A chi-square method for priority derivation in group decision making with incomplete reciprocal preference relations

This paper proposes a chi-square method (CSM) to obtain a priority vector for group 11 decision making (GDM) problems where decision-makers’(DMs’) assessment on alternative is 12 furnished as incomplete reciprocal preference relations with missing values. Relevant theorems 13 and iterative algorithm about CSM are proposed. Satty’s consistency ratio concept is adapted to 14 judge whether an incomplete reciprocal preference relation provided by a DM is of acceptable 15 consistency. If its consistency is unacceptable, an algorithm is proposed to repair it until its 16 consistency ratio reaches a satisfactory threshold. The repairing algorithm aims to rectify an 17 inconsistent incomplete reciprocal preference relation to one with acceptable consistency in 18 addition to preserving the initial preference information as much as possible. Finally, four 19 examples are examined to illustrate the applicability and validity of the proposed method, and 20 comparative analyses are provided to show its advantages over existing approaches. 21 22