Group decision making with a fuzzy linguistic majority. (English) Zbl 0604.90012

Considered is a collection of m individual fuzzy preference relations \(R_ k\), \(k=1,...,m\), where \(R_ k:\) \(S\times S\to [0,1]\) and S is a set of n alternatives \(S=\{s_ 1,...,s_ n\}\). The higher \(R_ k(s_ i,s_ j)\) the higher the preference of \(s_ i\) over \(s_ j\) for the individual k. A group decision making solution should reflect what a majority of individuals prefers. A fuzzy majority concept is introduced as a counterpart to the linguistic qualifier ”most”. Various approaches to the problem are then suggested leading to different solutions, e.g. the formalization of a property over S expressing ”most individuals are not against (an alternative)”.
Reviewer: J.Sustal


91B08 Individual preferences
91B14 Social choice
03E72 Theory of fuzzy sets, etc.
Full Text: DOI


[1] Arrow, K. J., Social Choice and Individual Values (1963), Wiley: Wiley New York · Zbl 0984.91513
[2] 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
[3] 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
[4] Blin, J. M., Fuzzy relations in group decision theory, J. Cybernet., 4, 17-22 (1974) · Zbl 0363.90011
[5] Blin, J. M.; Whinston, A. P., Fuzzy sets and social choice, J. Cybernet., 3, 28-33 (1973) · Zbl 0303.90009
[6] Dimitrov, V. N., Group choice under fuzzy information, Fuzzy Sets and Systems, 9, 25-40 (1983) · Zbl 0506.90006
[7] Fiorina, M. P.; Plott, C. R., Committee decisions under majority rule: An experimental study, Amer. Political Sci. Rev., 72, 525-595 (1978)
[8] Kacprzyk, J., Multistage Decision-Making under Fuzziness (1983), Verlag TÜV Rheinland: Verlag TÜV Rheinland Köln, ISR Series 79 · Zbl 0507.90023
[9] Kacprzyk, J., A generalization of fuzzy multistage decision-making and control via linguistic quantifiers, Internat. J. Control, 38, 1249-1270 (1983) · Zbl 0544.93004
[10] Kacprzyk, J.; Yager, R. R., Linguistic quantifiers and belief qualification in fuzzy multicriteria and multistage decision making, Control and Cybernetics, 13, 155-173 (1984) · Zbl 0551.90091
[11] Kacprzyk, J.; Yager, R. R., ‘Softer’ optimization and control models via fuzzy linguistic quantifiers, Inform. Sci., 34, 157-178 (1984) · Zbl 0562.90098
[12] Kelly, J. S., Arrow Impossibility Theorems (1978), Academic Press: Academic Press New York · Zbl 0462.90004
[13] Nurmi, H., Approaches to collective decision making with fuzzy preference relations, Fuzzy Sets and Systems, 6, 249-259 (1981) · Zbl 0465.90006
[14] Tanino, T., Fuzzy preference orderings in group decision making, Fuzzy Sets and Systems, 12, 117-131 (1984) · Zbl 0567.90002
[15] Yager, R. R., Quantifiers in the formulation of multiple objective decision functions, Inform. Sci., 31, 107-139 (1983) · Zbl 0551.90084
[16] Zadeh, L. A., A theory of approximate reasoning, (Hayes, J. E.; Michie, M.; Mikulich, L. I., Machine Intelligence, Vol. 9 (1979), Wiley: Wiley New York), 149-193
[17] Zadeh, L. A., A computational approach to fuzzy quantifiers in natural languages, Comput. Math. Appl., 9, 149-184 (1983) · Zbl 0517.94028
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.