Duo-Stage Decision: A Framework for Filling Missing Values, Consistency Check, and Repair of Decision Matrices in Multicriteria Group Decision Making

With high uncertainty and vagueness in the decision-making process, maintaining consistency in the decision matrix is an open challenge. Previous studies on the intuitionistic fuzzy (IF) theory focused on the consistency of preference relation but ignored consistency of the decision matrix. In this article, efforts are made to propose a new duo-stage decision framework in the context of IF set to better circumvent the challenge. Often, decision makers (DMs) hesitate to provide certain values in the decision matrix that are filled randomly, resulting in inaccuracies in the decision-making process. To alleviate this issue, a new systematic procedure is developed that sensibly fills the missing data in the first stage. Following the first stage, consistency of the decision matrix is determined by extending Cronbach's alpha coefficient to IF context. Furthermore, efforts are made to repair inconsistent decision matrix iteratively. In the second stage, a new aggregation operator is presented for aggregation of DMs' preferences. Also, a new mathematical model is proposed for criteria weight estimation, and a procedure is developed for ranking objects. The practical use of the proposed framework is demonstrated using a numerical example, and the strengths and weaknesses of the framework are investigated.