A consensus reaching process in the context of non-uniform ordered qualitative scales

Fuzzy Optimization and Decision Making volume 16, pages449–461(2017)Cite this article

Abstract

In this paper, we consider that a group of agents judge a set of alternatives by means of an ordered qualitative scale. The scale is not assumed to be uniform, i.e., the psychological distance between adjacent linguistic terms is not necessarily always the same. In this setting, we propose how to measure the consensus in each subset of at least two agents over each subset of alternatives. We introduce a consensus reaching process where some agents may be invited to change their assessments over some alternatives in order to increase the consensus. All the steps are managed in a purely ordinal way through ordinal proximity measures.

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Notes

  1. 1.

    For instance, Malkevitch (1990) provides an “evil example” where six well-known voting systems generate different outcomes from the same profile of individual preferences.

  2. 2.

    We have to note that the International Association of Oenologists assigns numbers to these linguistic terms and does manage the assessments in a numerical way.

  3. 3.

    In Majority Judgment the inputs are arranged in an increasing fashion.

  4. 4.

    In order to avoid loss of information, we will take into account the two medians in the even case.

  5. 5.

    This linear order is equivalent to the one provided by Delgado et al. (1998) in the set of trapezoidal fuzzy numbers when it is applied to intervals of real numbers.

  6. 6.

    For instance, the one introduced by García-Lapresta and Pérez-Román (2015b) in the same setting.

References

  1. Balinski, M., & Laraki, R. (2011). Majority judgment. Measuring ranking, and electing. Cambridge, MA: The MIT Press.

    Google Scholar 

  2. Balinski, M., & Laraki, R. (2013). How best to rank wines: Majority Judgment. Wine Economics: Quantitative Studies and Empirical Observations (pp. 149–172). Basingstoke: Palgrave-MacMillan.

    Google Scholar 

  3. Bentkowska, U., Bustince, H., Jurio, A., Pagola, M., & Pekala, B. (2015). Decision making with an interval-valued fuzzy preference relation and admissible orders. Applied Soft Computing, 35, 792–801.

    Article  Google Scholar 

  4. Bosch, R. (2005). Characterizations of Voting Rules and Consensus Measures. Ph. D. Dissertation, Tilburg University,

  5. Bustince, H., Fernández, J., Kolesárová, A., & Mesiar, R. (2013). Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets and Systems, 220, 69–77.

    Article  MATH  MathSciNet  Google Scholar 

  6. Cabrerizo, F. J., Chiclana, F., Al-Hmouz, R., Morfeq, A., Balamash, A. S., & Herrera-Viedma, E. (2015). Fuzzy decision making and consensus: Challenges. Journal of Intelligent & Fuzzy Systems, 29, 1109–1118.

    Article  MATH  MathSciNet  Google Scholar 

  7. Cabrerizo, F. J., Ureña, M. R., Pedrycz, W., & Herrera-Viedma, E. (2014). Building consensus in group decision making with an allocation of information granularity. Fuzzy Sets and Systems, 255, 115–127.

    Article  MATH  MathSciNet  Google Scholar 

  8. Delgado, M., Vila, M. A., & Voxman, W. (1998). On a canonical representation of fuzzy numbers. Fuzzy Sets and Systems, 93, 125–135.

    Article  MATH  MathSciNet  Google Scholar 

  9. Derrac, J., Chiclana, F., García, S., & Herrera, F. (2016). Evolutionary fuzzy k-nearest neighbors algorithm using interval-valued fuzzy sets. Information Sciences, 329, 144–163.

    Article  Google Scholar 

  10. Erdamar, B., García-Lapresta, J. L., Pérez-Román, D., & Sanver, M. R. (2014). Measuring consensus in a preference-approval context. Information Fusion, 17, 14–21.

    Article  Google Scholar 

  11. Fedrizzi, M., Kacprzyk, J., & Zadrożny, 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  MATH  Google Scholar 

  12. García-Lapresta, J. L. (2008). Favoring consensus and penalizing disagreement in group decision making. Journal of Advanced Computational Intelligence and Intelligent Informatics, 12(5), 416–421.

