Abstract
•An inconsistency index of interval multiplicative reciprocal matrices is proposed.•A new operator is formed to aggregate individual interval-valued preference matrices.•The concept of approximate consistency is extended to a group decision making model.
In order to cope with uncertainty experienced by decision makers, interval multiplicative reciprocal matrices are used to express judgments in the framework of the fuzzy analytic hierarchy process (FAHP). When considering the logical consistency of the judgments, it is important to study the consistency of interval multiplicative reciprocal matrices developed in the AHP. In this study, an inconsistency index is proposed to quantify the inconsistency degree of interval multiplicative reciprocal matrices. The concept of the approximate consistency is extended to study group decision making problems with interval multiplicative reciprocal matrices. A new aggregation operator is formed to combine individual matrices. By considering permutations of alternatives, the properties of the collective interval multiplicative reciprocal matrix are studied in detail. Numerical results are reported to show the applications of the proposed indexes to group decision making. The advantages of the proposed group decision making model together with the inconsistency indexes are involved of handling the uncertainty factor, the permutations of alternatives and the reciprocity exhibited in interval multiplicative reciprocal matrices.