zbMATH — the first resource for mathematics

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 New York · Zbl 0444.94049
[5] Fung, L.W.; Fu, K.S., An axiomatic approach to rational decision-making in a fuzzy environment, () · 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 New York · Zbl 0093.31708
[9] Luce, R.D.; Suppes, P., Preferences, utility and subjective probability, ()
[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, () · Zbl 0374.90059
[13] Zadeh, L.A., Fuzzy sets, Information and control, 8, 338-353, (1965) · Zbl 0139.24606
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.