The group consensus based evidential reasoning approach for multiple attributive group decision analysis.

*(English)*Zbl 1188.90126Summary: Many multiple attribute decision analysis problems include both quantitative and qualitative attributes with various kinds of uncertainties such as ignorance, fuzziness, interval data, and interval belief degrees. An evidential reasoning (ER) approach developed in the 1990s and in recent years can be used to model these problems. In this paper, the ER approach is extended to group consensus (GC) situations for multiple attributive group decision analysis problems. In order to construct and check the GC, a compatibility measure between two belief structures is developed first. Considering two experts’ utilities, the compatibility between their assessments is naturally constructed using the compatibility measure. Based on the compatibility between two experts’ assessments, the GC at a specific level that may be the attribute level, the alternative level, or the global level, can be constructed and reached after the group analysis and discussion within specified times. Under the condition of GC, we conduct a study on the forming of group assessments for alternatives, the achievement of the aggregated utilities of assessment grades, and the properties and procedure of the extended ER approach. An engineering project management software selection problem is solved by the extended ER approach to demonstrate its detailed implementation process, and its validity and applicability.

##### MSC:

90B50 | Management decision making, including multiple objectives |

##### Keywords:

decision analysis; multiple attributive group decision analysis; evidential reasoning approach; group consensus; compatibility measure
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\textit{C. Fu} and \textit{S.-L. Yang}, Eur. J. Oper. Res. 206, No. 3, 601--608 (2010; Zbl 1188.90126)

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[1] | Alonso, S.; Chiclana, F.; Herrera, F.; Herrera-Viedma, E.; Alcala-Fdez, J.; Porcel, C., A consistency-based procedure to estimate missing pairwise preference values, International journal of intelligent systems, 23, 2, 155-175, (2008) · Zbl 1148.68470 |

[2] | Ben-Arieh, D.; Chen, Z.F., Linguistic-labels aggregation and consensus measure for autocratic decision making using group recommendations, IEEE transactions on systems, man, and cybernetics, part A: systems and human, 36, 3, 558-568, (2006) |

[3] | Bordogna, G.; Fedrizzi, M.; Pasi, G., A linguistic modeling of consensus in group decision making based on OWA operators, IEEE transactions on systems, man, and cybernetics, part A: systems and humans, 27, 1, 126-132, (1997) |

[4] | Bryson, N., Group decision-making and the analytic hierarchy process: exploring the consensus-relevant information content, Computers and operations research, 1, 23, 27-35, (1996) · Zbl 0838.90014 |

[5] | Cabrerizo, F.J.; Alonso, S.; Herrera-Viedma, E., A consensus model for group decision making problems with unbalanced fuzzy linguistic information, International journal of information technology and decision making, 8, 1, 109-131, (2009) · Zbl 1178.68533 |

[6] | Chin, K.S.; Wang, Y.M.; Poon, G.K.; Yang, J.B., Failure mode and effects analysis using a group-based evidential reasoning approach, Computers and operations research, 36, 6, 1768-1779, (2009) · Zbl 1179.90089 |

[7] | Chin, K.S.; Xu, D.L.; Yang, J.B.; Lam, J.P.K., Group-based ER-AHP system for product project screening, Expert systems with applications, 35, 4, 1909-1929, (2008) |

[8] | Choudhury, A.K.; Shankar, R.; Tiwari, M.K., Consensus-based intelligent group decision-making model for the selection of advanced technology, Decision support systems, 42, 1776-1799, (2006) |

[9] | Dempster, A.P., Upper and lower probabilities induced by a multi-valued mapping, Annals of mathematical statistics, 38, 325-339, (1967) · Zbl 0168.17501 |

[10] | Denoeux, T., Reasoning with imprecise belief structures, International journal of approximate reasoning, 20, 79-111, (1999) · Zbl 0942.68126 |

