Abstract
A definition of the degree to which a normalized convex fuzzy number is greater or equal to another fuzzy number is proposed which satisfies the Ferrer’s condition and consequently the max-min transitivity.
It is based on the compensation of areas determined by the membership functions.
Using the fuzzy preference relation, one can handle inequality constraints, the related conditions being free from any parametrization.
The particular case of L — R fuzzy numbers is considered and its is proved that in this case, comparison of areas is reduced to the comparison of upper and lower bounds of α-cuts.
Two examples related to comparison of fuzzy numbers and fuzzy optimization are also presented.
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References
Baldwin, F.F. and Guild, N.C.F. (1979) Comparison of fuzzy sets on the same decision space’, Fuzzy Sets and Systems 2, 213–231.
Dubois, D. and Pralle, H. (1980) Systems of linear fuzzy constraints’, Fuzzy Sets and Systems 3, 37–48.
Nakamura, I (1986) Preference relations on a set of fuzzy utilities’, Fuzzy Sets and Systems 20, 147–162.
Ramik, J. and Rimanek, J. (1985) Inequality relation between fuzzy numbers and its use in fuzzy optimization’, Fuzzy Sets and Systems 16, 123–138.
Roubens, M. (1986) Comparison of flat fuzzy numbers’, in N. Bandler and A. Kandel (eds.), Proceedings of NAFIPS’86, pp. 462–476.
Roubens, M. and Vincke, P. (1988) Fuzzy possibility graphs and their application to ranking fuzzy numbers’. in J. Kacprzyk and M. Roubens (eds.). Non-conventional Preference Relations in Decision Making, Springer-Verlag, pp.119128.
Slowinski, R. (1986) A multicriteria fuzzy linear programming method for supply system development planning’, Fuzzy Sets and Systems 19, 217–237.
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© 1990 Kluwer Academic Publishers
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Roubens, M. (1990). Inequality Constraints between Fuzzy Numbers and Their Use in Mathematical Programming. In: Slowinski, R., Teghem, J. (eds) Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty. Theory and Decision Library, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2111-5_16
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DOI: https://doi.org/10.1007/978-94-009-2111-5_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7449-0
Online ISBN: 978-94-009-2111-5
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