Abstract
Group decision making, as meant in this paper, is the following choice problem which proceeds in a multiperson setting. There is a group of individuals (decision makers, experts, …) who provide their testimonies concerning an issue in question as individual preference relations over some set of option (alternatives, variants, …). The problem is to find a solution, i.e., an alternative or a set of alternatives which best reflects the preferences of the group of individuals as a whole. First, we survey main developments in group decision making under fuzziness and outline some basic inconsistencies and negative results in group decision making and social choice, and show how they can be alleviated by some plausible modifications of underlying assumptions, mainly by introducing fuzzy preference relations and a fuzzy majority. We concentrate on how to derive solutions under individual fuzzy preference relations, and a fuzzy majority equated with a fuzzy linguistic quantifier (e.g., most, almost all, …), and discuss a related issue of how to define a “soft” degree of consensus in the group. Finally, we show how fuzzy preferences can help alleviate some known voting paradoxes.
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Arrow, K.J.: Social Choice and Individual Values, 2nd edn. Wiley, New York (1963)
Black, D.: Theory of Committees and Elections. Cambridge University Press, Cambridge (1958)
Bordogna, G., Fedrizzi, M., Pasi, G.: A linguistic modelling of consensus in group decision making based on OWA operators. IEEE Trans. on Systems, Man and Cybernetics SMC-27, 126–132 (1997)
Chiclana, F., Herrera, F., Herrera-Viedma, E.: Integrating multiplicative preference relations in a multipurpose decision making model based on fuzzy preference relations. Fuzzy Sets and Systems 122, 277–291 (2001)
DeGrazia, A.: Mathematical Derivation of an Election System. Isis 44, 42–51 (1953)
Fedrizzi, M., Kacprzyk, J., Nurmi, H.: Consensus degrees under fuzzy majorities and fuzzy preferences using OWA (ordered weighted average) operators. Control and Cybernetics 22, 71–80 (1993)
Fedrizzi, M., Kacprzyk, J., Nurmi, H.: How different are social choice functions: a rough sets approach. Quality and Quantity 30, 87–99 (1996)
Fedrizzi, M., Kacprzyk, J., Zadrożny, S.: An interactive multi-user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers. Decision Support Systems 4, 313–327 (1988)
Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht (1994)
García-Lapresta, J.L., Llamazares, B.: Aggregation of fuzzy preferences: Some rules of the mean. Social Choice and Welfare 17, 673–690 (2000)
Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets and Systems 88, 31–49 (1997a)
Herrera, F., Martínez, L.: An approach for combining numerical and linguistic information based on the 2-tuple fuzzy linguistic representation model in decision making. International J. of Uncertainty, Fuzziness and Knowledge-Based Systems 8, 539–562 (2000)
Intrilligator, M.D.: A probabilistic model of social choice. Review of Economic Studies 40, 553–560 (1973)
Intrilligator, M.D.: Probabilistic models of choice. Mathematical Social Sciences 2, 157–166 (1982)
Kacprzyk, J.: Group decision-making with a fuzzy majority via linguistic quantifiers. Part I: A consensory-like pooling; Part II: A competitive-like pooling. Cybernetics and Systems: an International J 16, 119–129 (Part I), 131–144 (Part II) (1985)
Kacprzyk, J.: Group decision making with a fuzzy linguistic majority. Fuzzy Sets and Systems 18, 105–118 (1986)
Kacprzyk, J., Fedrizzi, M.: “Soft” consensus measures for monitoring real consensus reaching processes under fuzzy preferences. Control and Cybernetics 15, 309–323 (1986)
Kacprzyk, J., Fedrizzi, M.: A “soft” measure of consensus in the setting of partial (fuzzy) preferences. European Journal of Operational Research 34, 315–325 (1988)
Kacprzyk, J., Fedrizzi, M.: A ’human-consistent‘ degree of consensus based on fuzzy logic with linguistic quantifiers. Mathematical Social Sciences 18, 275–290 (1989)
Kacprzyk, J., Fedrizzi, M. (eds.): Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory. Kluwer, Dordrecht (1990)
Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Systems 49, 21–31 (1992)
Kacprzyk, J., Nurmi, H.: Group decision making under fuzziness, in R. Słowiński (Ed.). In: Fuzzy Sets in Decision Analysis, Operations Research and Statistics, pp. 103–136. Kluwer, Boston (1998)
Kacprzyk, J., Nurmi, H., Fedrizzi, M. (eds.): Consensus under Fuzziness. Kluwer, Boston (1996)
Kacprzyk, J., Nurmi, H., Fedrizzi, M.: Group decision making and a measure of consensus under fuzzy preferences and a fuzzy linguistic majority. In: Zadeh, L.A., Kacprzyk, J. (eds.) Computing with Words in Information/Intelligent Systems. Part 2. Foundations, pp. 233–243. Physica–Verlag, Springer, Heidelberg, New York (1999)