[11] | Dong, Y.C.; Xu, Y.F.; Li, H.Y., On consistency measures of linguistic preference relations, European journal of operational research, 189, 430-444, (2008) · Zbl 1149.90349 |

[12] | Dong, Y.C.; Xu, Y.F.; Li, H.Y.; Feng, B., The OWA-based consensus operator under linguistic representation models using position indexes, European journal of operational research, (2009) |

[13] | Doyle, J.R.; Green, R.H.; Bottomley, P.A., Judging relative importance: direct rating and point allocation are not equivalent, Organizational behavior and human decision processes, 70, 55-72, (1997) |

[14] | Farguhar, P.H., Utility assessment methods, Management science, 30, 11, 1280-1300, (1984) |

[15] | Guo, M.; Yang, J.B.; Chin, K.S.; Wang, H.W., Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty, European journal of operational research, 182, 1294-1312, (2007) · Zbl 1127.90363 |

[16] | Herrera, F.; Herrera-Viedma, E.; Verdegay, J.L., A model of consensus in group decision making under linguistic assessments, Fuzzy sets and systems, 78, 73-87, (1996) · Zbl 0870.90007 |

[17] | 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, (1997) · Zbl 0949.68571 |

[18] | Herrera-Viedma, E.; Alonso, S.; Chiclana, F.; Herrera, F., A consensus model for group decision making with incomplete fuzzy preference relations, IEEE transactions on fuzzy systems, 15, 5, 863-877, (2007) · Zbl 1128.90513 |

[19] | Herrera-Viedma, E.; Herrera, F.; Chiclana, F., A consensus model for multiperson decision making with different preference structures, IEEE transactions on systems, man, and cybernetics, part A: systems and human, 32, 3, 394-402, (2002) · Zbl 1027.91014 |

[20] | Herrera-Viedma, E.; Herrera, F.; Chiclana, F.; Luque, M., Some issues on consistency of fuzzy preference relations, European journal of operational research, 154, 98-109, (2004) · Zbl 1099.91508 |

[21] | Herrera-Viedma, E.; Martinez, L.; Mata, F.; Chiciana, F., A consensus support system model for group decision-making problems with multigranular linguistic preference relations, IEEE transactions on fuzzy systems, 13, 644-658, (2005) |

[22] | Hwang, C.L.; Lin, M.J., Group decision making under multiple criteria, Lecture notes in economics and mathematical systems, vol. 281, (1987), Springer-Verlag Berlin/Heidelberg |

[23] | Hwang, C.L.; Yoon, K., Multiple attribute decision-making: methods and applications, (1981), Springer Berlin |

[24] | Keeney, R.L.; Raiffa, H., Decision with multiple objective: preference and value tradeoffs, (1976), Wiley New York · Zbl 0488.90001 |

[25] | Li, D.F.; Yang, J.B., Fuzzy linear programming technique for multiattribute group decision making in fuzzy environments, Information sciences, 158, 263-275, (2004) · Zbl 1064.91035 |

[26] | () |

[27] | Liu, W., Analyzing the degree of conflict among belief functions, Artificial intelligence, 170, 909-924, (2006) · Zbl 1131.68539 |

[28] | Mata, F.; MartĂnez, L.; Herrera-Viedma, E., An adaptive consensus support model for group decision making problems in a multi-granular fuzzy linguistic context, IEEE transactions on fuzzy systems, 17, 2, 279-290, (2009) |

[29] | Olcer, A.I.; Odabasi, A.Y., A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem, European journal of operational research, 166, 93-114, (2005) · Zbl 1066.90536 |

[30] | Parreiras, R.O.; Ekel, P.Ya.; Martini, J.S.C.; Palhares, R.M., A flexible consensus scheme for multicriteria group decision making under linguistic assessments, Information sciences, 180, 1075-1089, (2010) |

[31] | Roberts, R.; Goodwin, P., Weight approximations in multi-attribute decision analysis, Journal of multi-criteria decision analysis, 11, 291-303, (2002) · Zbl 1103.90360 |

