A probabilistic linguistic VIKOR method to solve MCDM problems with inconsistent criteria for different alternatives

Abstract

VIKOR is a well-defined multiple criteria decision-making (MCDM) method since it reflects different risk attitudes of decision-makers by measuring the overall performance of an alternative under all criteria as “group value” and the worst performance of the alternative under all criteria as “individual regret”, but it cannot deal with MCDM problems where the criteria of different alternatives are inconsistent (different) and the decision information is uncertain. To address these problems, we present a probabilistic linguistic VIKOR method by combining with probabilistic linguistic term sets which portrays uncertain information such as individual hesitancy and incomplete belief flexibly. In addition, we introduce the aspired and tolerable values of criteria as reference points to measure the closeness degrees of alternatives to the ideal solution. To compare group values and individual regrets of different alternatives, we develop a vector normalization method that considers the number of criteria. The robustness of the aggregation results of group values and individual regrets is improved based on the extended Borda rule, which takes into account both values and ranks of alternatives in the aggregation. A case study of personnel evaluation demonstrates the effectiveness of the proposed method for solving MCDM problems with inconsistent criteria and uncertain decision information.