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Group Decision Making and a Measure of Consensus under Fuzzy Preferences and a Fuzzy Linguistic Majority

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Book cover Computing with Words in Information/Intelligent Systems 2

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 34))

Summary

The essence of group decision making is: there is a group of individuals (decisionmakers, experts, ...) who provide their testimonies concerning an issue in question. These testimonies are assumed here to be 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, from among the feasible ones, which best reflects the preferences of the group of individuals as a whole.In this paper we will survey main developments in group decision making under fuzziness, mainly under fuzzy preference relations and a fuzzy (linguistic) majority. We will 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 dealt with in terms of a fuzzy logic based calculus of linguistically quantified statements or via the ordered weighted averaging (OWA) operators. Finally, we will discuss a related issue of how to define a “soft” degree of consensus in the group under individual fuzzy preference relations and a fuzzy majority.

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Bibliography

  • Arrow, K.J. (1963). Social Choice and Individual Values. Second Edition. Wiley, New York.

    Google Scholar 

  • Barrett, C.R. and Pattanaik, P.K. (1990). Aggregation of fuzzy preferences. In J. Kacprzyk and M. Fedrizzi, (Eds.): Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 155–162.

    Chapter  Google Scholar 

  • Barrett, C.R., Pattanaik, P.K. and Salles, M. (1986). On the structure of fuzzy social welfare functions. Fuzzy Sets and Systems, 19, 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  • Barrett, C.R., Pattanaik, P.K. and Salles, M. (1990). On choosing rationally when preferences are fuzzy. Fuzzy Sets and Systems, 34, 197–212.

    Article  MathSciNet  MATH  Google Scholar 

  • Barrett, C.R., Pattanaik, P.K. and Salles, M. (1992). Rationality and aggregation of preferences in an ordinally fuzzy framework. Fuzzy Sets and Systems, 49, 9–13.

    Article  MathSciNet  MATH  Google Scholar 

  • Bezdek, J.C., Spillman, B. Spillman, R. (1978). A fuzzy relation space for group decision theory, Fuzzy Sets and Systems, 1, 255–268.

    Article  MathSciNet  MATH  Google Scholar 

  • Bezdek, J.C., Spillman, B. and Spillman, R. (1979). Fuzzy relation space for group decision theory: An application, Fuzzy Sets and Systems 2, 5–14.

    Article  MATH  Google Scholar 

  • Blin, J.M. (1974). Fuzzy relations in group decision theory, J. of Cybernetics, 4, 17–22.

    Article  MathSciNet  Google Scholar 

  • Blin, J.M. and Whinston, A.P. (1973). Fuzzy sets and social choice, J. of Cybernetics, 4, 17–22.

    Article  MathSciNet  Google Scholar 

  • Carlsson, Ch. et al. (1992). Consensus in distributed soft environments, Europ. J. of Operational Research, 61, 165–185.

    Article  Google Scholar 

  • Delgado, M., Verdegay, J.L. and Vila, M.A. (1993). On aggregation opera- tions of linguistic labels, Int. J. of Intelligent Systems, 8, 351–370.

    Article  MATH  Google Scholar 

  • Fedrizzi, M. and Kacprzyk, J. (1988). On measuring consensus in the setting of fuzzy preference relations. In J. Kacprzyk and M. Roubens (Eds.): Non-Conventional Preference Relations in Decision Making, pp. 129–141.

    Google Scholar 

  • Fedrizzi, M. and Kacprzyk, J. (1993). Consensus degrees under fuzzy majorities and preferences using OWA (ordered weighted average) operators“, Proc. of Fifth IFSA World Congress ‘83 (Seoul, Korea, July 1993 ), Vol. I, pp. 624–626.

    Google Scholar 

  • Fedrizzi, M., Kacprzyk, J. and Nurmi, H. (1993). Consensus degrees under fuzzy majorities and fuzzy preferences using OWA (ordered weighted average) operators, Control and Cybernetics, 22, 71–80.

    MathSciNet  Google Scholar 

  • Fedrizzi, M., Kacprzyk, J. and Nurmi, H. (1996). How different are social choice functions: a rough sets approach, Quality and Quantity, 30, 8799.

    Google Scholar 

  • Fedrizzi, M., Kacprzyk, J., Owsinski, J.W. and Zadrozny, S. (1994). Consensus reaching via a GDSS with fuzzy majority and clustering of preference profiles, Annals of Operations Research, 51, 127–139.

