press, Inc., Florida, 241–263Google Scholar
- 7.Dubois D., Prade H. (1983) Ranking fuzzy numbers in the setting of possibility theory. Information Science 30, New York, 183–224Google Scholar
- 8.Kacprzyk J. (1986) Fuzzy sets in system analysis. PWN, Warsaw (in polish)Google Scholar
- 9.Lee E.S., Li R.J. (1993) Fuzzy multiple objective programming and compromise programming with Pareto optimum. Fuzzy Sets and Systems 53, North-Holland, 275–288Google Scholar
- 13.Rommelfanger H. (1989) Inequality relations in fuzzy constraint and its use in linear fuzzy optimization. In: Verdegay J.L., Delgado M. (eds) The interface between artificial intelligence and operational research in fuzzy environment. Verlag TÜV Rheinland, Köln, 195–211Google Scholar
- 17.Sakawa M., Yano H. (1990c) Feasibility and Pareto optimality for multiobjective linear and linear fractional programming problems with fuzzy parameters. In: Verdegay J.L., Delgado M. (eds) The interface between artificial intelligence and operational research in fuzzy environment. Verlag TÜV Rheinland, Köln, 213–232Google Scholar