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Soft Consensus Models in Group Decision Making

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Fuzzy Logic and Information Fusion

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 339))

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Abstract

In group decision making problems, when a consensual solution is required, a natural question is how to measure the closeness among experts’ opinions in order to obtain the consensus level. To do so, different approaches have been proposed. Following this research line, several authors have introduced hard consensus measures varying between 0 (no consensus or partial consensus) and 1 (full consensus or complete agreement). However, consensus as a full and unanimous agreement is far from being achieved in real situations. So, in practice, a more realistic approach is to use some softer consensus measures, which assess the consensus degree in a more flexible way reflecting better all possible partial agreements obtained through the process. The aim of this chapter is to identify and describe the different existing approaches to compute soft consensus measures in fuzzy group decision making problems. Additionally, we analyze the current models and new challenges on this field.

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References

  1. S. Alonso, F.J. Cabrerizo, F. Chiclana, F. Herrera, E. Herrera-Viedma, Group decision-making with incomplete fuzzy linguistic preference relations. Int. J. Intell. Syst. 24(2), 201–222 (2009)

    Article  MATH  Google Scholar 

  2. S. Alonso, E. Herrera-Viedma, F.J. Cabrerizo, F. Chiclana, F. Herrera, Visualizing consensus in group decision making situations, in Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 1823–1828 (2007)

    Google Scholar 

  3. S. Alonso, I.J. Pérez, F.J. Cabrerizo, E. Herrera-Viedma, A linguistic consensus model for web 2.0 communities. Appl. Soft Comput. 13(1), 149–157 (2013)

    Article  Google Scholar 

  4. D. Ben-Arieh, Z. Chen, Linguistic-labels aggregation and consensus measure for autocratic decision making using group recommendations. IEEE Trans. Syst. Man Cybern.-Part A: Syst. Hum. 36(3), 558–568 (2006)

    Article  Google Scholar 

  5. J.C. Bezdek, B. Spillman, R. Spillman, A fuzzy relation space for group decision theory. Fuzzy Sets Syst. 1(4), 255–268 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  6. G. Bordogna, M. Fedrizzi, G. Pasi, A linguistic modeling of consensus in group decision making based on OWA operators. IEEE Trans. Syst. Man Cybern.-Part A: Syst. Hum. 27(1), 126–133 (1997)

    Article  Google Scholar 

  7. C.T. Butler, A. Rothstein, On Conflict and Consensus: A Handbook on Formal Consensus Decision Making (Takoma Park, 2006)

    Google Scholar 

  8. F.J. Cabrerizo, S. Alonso, E. Herrera-Viedma, A consensus model for group decision making problems with unbalanced fuzzy linguistic information. Int. J. Inf. Technol. Decis. Mak. 8(1), 109–131 (2009)

    Article  MATH  Google Scholar 

  9. F.J. Cabrerizo, R. Heradio, I.J. Pérez, E. Herrera-Viedma, A selection process based on additive consistency to deal with incomplete fuzzy linguistic information. J. Univ. Comput. Sci. 16(1), 62–81 (2010)

    MathSciNet  MATH  Google Scholar 

  10. F.J. Cabrerizo, J.M. Moreno, I.J. Pérez, E. Herrera-Viedma, Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks. Soft. Comput. 14(5), 451–463 (2010)

    Article  Google Scholar 

  11. F.J. Cabrerizo, I.J. Pérez, E. Herrera-Viedma, Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information. Knowl.-Based Syst. 23(2), 169–181 (2010)

    Article  Google Scholar 

  12. F.J. Cabrerizo, E. Herrera-Viedma, W. Pedrycz, A method based on pso and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. Eur. J. Oper. Res. 230(3), 624–633 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. C. Carlsson, D. Ehrenberg, P. Eklund, M. Fedrizzi, P. Gustafsson, P. Lindholm, G. Merkuryeva, T. Riissanen, A.G.S. Ventre, Consensus in distributed soft environments. Eur. J. Oper. Res. 61(1–2), 165–185 (1992)

    Article  Google Scholar 

  14. F. Chiclana, E. Herrera-Viedma, F. Herrera, S. Alonso, Some induced ordered weighted averaging operators and their use for solving group decision making problems based on fuzzy preference relations. Eur. J. Oper. Res. 182(1), 383–399 (2007)

    Article  MATH  Google Scholar 

  15. F. Chiclana, F. Mata, L. Martinez, E. Herrera-Viedma, S. Alonso, Integration of a consistency control module within a consensus model. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 16(Suppl. 1), 35–53 (2008)