Kacprzyk, J., Zadrożny, S.: Collective choice rules in group decision making under fuzzy preferences and fuzzy majority: a unified OWA operator based approach. Control and Cybernetics 31, 937–948 (2002)
Kacprzyk, J., Zadrożny, S.: Dealing with imprecise knowledge on preferences and majority in group decision making: towards a unified characterization of individual and collective choice functions. Bulletin of the Polish Academy of Sciences. Tech. Sci. 3, 286–302 (2003)
Kacprzyk, J., Zadrony, S., Fedrizzi, M., Nurmi, H.: On group decision making, consensus reaching, voting and voting paradoxes under fuzzy preferences and a fuzzy majority: a survey and a granulation perspective. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, pp. 906–929. Wiley, Chichester (2008a)
Kacprzyk, J., Zadrony, S., Fedrizzi, M., Nurmi, H.: On group decision making, consensus reaching, voting and voting paradoxes under fuzzy preferences and a fuzzy majority: a survey and some perspectives. In: Bustince, H., Herrera, F., Montero, J. (eds.) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, pp. 263–295. Springer, Heidelberg (2008b)
Kacprzyk, J., Zadrony, S., Nurmi, H., Fedrizzi, M.: Fuzzy preferences as a convenient tool in group decision making and a remedy for voting paradoxes. In: Seising, R. (ed.) Views on Fuzzy Sets and Systems from Different Perspectives: Philosophy and Logic, Criticisms and Applications, pp. 345–360. Springer, Heidelberg (2009)
Kelly, J.S.: Arrow Impossibility Theorems. Academic Press, New York (1978)
Kelly, J.S.: Social Choice Theory: An Introduction. Academic Press, New York (1988)
Lagerspetz, E.: Paradoxes and representation. Electoral Studies 15, 83–92 (1995)
Loewer, B., Laddaga, R.: Destroying the consensus. Special Issue on Consensus, Synthese 62(1), 79–96 (1985)
Montero, J.: Arrow‘s theorem under fuzzy rationality. Behavioral Science 32, 267–273 (1987)
Montero, J., Tejada, J., Cutello, V.: A general model for deriving preference structures from data. European Journal of Operational Research 98, 98–110 (1997)
Nurmi, H.: Approaches to collective decision making with fuzzy preference relations. Fuzzy Sets and Systems 6, 249–259 (1981)
Nurmi, H.: Imprecise notions in individual and group decision theory: resolution of Allais paradox and related problems. Stochastica VI, 283–303 (1982)
Nurmi, H.: Voting procedures: a summary analysis. British Journal of Political Science 13, 181–208 (1983)
Nurmi, H.: Probabilistic voting. Political Methodology 10, 81–95 (1984)
Nurmi, H.: Comparing Voting Systems. Reidel, Dordrecht (1987)
Nurmi, H.: Referendum design: an exercise in applied social choice theory. Scandinavian Political Studies 20, 33–52 (1997)
Nurmi, H.: Voting paradoxes and referenda. Social Choice and Welfare 15, 333–350 (1998)
Nurmi, H.: Voting Paradoxes and How to Deal with Them. Springer, Heidelberg (1999)
Nurmi, H.: Voting Procedures under Uncertainty. Springer, Heidelberg (2002)
Nurmi, H., Kacprzyk, J.: On fuzzy tournaments and their solution concepts in group decision making. European Journal of Operational Research 51, 223–232 (1991)
Nurmi, H., Kacprzyk, J.: Social choice under fuzziness: a perspective. In: Fodor, J., De Baets, B., Perny, P. (eds.) Preferences and Decisions under Incomplete Knowledge, pp. 107–130. Physica–Verlag, Springer, Heidelberg, New York (2000)
Nurmi, H., Kacprzyk, J., Fedrizzi, M.: Probabilistic, fuzzy and rough concepts in social choice. European Journal of Operational Research 95, 264–277 (1996)
Nurmi, H., Meskanen, T.: Voting paradoxes and MCDM. Group Decision and Negotiation 9(4), 297–313 (2000)
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. on Systems, Man and Cybernetics SMC-18, 183–190 (1988)
Yager, R.R., Kacprzyk, J. (eds.): The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer, Boston (1997)
Yager, R.R., Kacprzyk, J., Beliakov, G.: Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Springer, Berlin (2011)
Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Computers and Maths. with Appls. 9, 149–184 (1983)
Zadrożny, S.: An approach to the consensus reaching support in fuzzy environment. In: Kacprzyk, J., Nurmi, H., Fedrizzi, M. (eds.) Consensus under Fuzziness, pp. 83–109. Kluwer, Boston (1997)
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Kacprzyk, J., Zadrożny, S., Nurmi, H., Fedrizzi, M. (2013). On Some Voting Paradoxes: A Fuzzy Preference and a Fuzzy Majority Perspective. In: Ventre, A., Maturo, A., Hošková-Mayerová, Š., Kacprzyk, J. (eds) Multicriteria and Multiagent Decision Making with Applications to Economics and Social Sciences. Studies in Fuzziness and Soft Computing, vol 305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35635-3_17
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