    Article  MATH  Google Scholar 

  • Fedrizzi, M., Kacprzyk, J. and Zadrozny, S. (1988). An interactive multi-user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers, Decision Support Systems, 4, 313–327.

    Article  Google Scholar 

  • Fishburn, P.C. (1990). Multiperson decision making: a selective review. In J. Kacprzyk and M. Fedrizzi (Eds.): Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 3–27.

    Chapter  Google Scholar 

  • Gibbard A. (1973). Manipulation of schemes that mixvoting with chance, Econometrica, 45, 665–681.

    Article  MathSciNet  Google Scholar 

  • Herrera, F., Herrera-Viedma, E. and Verdegay, J.L. (1996). A model of consensus in group decision making under linguistic assessments, Fuzzy Sets and Systems, 78, 73–88.

    Article  MathSciNet  Google Scholar 

  • Herrera, F. and Verdegay, J.L. (1995). On group decision making under linguistic preferences and fuzzy linguistic quantifiers. In B. Bouchon-Meunier, R.R. Yager and L.A. Zadeh (Eds.): Fuzzy Logic and Soft Computing, World Scientific, Singapore, pp. 173–180.

    Chapter  Google Scholar 

  • Intriligator, M.D. (1973). A probabilistic model of social choice, Review of Economic Studies, 40, 553–560.

    Article  Google Scholar 

  • Intriligator, M.D. (1982). Probabilistic models of choice, Mathematical Social Sciences, 2, 157–166.

    Article  MATH  Google Scholar 

  • Kacprzyk, J. (1984). Collective decision making with a fuzzy majority rule, Proc. of WOGSC Congress, AFCET, Paris, pp. 153–159.

    Google Scholar 

  • Kacprzyk, J. (1985a). Zadeh’s commonsense knowledge and its use in multicriteria, multistage and multiperson decision making. In M.M. Gupta et al. (Eds.): Approximate Reasoning in Expert Systems, North—Holland, Amsterdam, pp. 105–121.

    Google Scholar 

  • Kacprzyk, J. (1985b). Some ‘commonsense’ solution concepts in group decision making via 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, pp. 125–135.

    Google Scholar 

  • Kacprzyk, J. (1985c). 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 Int. J., 16, 119–129 (Part I ), 131–144 (Part II).

    MathSciNet  MATH  Google Scholar 

  • Kacprzyk, J. (1986a). Group decision making with a fuzzy linguistic majority, Fuzzy Sets and Systems, 18, 105–118.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk, J. (1986b). Towards an algorithmic/procedural ‘human consistency’ of decision support systems: a fuzzy logic approach. In W. Karwowski and A. Mital (Eds.): Applications of Fuzzy Sets in Human Factors, Elsevier, Amsterdam, pp. 101–116.

    Google Scholar 

  • Kacprzyk, J. (1987a). On some fuzzy cores and ‘soft’ consensus measures in group decision making. In J.C. Bezdek (Ed.): The Analysis of Fuzzy Information, Vol. 2, CRC Press, Boca Raton, pp. 119–130.

    Google Scholar 

  • Kacprzyk, J. (1987b). Towards ‘human consistent’ decision support systems through commonsense-knowledge-based decision making and control models: a fuzzy logic approach, Computers and Artificial Intelligence, 6, 97–122.

    MATH  Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M. (1986). ‘Soft’ consensus measures for monitoring real consensus reaching processes under fuzzy preferences, Control and Cybernetics, 15, 309–323.

    Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M. (1988). A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences, Europ. J. of Operational Research, 34, 315–325.

    MathSciNet  Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M. (1989). A ‘human-consistent’ degree of consensus based on fuzzy logic with linguistic quantifiers, Mathematical Social Sciences, 18, 275–290.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M., Eds. (1990). Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht.

    MATH  Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M. (1995a). A fuzzy majority in group DM and consensus via the OWA operators with importance qualification, Proc. of CIFT’95–Current Issues in Fuzzy Technologies ( Trento, Italy ), pp. 128–137.

    Google Scholar 

  • Kacprzyk, J. and Fedrizzi, M. (1995b). Consensus degrees under fuzziness via ordered weighted average (OWA) operators. In Z. Bien and K.C. Min (Eds.): Fuzzy Logic and its Applications in Engineering, Information Sciences and Intelligent Systems, Kluwer, Dordrecht, pp. 447–454.