[32] | Shafer, G., A mathematical theory of evidence, (1976), Princeton University Press Princeton, NJ · Zbl 0359.62002 |

[33] | Smets, P., Decision making in the TBM: the necessity of the pignistic transformation, International journal of approximate reasoning, 38, 133-147, (2004) · Zbl 1065.68098 |

[34] | Smets, P.; Kennes, K., The transferable belief model, Artificial intelligence, 66, 2, 191-234, (1994) · Zbl 0807.68087 |

[35] | Srinivasan, V.; Shocker, A.D., Linear programming techniques for multidimensional analysis of preferences, Psychometrika, 38, 337-369, (1973) · Zbl 0316.92024 |

[36] | Szmidt, E.; Kacprzyk, J., A consensus-reaching process under intuitionistic fuzzy preference relations, International journal of intelligent systems, 18, 837-852, (2003) · Zbl 1048.68098 |

[37] | Takeda, E.; Cogger, K.O.; Yu, P.L., Estimating criterion weights using eigenvectors: A comparative study, European journal of operational research, 29, 360-369, (1987) · Zbl 0618.90046 |

[38] | Tavana, M.; Kennedy, D.T.; Joglekar, P., A group decision support framework for consensus ranking of technical manager, Omega, 24, 5, 523-538, (1996) |

[39] | Wang, Y.M.; Greatbanks, R.; Yang, J.B., Interval efficiency assessment using data envelopment analysis, Fuzzy sets and systems, 153, 3, 347-370, (2005) · Zbl 1122.91339 |

[40] | Wang, Y.M.; Yang, J.B.; Xu, D.L., Environmental impact assessment using the evidential reasoning approach, European journal of operational research, 174, 1885-1913, (2006) · Zbl 1103.90364 |

[41] | Wang, Y.M.; Yang, J.B.; Xu, D.L.; Chin, K.S., The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees, European journal of operational research, 175, 35-66, (2006) · Zbl 1137.90568 |

[42] | Winston, W., Operations research applications and algorithms, (1994), Duxburg Press California · Zbl 0867.90079 |

[43] | Wu, Z.B.; Chen, Y.H., The maximizing deviation method for group multiple attribute decision making under linguistic environment, Fuzzy sets and systems, 158, 1608-1617, (2007) · Zbl 1301.91014 |

[44] | Yang, J.B., Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties, European journal of operational research, 131, 31-61, (2001) · Zbl 0979.90081 |

[45] | Yang, J.B.; Sen, P., A general multi-level evaluation process for hybrid MADA with uncertainty, IEEE transactions on systems, man, and cybernetics, 24, 10, 1458-1473, (1994) |

[46] | Yang, J.B.; Sen, P., Multiple attribute design evaluation of large engineering products using the evidential reasoning approach, Journal of engineering design, 8, 3, 211-230, (1997) |

[47] | Yang, J.B.; Singh, M.G., An evidential reasoning approach for multiple attribute decision making with uncertainty, IEEE transactions on systems, man, and cybernetics, 24, 1, 1-18, (1994) |

[48] | Yang, J.B.; Wang, Y.M.; Xu, D.L.; Chin, K.S., The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties, European journal of operational research, 171, 309-343, (2006) · Zbl 1091.90525 |

[49] | Yang, J.B.; Xu, D.L., On the evidential reasoning algorithm for multiattribute decision analysis under uncertainty, IEEE transactions on systems, man, and cybernetics, part A: systems and humans, 32, 2, 289-304, (2002) |

[50] | Yang, J.B.; Xu, D.L., Nonlinear information aggregation via evidential reasoning in multiattribute decision analysis under uncertainty, IEEE transactions on systems, man, and cybernetics, part A: systems and humans, 32, 3, 376-393, (2002) |

[51] | Zeleny, M., Multiple criteria decision making, (1982), McGraw-Hill New York · Zbl 0588.90019 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.