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Direct Iterative Procedures for Consensus Building with Additive Preference Relations Based on the Discrete Assessment Scale

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Abstract

Individual consistency and group consensus are both important when seeking reliable and satisfying solutions for group decision making (GDM) problems using additive preference relations (APRs). In this paper, two new algorithms are proposed to facilitate the consensus reaching process, the first of which is used to improve the individual consistency level, and the second of which is designed to assist the group to achieve a predefined consensus level. Unlike previous GDM studies for consistency and consensus building, the proposed algorithms are essentially heuristic, modify only some of the elements in APRs to reduce the number of preference modifications in the consistency and consensus process, and have modified preferences that belong to the original evaluation scale to make the generated suggestions easier to understand. In particular, the consensus algorithm ensures that the individual consistency level is still acceptable when the predefined consensus level is achieved. Finally, classical examples and simulations are given to demonstrate the effectiveness of the proposed approaches.

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References

  • Alonso S, Chiclana F, Herrera F, Herrera-Viedma E, Alcalá-Fdez J, Porcel C (2008) A consistency-based procedure to estimate missing pairwise preference values. Int J Intell Syst 23:155–175

    Article  Google Scholar 

  • Cabrerizo FJ, Morente-Molinera JA, Pedrycz W, Taghavi A, Herrera-Viedma E (2018) Granulating linguistic information in decision making under consensus and consistency. Expert Syst Appl 99:83–92

    Article  Google Scholar 

  • Cao D, Leung LC, Law JS (2008) Modifying inconsistent comparison matrix in analytic hierarchy process: a heuristic approach. Decis Support Syst 44(4):944–953

    Article  Google Scholar 

  • Cavallo B, D’Apuzzo L (2009) A general unified framework for pairwise comparison matrices in multicriterial methods. Int J Intell Syst 24:377–398

    Article  Google Scholar 

  • Chiclana F, Herrera F, Herrera-Viedma E (1998) Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst 97:33–48

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Chu JF, Liu XW, Wang YM, Chin KS (2016) A group decision making model considering both the additive consistency and group consensus of intuitionistic fuzzy preference relations. Comput Ind Eng 101:227–242

    Article  Google Scholar 

  • Contreras I (2010) A distance-based consensus model with flexible choice of rank-position weights. Group Decis Negot 19(5):441–456

    Article  Google Scholar 

  • Dong YC, Xu JP (2016) Consensus building in group decision making: searching the consensus path with minimum adjustments. Springer, New York

    Book  Google Scholar 

  • Dong YC, Zhang HJ, Herrera-Viedma E (2016) Integrating experts’ weights generated dynamically into the consensus reaching process and its applications in managing non-cooperative behaviors. Decis Support Syst 84:1–15

    Article  Google Scholar 

  • Dong QX, Zhou X, Martínez L (2019) A hybrid group decision making framework for achieving agreed solutions based on stable opinions. Inf Sci 490(2019):227–243

    Article  Google Scholar 

  • Gong ZW, Xu C, Chiclana F, Xu XX (2016) Consensus measure with multi-stage fluctuation utility based on China’s urban demolition negotiation. Group Decis Negot 26(2):1–29

    Google Scholar 

  • González-Arteaga T, Andrés-Calle R, Chiclana F (2016) A new measure of consensus with reciprocal preference relations: the correlation consensus degree. Knowl Based Syst 107:104–116

    Article  Google Scholar 

  • Gupta M (2018) Consensus building process in group decision making-an adaptive procedure based on group dynamics. IEEE Trans Fuzzy Syst 26(4):1923–1933

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Herrera-Viedma E, Chiclana F, Herrera F, Alonso S (2007) Group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans Syst Man Cybern Part B 37(1):176–189

    Article  Google Scholar 

  • Hou F (2015) A consensus gap indicator and its application to group decision making. Group Decis Negot 24(3):415–428

    Article  Google Scholar 

  • Kim J (2008) A model and case for supporting participatory public decision making in e democracy. Int J Intell Syst 17:179–193

    Google Scholar 

  • Li CC, Rodríguez R, Martínez L, Dong YC, Herrera F (2019) Consensus building with individual consistency control in group decision making. IEEE Trans Fuzzy Syst 27:319–332

    Article  Google Scholar 

  • Li KW, Wang ZJ, Tong XY (2016) Acceptability analysis and priority weight elicitation for interval multiplicative comparison matrices. Eur J Oper Res 250:628–638

