Fuzzy preference orderings in group decision making. (English) Zbl 0567.90002

An \(n\times n\) matrix \(R=[r_{ij}]\) with \(0\leq r_{ij}\leq 1\) and satisfying additional conditions determines various types of fuzzy preference orderings on a set of alternatives \((x_ 1,...,x_ n)\). \(r_{ij}\) represents the degree of preference of the alternative \(x_ i\) to the alternative \(x_ j\). From individual fuzzy preference orderings \(R^ p\) \((p=1,...,m)\) a group preference ordering R can be constructed. Several constructions are given in order that the final group ordering R shall again be fuzzy. The group matrix R can be used as data for the extended contributive rule method developed by the author and his collaborators.
Reviewer: J.Sustal


91B08 Individual preferences
03E72 Theory of fuzzy sets, etc.
91B16 Utility theory
Full Text: DOI


[1] Bezdek, J. C.; Spillman, B.; Spillman, R., A fuzzy relation space for group decision theory, Fuzzy Sets and Systems, 1, 255-268 (1978) · Zbl 0398.90009
[2] Bezdek, J. C.; Spillman, B.; Spillman, R., Fuzzy relation spaces for group decision theory: an application, Fuzzy Sets and Systems, 2, 5-14 (1979) · Zbl 0407.90003
[3] Blin, J. M., Fuzzy relation in group decision theory, J. Cybernetics, 4, 17-22 (1974) · Zbl 0363.90011
[4] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049
[5] Fung, L. W.; Fu, K. S., An axiomatic approach to rational decision-making in a fuzzy environment, (Zadeh, A. L.; etal., Fuzzy Sets and Their Applications to Cognitive and Decision Process (1975), Academic Press: Academic Press New York) · Zbl 0366.90003
[6] Kuz’min, V. B.; Ovchinnikov, S. V., Group decisions I. In arbitrary spaces of fuzzy binary relations, Fuzzy Sets and Systems, 4, 53-62 (1980) · Zbl 0435.90018
[7] Kuz’min, V. B.; Ovchinnikov, S. V., Design of group decisions II. In spaces of partial order fuzzy relations, Fuzzy Sets and Systems, 4, 153-165 (1980) · Zbl 0444.90007
[8] Luce, R. D., Individual Choice Behavior: A Theoretic Analysis (1959), Wiley: Wiley New York · Zbl 0093.31708
[9] Luce, R. D.; Suppes, P., Preferences, utility and subjective probability, (Luce, R. D.; etal., Handbook of Mathematical Psychology, Vol. III (1965), Wiley: Wiley New York)
[10] Nakayama, H.; Tanino, T.; Matsumoto, K.; Matsuo, H.; Inoue, K.; Sawaragi, Y., Methodology for group decision making with an application to assessment of residential environment, IEEE Trans. Systems Man Cybernet, 9, 477-485 (1979) · Zbl 0422.90008
[11] Nurmi, H., Approaches to collective decision making with fuzzy preference relations, Fuzzy Sets and Systems, 6, 249-259 (1981) · Zbl 0465.90006
[12] Tanino, T.; Nakayama, H.; Sawaragi, Y., On methodology for group decision support, (Morse, J. N., Organizations: Multiple Agents with Multiple Criteria (1981), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0374.90059
[13] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606
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