Statistics-based method for large-scale group decision-making with incomplete linguistic distribution fuzzy information: Incorporating reliability and entropy

Abstract

Aiming at large-scale decision-makers (DMs) and the loss of decision sample information in large-scale group decision-making (LSGDM), a novel statistical estimation method incorporating the reliability and entropy of linguistic distribution assessment is proposed. First, classify the large-scale DMs into several subgroups according to their prior decision efficiency distribution. After clustering, collect the five-number summary of the incomplete decision sample information provided by the DMs in the subgroups. Second, estimate the mean, standard deviation, skewness and kurtosis of the decision sample via the Cornish–Fisher expansion. Then utilize the Bayes estimation to address the reliability of the subgroups, thereby obtaining the confidence interval, which is used to develop the interval linguistic distribution preference relation (ILDPR) for the subgroups. Moreover, combine the reliability and the entropy measure constructed by the above four estimators to determine subgroup weights. Furthermore, present the expectation and variance of the ILDPR to sort the alternatives. Finally, demonstrate the feasibility and validity of the proposed LSGDM method based on a case and a comparison.