    Article  MathSciNet  Google Scholar 

  16. F. Chiclana, J.M. Tapia-Garcia, M.J. del Moral, E. Herrera-Viedma, A statistical comparative study of different similarity measures of consensus in group decision making. Inf. Sci. 221, 110–123 (2013)

    Article  MathSciNet  Google Scholar 

  17. L. Coch, J.R.P. French, Overcoming resistance to change. Hum. Relat. 1(4), 512–532 (1948)

    Article  Google Scholar 

  18. V. Cutello, J. Montero, Fuzzy rationality measures. Fuzzy Sets Syst. 62(1), 39–54 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  19. M.M. Deza, E. Deza, Encyclopedia of Distances (Springer, New York, 2009)

    Google Scholar 

  20. D. Dubois, J.L. Koning, Social choice axioms for fuzzy set aggregation. Fuzzy Sets Syst. 43(3), 257–274 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  21. D. Dubois, H. Prade, C. Testemale, Weighted fuzzy pattern matching. Fuzzy Sets Syst. 28(3), 313–331 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  22. M. Fedrizzi, M. Fedrizzi, R.A. Marques-Pereira, On the issue of consistency in dynamical consensual aggregation, in Technologies for Constructing Intelligent Systems, ed. by B. Bouchon-Meunier, J. Gutierrez-Rios, L. Magdalena, R.R. Yager (Springer, New York, 2002), pp. 129–137

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  24. M. Fedrizzi, J. Kacprzyk, S. Zadrozny, An interactive multi-user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers. Decis. Support Syst. 4(3), 313–327 (1988)

    Article  MATH  Google Scholar 

  25. M. Fedrizzi, G. Pasi, Fuzzy logic approaches to consensus modeling in group decision making, in Intelligent Decision and Policy Making Support Systems, ed. by D. Ruan, F. Hardeman, K. Van Der Meer (Springer-Verlag, Berlin-Heidelberg, 2008), pp. 19–37

    Chapter  Google Scholar 

  26. J. Fodors, M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support (Kluwer Academic Publishers, Dordrecht, 1994)

    Book  MATH  Google Scholar 

  27. J.R.P. French, A formal theory of social power. Psychol. Rev. 63(3), 181–194 (1956)

    Article  MathSciNet  Google Scholar 

  28. F. Harary, On the measurement of structural balance. Behav. Sci. 4(4), 316–323 (1959)

    Article  MathSciNet  Google Scholar 

  29. F. Herrera, S. Alonso, F. Chiclana, E. Herrera-Viedma, Computing with words in decision making: foundations, trends and prospects. Fuzzy Optim. Decis. Making 8(4), 337–364 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  30. F. Herrera, E. Herrera-Viedma, J.L. Verdegay, A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst. 78(1), 73–87 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  31. F. Herrera, E. Herrera-Viedma, J.L. Verdegay, A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets Syst. 88(1), 31–49 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  32. F. Herrera, E. Herrera-Viedma, J.L. Verdegay, Choice processes for non-homogeneous group decision making in linguistic setting. Fuzzy Sets Syst. 94(3), 287–308 (1998)

    Article  MathSciNet  Google Scholar 

  33. E. Herrera-Viedma, S. Alonso, F. Chiclana, F. Herrera, A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Trans. Fuzzy Syst. 15(5), 863–877 (2007)

    Article  MATH  Google Scholar 

  34. E. Herrera-Viedma, F.J. Cabrerizo, J. Kacprzyk, W. Pedrycz, A review of soft consensus models in a fuzzy environment. Inf. Fusion 17, 4–13 (2014)

    Article  Google Scholar 

  35. E. Herrera-Viedma, F. Herrera, F. Chiclana, A consensus model for multiperson decision making with different preference structures. IEEE Trans. Syst. Man Cybern.-Part A: Syst. Hum. 32(3), 394–402 (2002)

    Article  MATH  Google Scholar 

  36. E. Herrera-Viedma, F. Herrera, F. Chiclana, M. Luque, Some issues on consistency of fuzzy preference relations. Eur. J. Oper. Res. 154(1), 98–109 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  37. E. Herrera-Viedma, L. Martinez, F. Mata, F. Chiclana, A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Trans. Fuzzy Syst. 13(5), 644–658 (2005)

    Article  Google Scholar 

  38. G. Hesamian, M. Shams, Measuring similarity and ordering based on hesitant fuzzy linguistic term sets. J. Intell. Fuzzy Syst. 28(2):983–990 (2015)