    Google Scholar 

  • Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1990). Group decision making with fuzzy majorities represented by linguistic quantifiers. In J.L. Verde-gay and M. Delgado (Eds.): Approximate Reasoning Tools for Artificial Intelligence, Verlag TUV Rheinland, Cologne, pp. 126–145.

    Google Scholar 

  • Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1992a). Fuzzy logic with linguistic quantifiers in group decision making and consensus formation. In R.R. Yager and L.A. Zadeh (Eds.): An Introduction to Fuzzy Logic Applications in Intelligent Systems, Kluwer, Dordrecht, 263–280.

    Chapter  Google Scholar 

  • Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1992b). Group decision making and consensus under fuzzy preferences and fuzzy majority, Fuzzy Sets and Systems, 49, 21–31.

    Article  MathSciNet  MATH  Google Scholar 

  • Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1996). “Soft” degrees of consensus under fuzzy preferences and fuzzy majorities. In J. Kacprzyk, H. Nurmi i M. Fedrizzi (Eds.): Consensus under Fuzziness, Kluwer, Boston, pp. 55–83.

    Google Scholar 

  • Kacprzyk, J., Fedrizzi, M. and Nurmi, H. (1997). OWA operators in group decision making and consensus reaching under fuzzy preferences and fuzzy majority. In R.R. Yager and J. Kacprzyk (Eds.): The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer, Boston, pp. 193206.

    Google Scholar 

  • Kacprzyk, J. and Nurmi, H. (1989). Linguistic quantifiers and fuzzy majorities for more realistic and human-consistent group decision making. In G. Evans, W. Karwowski and M. Wilhelm (Eds.): Fuzzy Methodologies for Industrial and Systems Engineering, Elsevier, Amsterdam, pp. 267–281.

    Google Scholar 

  • Kacprzyk J. and Nurmi H. (1998). Group decision making under fuzziness. In R. Slowinski (Ed.): Fuzzy Sets in Decision Analysis, Operations Research and Statistics, Kluwer, Boston, pp. 103–136.

    Google Scholar 

  • Kacprzyk, J., Nurmi, H. and Fedrizzi, M., Eds. (1996). Consensus under Fuzziness, Kluwer, Boston.

    Google Scholar 

  • Kacprzyk, J. and Roubens, M., Eds. (1988). Non-Conventional Preference Relations in Decision Making, Springer-Verlag, Heidelberg.

    MATH  Google Scholar 

  • Kacprzyk, J. and Yager, R.R. (1984a). Linguistic quantifiers and belief qualification in fuzzy multicriteria and multistage decision making, Control and Cybernetics, 13, 155–173.

    MathSciNet  MATH  Google Scholar 

  • Kacprzyk, J. and Yager, R.R. (1984b). ‘Softer’ optimization and control mod- els via fuzzy linguistic quantifiers, Information Sciences, 34, 157–178.

    Google Scholar 

  • Kacprzyk, J., Zadrozny, S. and Fedrizzi, M. (1988). An interactive user-friendly decision support system for consensus reaching based on fuzzy logic with linguistic quantifiers. In M.M. Gupta and T. Yamakawa (Eds.): Fuzzy Computing, Elsevier, Amsterdam, pp. 307–322.

    Google Scholar 

  • Kacprzyk, J., Zadrony, S. and Fedrizzi, M. (1997). An interactive GDSS for consensus reaching using fuzzy logic with linguistic quantifiers. In D. Dubois, H. Prade and R.R. Yager (Eds.): Fuzzy Information Engineering-A Guided Tour of Applications, Wiley, New York, pp. 567–574.

    Google Scholar 

  • Kelly, J.S. (1978) Social Choice Theory, Springer-Verlag, Berlin.

    Google Scholar 

  • Kuzmin, V.B. and Ovchinnikov, S.V. (1980a). Group decisions I: In arbitrary spaces of fuzzy binary relations, Fuzzy Sets and Systems, 4, 53–62.

    Article  MathSciNet  Google Scholar 

  • Kuzmin, V.B. and Ovchinnikov, S.V. (1980b). Design of group decisions II: In spaces of partial order fuzzy relations, Fuzzy Sets and Systems, 4, 153–165.

    Article  MathSciNet  Google Scholar 

  • Loewer, B. and Laddaga, R. (1985). Destroying the consensus, in Loewer B., Guest Ed., Special Issue on Consensus, Synthese, 62 (1), pp. 79–96. Nurmi, H. (1981).