    Article  Google Scholar 

  13. García-Lapresta, J. L., & Pérez-Román, D. (2011). Measuring consensus in weak orders. In E. Herrera-Viedma, J. L. García-Lapresta, J. Kacprzyk, H. Nurmi, M. Fedrizzi, & S. Zadrożny (Eds.), Consensual Processes, STUDFUZZ (Vol. 267, pp. 213–234). Berlin: Springer-Verlag.

    Google Scholar 

  14. García-Lapresta, J. L., & Pérez-Román, D. (2015a). Ordinal proximity measures in the context of unbalanced qualitative scales and some applications to consensus and clustering. Applied Soft Computing, 35, 864–872.

  15. García-Lapresta, J.L., & Pérez-Román, D. (2015b). Aggregating opinions in non-uniform qualitative scales. In USB Proceedings of the 12th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2015), (pp. 152-163).

  16. García-Lapresta, J. L., & Pérez-Román, D. (2016). Consensus-based clustering under hesitant qualitative assessments. Fuzzy Sets and Systems, 292, 261–273.

    Article  MathSciNet  Google Scholar 

  17. García-Lapresta, J.L., Pérez-Román, D., & Falcó, E. (2014). Consensus reaching processes under hesitant linguistic assessments. In: Angelov, P. et al. (eds.), Intelligent Systems’2014, Advances in Intelligent Systems and Computing 322, (pp. 257–268).

  18. Herrera, F., Herrera-Viedma, E., & Verdegay, J. L. (1997). Linguistic measures based on fuzzy coincidence for reaching consensus in group decision making. International Journal of Approximate Reasoning, 16, 309–334.

    Article  MATH  Google Scholar 

  19. Herrera-Viedma, E., Herrera, F., & Chiclana, F. (2002). A consensus model for multiperson decision making with different preference structures. IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans, 32, 394–402.

    Article  MATH  Google Scholar 

  20. Malkevitch, J. (1990). Mathematical theory of elections. Annals of the New York Academy of Sciences, 607, 89–97.

    Article  MathSciNet  Google Scholar 

  21. Palomares, I., Estrella, F. J., Martínez, L., & Herrera, F. (2014). Consensus under a fuzzy context: Taxonomy, analysis framework AFRYCA and experimental case of study. Information Fusion, 20, 252–271.

    Article  Google Scholar 

  22. Pérez, I. J., Cabrerizo, F. J., & Herrera-Viedma, E. (2010). A mobile decision support system for dynamic group decision making problems. IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans, 40, 1244–1256.

    Article  Google Scholar 

  23. Saint, S., & Lawson, J. R. (1994). Rules for Reaching Consensus. A Modern Approach to Decision Making. San Francisco: Jossey-Bass.

    Google Scholar 

  24. Wu, J., & Chiclana, F. (2014a). Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus building. Knowledge-Based Systems, 71, 187–200.

  25. Wu, J., & Chiclana, F. (2014b). Visual information feedback mechanism and attitudinal prioritisation method for group decision making with triangular fuzzy complementary preference relations. Information Sciences, 279, 716–734.

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Acknowledgements

The authors are grateful to Tomasa Calvo and two anonymous referees for their comments and suggestions. The financial support of the Spanish Ministerio de Economía y Competitividad (project ECO2012-32178) and Consejería de Educación de la Junta de Castilla y León (project VA066U13) are acknowledged.

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Affiliations

  1. PRESAD Research Group, BORDA Research Unit, IMUVA, Dept. de Economía Aplicada, Universidad de Valladolid, Valladolid, Spain

    José Luis García-Lapresta

  2. PRESAD Research Group, BORDA Research Unit, Dept. de Organización de Empresas y Comercialización e Investigación de Mercados, Universidad de Valladolid, Valladolid, Spain

    David Pérez-Román

Authors
  1. José Luis García-Lapresta
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  2. David Pérez-Román
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Corresponding author

Correspondence to José Luis García-Lapresta.

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García-Lapresta, J.L., Pérez-Román, D. A consensus reaching process in the context of non-uniform ordered qualitative scales. Fuzzy Optim Decis Making 16, 449–461 (2017). https://doi.org/10.1007/s10700-016-9256-6

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Keywords

  • Group decision making
  • Consensus
  • Qualitative scales
  • Ordinal proximity measures