    Google Scholar 

  39. J. Kacprzyk, Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst. 18(2), 105–118 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  40. J. Kacprzyk, On some fuzzy cores and ‘soft’ consensus measures in group decision making, in The Analysis of Fuzzy Information, ed. by J.C. Bezdek (CRC Press, Boca Raton, 1987), pp. 119–130

    Google Scholar 

  41. J. Kacprzyk, M. Fedrizzi, ‘Soft’ consensus measures for monitoring real consensus reaching processes under fuzzy preferences. Control Cybern. 15(3–4), 309–323 (1986)

    MathSciNet  MATH  Google Scholar 

  42. J. Kacprzyk, M. Fedrizzi, A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences. Eur. J. Oper. Res. 34(3), 316–325 (1988)

    Article  MathSciNet  Google Scholar 

  43. J. Kacprzyk, M. Fedrizzi, A ‘human-consistent’ degree of consensus based on fuzzy logic with linguistic quantifiers. Math. Soc. Sci. 18(3), 275–290 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  44. J. Kacprzyk, M. Fedrizzi, H. Nurmi, Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets Syst. 49(1), 21–31 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  45. J. Kacprzyk, S. Zadrozny, Soft computing and web intelligence for supporting consensus reaching. Soft. Comput. 14(8), 833–846 (2010)

    Article  Google Scholar 

  46. J. Kacprzyk, S. Zadrozny, Z.W. Ras, How to support consensus reaching using action rules: a novel approach. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 18(4), 451–470 (2010)

    Article  MathSciNet  Google Scholar 

  47. J. Lu, G. Zhang, D. Ruan, Intelligent multi-criteria fuzzy group decision making for situation assessments. Soft. Comput. 12(3), 289–299 (2008)

    Article  MATH  Google Scholar 

  48. S. Massanet, J.V. Rieranad, J. Torrens, E. Herrera-Viedma, A new linguistic computational model based on discrete fuzzy numbers for computing with words. Inf. Sci. 258, 277–290 (2014)

    Google Scholar 

  49. F. Mata, L. Martinez, E. Herrera-Viedma, An adaptive consensus support model for group decision-making problems in a multigranular fuzzy linguistic context. IEEE Trans. Fuzzy Syst. 17(2), 279–290 (2009)

    Article  Google Scholar 

  50. J. Montero, Aggregation of fuzzy opinion in a non-homogeneous group. Fuzzy Sets Syst. 25(1), 15–20 (1987)

    Google Scholar 

  51. J. Montero, The impact of fuzziness in social choice paradoxes. Soft. Comput. 12, 177–182 (2008)

    Article  MATH  Google Scholar 

  52. H. Nurmi, Fuzzy social choice: a selective retrospect. Soft. Comput. 12, 281–288 (2008)

    Article  MATH  Google Scholar 

  53. I. Palomares, F.J. Estrella, L. Martinez, F. Herrera, Consensus under a fuzzy context: taxonomy, analysis framework afryca and experimental case of study. Inf. Fusion 20, 252–271 (2014)

    Article  Google Scholar 

  54. I. Palomares, L. Martinez, F. Herrera, Mentor: a graphical monitoring tool of preferences evolution in large-scale group decision making. Knowl.-Based Syst. 58, 66–74 (2014)

    Article  Google Scholar 

  55. Z. Pawlak, Information systems theoretical foundations. Inf. Syst. 6(3), 205–218 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  56. I.J. Pérez, F.J. Cabrerizo, S. Alonso, E. Herrera-Viedma, A new consensus model for group decision making problems with non homogeneous experts. IEEE Trans. Syst. Man Cybern.: Syst. 44(4), 494–498 (2014)

    Article  Google Scholar 

  57. I.J. Pérez, F.J. Cabrerizo, E. Herrera-Viedma, A mobile decision support system for dynamic group decision-making problems. IEEE Trans. Syst. Man Cybern.-Part A: Syst. Hum. 40(6), 1244–1256 (2010)

    Article  Google Scholar 

  58. I.J. Pérez, F.J. Cabrerizo, E. Herrera-Viedma, Group decision making problems in a linguistic and dynamic context. Expert Syst. Appl. 38(3), 1675–1688 (2011)

    Article  Google Scholar 

  59. I.J. Pérez, R. Wikstrom, J. Mezei, C. Carlsson, E. Herrera-Viedma, A new consensus model for group decision making using fuzzy ontology. Soft. Comput. 17(9), 1617–1627 (2013)

