Abstract
This paper should be considered as an introduction to the fundamental properties of binary fuzzy relations. It summarizes some of the proposed definitions of a fuzzy preference relation, compares them and introduces the reader to the difficult problems of ranking and choice on the basis of a preference relation. The last part points out an important role of fuzzy relations in multicriteria analysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Brans, J.P., B. Mareschal, and Ph. Vincke (1984). PROMETHEE: a new family of outranking methods in Multicriteria Analysis. In J.P. Brans (ed.), Operational Research’84. North-Holland, Amsterdam. (Proc. of the Tenth IFORS Intern. Conference on Operational Research, Washington, D.C.).
Blin, J.M. (1974). Fuzzy relations in group decision theory. J. Cyber. 4, 17–22.
Doignon, J.P., B. Monjardet, M. Roubens, and Ph. Vincke (1985). Biorders families, valued relations and preference modelling. To appear.
Dubois, D., and H. Prade (1980). Fuzzy Sets and Systems: Theory and Applications. Academic Press, New-York.
Fishburn, P.C. (1973). Binary choice probabilities: on the varieties of stochastic transitivity. J. Math. Psychology 7, 327–352.
Hashimoto, H. (1983). Szpilrajn’s theorem on fuzzy ordering. Fuzzy Sets and Syst. 10, 101–108.
Kacprzyk, J. (1984). Collective decision making with a fuzzy majority. Proc. 5th WOGSC Congress. AFCET, Paris.
Kacprzyk, J. (1985). Some ‘commonsense’ solution concepts in group decision making using fuzzy linguistic quantifiers. In J. Kacprzyk and R.R. Yager (eds.), Management Decision Support Systems Using Fuzzy Sets and Possibility Theory. Verlag TUV Rheinland, Cologne.
Monjardet, B. (1984). Probabilistic consistency, homogeneous families of relations and linear ∧-relations. In E. Degreef and J. Van Buggenhaut (eds.) , Trends in Mathematical Psychology. North-Holland, Amsterdam, 271–281.
Orlovsky, S.A. (1978). Decision making with a fuzzy preference relation. Fuzzy Sets and Syst. 1, 155–167.
Orlovsky, S.A. (1984). Two Approaches to Multiobjective Programming Problems with Fuzzy Parameters. Working paper, 84–3 7, IIASA, Laxenburg.
Ovchinnikov, S.V. (1981). Structure of fuzzy binary relations. Fuzzy Sets and Syst, 6, 169–195.
Roberts, F.S. (1979). Measurement Theory. Addison-Wesley, Reading, Mass.
Roubens, M., and Ph. Vincke (1983). Linear fuzzy graphs. Fuzzy Sets and Syst. 10, 79–86.
Roubens, M., and Ph. Vincke (1984). On families of semiorders and interval orders imbedded in a valued structure of preference: a survey. Inf. Sci. 34, 187–198.
Roubens, M., and Ph. Vincke. Preference Modelling. Springer Verlag, Berlin. To appear.
Roy, B.(1969). Algebre Moderne et Theorie des Graphes Orientées vers les Sciences Economiques et Sociales, Dunod, Paris.
Roy, B. (1978) . ELECTRE III: a classification algorithm based on a fuzzy preference representation in the presence of multiple criteria (in French). Cahiers du C.E.R.O. 20, 3–24.
Roy, B., and J.C. Hugonnard (1985). A programming method for determining which Metro stations should be renovated. Eur. J. Op. Res.. 22.
Siskos, J., and Ph. Hubert (1983). A survey and a new comparative approach. Eur, J. Op. Res. 13, 278–299.
Siskos, J., J. Lochard, and J. Lombard (1984), A multi-criteria Decision-making methodology under fuzziness: application to the evaluation of radiological protection in nuclear power plants. In H.J. Zimmermann, L. Zadeh and B. Gaines (eds.), Fuzzy Sets and Decision Making. North-Holland, Amsterdam.
Takeda, E., and T. Nishida (1980). Multicriteria decision problems with fuzzy domination structures. Fuzzy Sets and Syst. 3, 123–136.
Zadeh, L.A. (1971). Similarity relations and fuzzy orderings. Inf. Sci. 3, 177–200.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Roubens, M., Vincke, P. (1987). Fuzzy Preferences in an Optimization Perspective. In: Kacprzyk, J., Orlovski, S.A. (eds) Optimization Models Using Fuzzy Sets and Possibility Theory. Theory and Decision Library, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3869-4_5
Download citation
DOI: https://doi.org/10.1007/978-94-009-3869-4_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8220-4
Online ISBN: 978-94-009-3869-4
eBook Packages: Springer Book Archive