    Google Scholar 

  • Approaches to collective decision making with fuzzy preference relations, Fuzzy Sets and Systems,6, 249–259.

    Google Scholar 

  • Nurmi, H. (1982). Imprecise notions in individual and group decision theory: resolution of Allais paradox and related problems, Stochastica, VI, 283303.

    Google Scholar 

  • Nurmi, H. (1987). Comparing Voting Systems, Reidel, Dordrecht.

    Book  Google Scholar 

  • Nurmi, H. (1988). Assumptions on individual preferences in the theory of voting procedures. In J. Kacprzyk and M. Roubens (Eds.): Non-Conventional Preference Relations in Decision Making, Springer-Verlag, Heidelberg, pp. 142–155.

    Google Scholar 

  • Nurmi, H., Fedrizzi, M. and Kacprzyk, J. (1990). Vague notions in the theory of voting. In J. Kacprzyk and M. Fedrizzi (Eds.): Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 43–52.

    Chapter  Google Scholar 

  • Nurmi, H. and Kacprzyk, J. (1991). On fuzzy tournaments and their solution concepts in group decision making, Europ. J. of Operational Research, 51, 223–232.

    Article  MATH  Google Scholar 

  • Nurmi, H., Kacprzyk, J. and Fedrizzi, M. (1996). Probabilistic, fuzzy and rough concepts in social choice, Europ. J. of Operational Research, 95, 264–277.

    Article  MATH  Google Scholar 

  • Ovchinnikov, S.V. (1990). Means and social welfare functions in fuzzy binary relation spaces. In J. Kacprzyk and M. Fedrizzi (Eds.): Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 143–154.

    Chapter  Google Scholar 

  • Roubens, M. and Vincke, Ph. (1985). Preference Modelling, Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

  • Salles, M. (1996). Fuzzy utility. In S. Barbera, P.J. Hammond and C. Seidl (Eds.): Handbook of Utility Theory, Kluwer, Boston (forthcoming).

    Google Scholar 

  • Szmidt, E. and Kacprzyk, J. (1996). Intuitionistic fuzzy sets in group decision making, Notes on Intuitionistic Fuzzy Sets, 2, 15–32.

    MathSciNet  Google Scholar 

  • Tanino, T. (1984). Fuzzy preference orderings in group decision making, Fuzzy Sets and Systems, 12, 117–131.

    Article  MathSciNet  MATH  Google Scholar 

  • Tanino, T. (1990). On group decision making under fuzzy preferences. In J. Kacprzyk and M. Fedrizzi (Eds.): Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, pp. 172–185.

    Chapter  Google Scholar 

  • Yager, R.R. (1983). Quantifiers in the formulation of multiple objective decision functions, Information Sciences, 31, 107–139.

    Article  MathSciNet  MATH  Google Scholar 

  • Yager, R.R (1988). On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. on Systems, Man and Cybernetics, SMC-18, 183–190.

    Google Scholar 

  • Yager, R.R. (1993). On the Issue of Importance Qualifications in Fuzzy Multi-Criteria Decision Making. Tech. Report MII-1323, Machine Intelligence Institute, Iona College, New Rochelle, NY.

    Google Scholar 

  • Yager, R.R. and Kacprzyk, J. (Eds.) (1997). The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer, Boston.

    Google Scholar 

  • Zadeh, L.A. (1983). A computational approach to fuzzy quantifiers in natural languages, Computers and Maths. with Appls., 9, 149–184.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Department of Political Science, University of Turku, 20500, Turku, Finland

    Hannu Nurmi

  3. Department of Computer and Management Sciences, University of Trento, Via Inama 5, 38100, Trento, Italy

    Mario Fedrizzi

Authors
  1. Janusz Kacprzyk
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  2. Hannu Nurmi
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  3. Mario Fedrizzi
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Editors and Affiliations

  1. Berkeley Initiative in Soft Computing (BISC), Computer Science Division and Electronics Research Laboratory, Department of Electrical and Electronics, Engineering and Computer Science, University of California, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

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Kacprzyk, J., Nurmi, H., Fedrizzi, M. (1999). 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 2. Studies in Fuzziness and Soft Computing, vol 34. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1872-7_11

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  • DOI: https://doi.org/10.1007/978-3-7908-1872-7_11

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2461-2

  • Online ISBN: 978-3-7908-1872-7

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