    Article  Google Scholar 

  60. R.M. Rodriguez, L. Martinez, V. Torra, Z.S. Xu, F. Herrera, Hesitant fuzzy sets: state of the art and future directions. Int. J. Intell. Syst. 29(6), 495–524 (2014)

    Article  Google Scholar 

  61. M. Roubens, Fuzzy sets and decision analysis. Fuzzy Sets Syst. 90(2), 199–206 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  62. T.L. Saaty, The Analytic Hierarchy Process: Planning, Priority Setting (McGraw-Hill, Resource Allocation, New York, 1980)

    MATH  Google Scholar 

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

    Google Scholar 

  64. B. Spillman, R. Spillman, J.C. Bezdek, A fuzzy analysis of consensus in small groups, in Fuzzy Automata and Decision Processes, ed. by P.P. Wang, S.K. Chang (North-Holland, Amsterdam, 1980), pp. 331–356

    Google Scholar 

  65. T. Tanino, Fuzzy preference orderings in group decision making. Fuzzy Sets Syst. 12(2), 117–131 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  66. M. Tavana, D.T. Kennedy, N-site: a distributed consensus building and negotiation support system. Int. J. Inf. Technol. Decis. Mak. 5(1), 123–154 (2006)

    Article  Google Scholar 

  67. V. Torra, Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)

    MATH  Google Scholar 

  68. P. Victor, C. Cornelis, M.D. Cock, P. Pinheiro da Silva, Gradual trust and distrust in recommender systems. Fuzzy Sets Syst. 160(10), 1367–1382 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  69. P. Victor, C. Cornelis, M.D. Cock, E. Herrera-Viedma, Practical aggregation operators for gradual trust and distrust. Fuzzy Sets Syst. 184(1), 126–147 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  70. S. Wasserman, K. Faust, Social Networks Analysis: Methods and Applications (Cambridge University Press, Cambridge, 2009)

    Google Scholar 

  71. J. Wu, F. Chiclana, A social network analysis trust-consensus based approach to group decision-making problems with interval-valued fuzzy reciprocal preference relations. Knowl.-Based Syst. 59, 97–107 (2014)

    Article  Google Scholar 

  72. J. Wu, F. Chiclana, Visual information feedback mechanism and attitudinal prioritisation method for group decision making with triangular fuzzy complementary preference relations. Inf. Sci. 279, 716–734 (2014)

    Article  MathSciNet  Google Scholar 

  73. Z.B. Wu, J.P. Xu, A consistency and consensus based decision support model for group decision making with multiplicative preference relations. Decis. Support Syst. 52(3), 757–767 (2012)

    Article  Google Scholar 

  74. L.A. Zadeh, Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  75. L.A. Zadeh, The concept of a linguistic variable and its applications to approximate reasoning. Inf. Sci. Part I, II, III, 8, 8, 9, 199–249,301–357,43–80 (1975)

    Google Scholar 

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Acknowledgments

This paper has been developed with the financing of FEDER funds in TIN2013-40658-P and Andalusian Excellence Project TIC-5991.

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Authors and Affiliations

  1. Department of Computer Sciences and Engineering, University of Cadiz, 11519, Puerto Real, Spain

    Ignacio Javier Perez

  2. Department of Software Engineering and Computer Systems, Distance Learning University of Spain, 28040, Madrid, Spain

    Francisco Javier Cabrerizo

  3. Department of Software Engineering, University of Granada, 18071, Granada, Spain

    Sergio Alonso

  4. Faculty of Technology, Centre for Computational Intelligence, De Montfort University, Leicester, LE1 9BH, UK

    Francisco Chiclana

  5. Department of Computer Science and Artificial Intelligence, University of Granada, 18071, Granada, Spain

    Enrique Herrera-Viedma

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  1. Ignacio Javier Perez
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  2. Francisco Javier Cabrerizo
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Correspondence to Enrique Herrera-Viedma .

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    Tomasa Calvo Sánchez

  2. University of Balearic Islands, Palma, Spain

    Joan Torrens Sastre

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Perez, I.J., Cabrerizo, F.J., Alonso, S., Chiclana, F., Herrera-Viedma, E. (2016). Soft Consensus Models in Group Decision Making. In: Calvo Sánchez, T., Torrens Sastre, J. (eds) Fuzzy Logic and Information Fusion. Studies in Fuzziness and Soft Computing, vol 339. Springer, Cham. https://doi.org/10.1007/978-3-319-30421-2_10

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