Abstract
The paper presents a microcomputer implementation of a visual interactive method, called ‘FLIP’”, for solving multi-objective linear programming (MOLP) problems with fuzzy coefficients in the objective functions and on the both sides of the constraints. It is a modified version of the ‘FLIP’ method (cf.Cżyzak,1990 and Slowinski,1990) which relies on a special comparison principle of fuzzy numbers in order to transform the fuzzy MOLP problem into an associate deterministic multi-objective linear fractional programming (MOLFP) problem. The modification consists in permitting a different interpretation of fuzzy objectives and constraints, which leads to an associate deterministic MOLP (instead of MOLFP) problem. The associate MOLP problem is then solved using an interactive sampling method. The efficient solutions of the associate MOLP problem are presented to the decision maker (DM) in terms of the original fuzzy objectives and constraints. The quality of these solutions can be evaluated by the DM from three following points of view: (a) scores of fuzzy objectives in relation to the goals, (b) possible dispersion of values of the fuzzy objectives due to uncertainty and (c) safety of solutions or risk of violation of the constraints. In order to support the evaluation, an appropriate graphical interface has been implemented.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cżyzak, P. (1989) ‘Multicriteria agricultural problem solving under uncertainty’. Foundations of Control Engineering 14,2, 61–80.
Cżyzak, P. (1990) ‘Application of the FLIP method to farm structure optimization problems’, in R. Slowinski, J. Teghem (eds.), ’stochastic vs. Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty’, Kluwer Academic Publishers, Dodrecht, 263–278.
Cżyzak, P. Słowiński, R.(1989) ‘Multiobjective diet optimization problem under fuzziness’, in J.L. Verdegay, M. Delgado (eds.), ‘The Interface between Artificial Intelligence and Operations Research in Fuzzy Environment’, Verlag TUV Rheinland, Köln, 85–103.
Cżyzak, P. Słowiński, R.(1990) ’solving Multiobjective Diet Optimization Problem under Uncertainty’, in: P. Korhonen, A. Lewandowski, J. Wallenius, (eds.) ‘Multiple Criteria Decision Support’, ser. Lecture Notes in Economics and Mathematical Systems, 356, Springer Verlag, Berlin/Heidelberg/New York.
Cżyzak, P. Słowiński, R.(1991) ‘FLIP — multiobjective fuzzy linear programming software with graphical facilities’, in: M. Fedrizzi, J. Kacprzyk, M. Roubens (eds.): ‘Interactive Fuzzy Optimization and Mathematical Programming’, Springer-Verlag, Berlin/Heidelberg/New York.
Słowiński, R. (1986) ‘A multicriteria fuzzy linear programming method for water supply system development planning’. Fuzzy Sets and Systems 19, 217–237.
Słowiński, R. (1987) ‘An interactive method for multiobjective linear programming with fuzzy parameters and its application to water supply planning’, in: J. Kacprzyk, S.A. Orlovski (eds.), ‘Optimization Models using Fuzzy Sets and Possibility Theory’, D. Reidel, Dordrecht, 396–414.
Słowiński, R. (1990) ‘“FLIP”: An interactive method for multiobjective linear programming with fuzzy coefficients’, in: R. Slowinski, J. Teghem (eds.), ’stochastic vs. Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty’, Kluwer Academic Publishers, Dordrecht, 249–262.
Słowiński, R., Teghem, J. (1988) ‘Fuzzy Versus Stochastic Approaches to Multicriteria Linear Programming under Uncertainty”, Naval Research Logistics, 35, 673–695.
Słowiński, R., Teghem, J., eds. (1990), Stochastic vs. Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, Theory and Decision Library, ser.D, Kluwer Academic Publishers, Dordrecht.
Słowiński, R., Urbaniak, A., Weglarz, J. (1987) ‘Probabilistic and fuzzy approaches to capacity expansion planning of a water supply system’, in: L. Valadares Tavares, J. Evaristo da Silva (eds.), ’systems Analysis Applied to Water and Related Land Resources’, Pergamon Press, Oxford, 93–98.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Czyzak, P., SlowiŃski, R. (1993). A Visual Interactive Method for Molp Problems with Fuzzy Coefficients. In: Lowen, R., Roubens, M. (eds) Fuzzy Logic. Theory and Decision Library, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2014-2_30
Download citation
DOI: https://doi.org/10.1007/978-94-011-2014-2_30
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4890-3
Online ISBN: 978-94-011-2014-2
eBook Packages: Springer Book Archive