A Bayesian approach to incomplete fuzzy reciprocal preference relations in consensus reaching process and its application in project performance evaluations.

Due to the fact that individual knowledge is often inadequate and deficient in group decision-making problems, it is commonly seen that the preference information provided by the decision makers are incomplete. To encounter this problem lots of relevant researches have already been carried out. However, previous methods often only take into account either the information of the expert who provided incomplete preference, or information provided by the rest of the group. To be more thorough and comprehensive, this paper combined both parts of the information, by first setting the unknown preference values as output and known ones as inputs, training the Bayesian regression model with the complete observations of other experts to detect the associations between them, and then putting in the incomplete preference information to predict the unknown ones. Moreover, inspired by the empirical rule of the Gaussian distribution, this paper also propose to combine the concept of confidence interval with that of interval-valued preference relations, by expressing the prediction results with interval-valued fuzzy reciprocal relations to allow some degree of uncertainty. On the basis of that an iterative consensus reaching process incorporated with feedback mechanism is also proposed. Finally a case study of possible application of our proposed model in project performance evaluations is carried out, the results of which then further verify the practicality and validity of our model.