    Article  Google Scholar 

  • Ma J, Fan ZP, Jiang YP, Mao JY, Ma L (2006) A method for repairing the inconsistency of fuzzy preference relations. Fuzzy Sets Syst 157:20–33

    Article  Google Scholar 

  • Orlovsky SA (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1:155–167

    Article  Google Scholar 

  • Palomares I, Rodríguez RM, Martínez L (2013) An attitude-driven web consensus support system for heterogeneous group decision making. Expert Syst Appl 40(1):139–149

    Article  Google Scholar 

  • Parreiras RO, Ekel PY, Morais DC (2012) Fuzzy set based consensus schemes for multicriteria group decision making applied to strategic planning. Group Decis Negot 21:153–183

    Article  Google Scholar 

  • Pearl J (1984) Heuristics: intelligent search strategies for computer problem solving. Addison-Wesley, Boston

    Google Scholar 

  • Pérez IJ, Cabrerizo FJ, Alonso S, Herrera-Viedma E (2014) A new consensus model for group decision making problems with nonhomogeneous experts. IEEE Trans Syst Man Cybern Syst 44(4):494–498

    Article  Google Scholar 

  • Rezaei J, Ortt R (2013) Multi-criteria supplier segmentation using a fuzzy preference relations based AHP. Eur J Oper Res 225(1):75–84

    Article  Google Scholar 

  • Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York

    Google Scholar 

  • Wan SP, Wang F, Dong JY (2018) A group decision making method with interval valued fuzzy preference relations based on the geometric consistency. Inf Sci 40:87–100

    Google Scholar 

  • Wu ZB, Xu JP (2012) A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures. Fuzzy Sets Syst 206:58–73

    Article  Google Scholar 

  • Wu ZB, Huang S, Xu JP (2019) Multi-stage optimization models for individual consistency and group consensus with preference relations. Eur J Oper Res 275:182–194

    Article  Google Scholar 

  • Wu ZB, Jin BM, Xu JP (2018a) Local feedback strategy for consensus building with probability-hesitant fuzzy preference relations. Appl Soft Comput 67:691–705

    Article  Google Scholar 

  • Wu ZB, Xu JP (2018b) A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Inf Fusion 41:217–231

    Article  Google Scholar 

  • Xu YJ, Li KW, Wang HM (2013) Distance-based consensus models for fuzzy and multiplicative preference relations. Inf Sci 253:56–73

    Article  Google Scholar 

  • Zhang BW, Dong YC, Herrera-Viedma E (2019) Group decision making with heterogeneous preference structures: an automatic mechanism to support consensus reaching. Group Decis Negot. https://doi.org/10.1007/s10726-018-09609-y

    Article  Google Scholar 

  • Zhang GQ, Dong YC, Xu YF (2012) Linear optimization modeling of consistency issues in group decision making based on fuzzy preference relations. Expert Syst Appl 39:2415–2420

    Article  Google Scholar 

  • Zhang HJ, Dong YC, Herrera-Viedma E (2018a) Consensus building for the heterogeneous large-scale GDM with the individual concerns and satisfactions. IEEE Trans Fuzzy Syst 26(2):884–898

    Article  Google Scholar 

  • Zhang Z, Kou XY, Dong QX (2018b) Additive consistency analysis and improvement for hesitant fuzzy preference relations. Expert Syst Appl 98:118–128

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China under Grant 71671118.

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Authors and Affiliations

  1. Uncertainty Decision-Making Laboratory, Business School, Sichuan University, No. 24, South Section 1, Yihuan Road, Chengdu, 610065, Sichuan, People’s Republic of China

    Zhibin Wu & Jie Xiao

  2. School of Computer Science, Electrical and Electronic Engineering, and Engineering Mathematics, University of Bristol, Bristol, BS8 1TH, UK

    Ivan Palomares

Authors
  1. Zhibin Wu
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  2. Jie Xiao
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  3. Ivan Palomares
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Correspondence to Zhibin Wu.

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Wu, Z., Xiao, J. & Palomares, I. Direct Iterative Procedures for Consensus Building with Additive Preference Relations Based on the Discrete Assessment Scale. Group Decis Negot 28, 1167–1191 (2019). https://doi.org/10.1007/s10726-019-09636-3

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