A group decision-making model with interval multiplicative reciprocal matrices based on the geometric consistency index

- A group decision-making model is proposed by using the GCI index.
- The GCI of interval multiplicative reciprocal matrices is defined.
- The GCI-IOWGA operator is proposed to obtain a collective interval multiplicative reciprocal matrix.
- The sensitivity analysis of the associated exponential weighting vector with respect to the parameter is made.

A novel group decision-making model is proposed when the experts evaluate their judgments by using interval multiplicative reciprocal matrices. First, a geometric consistency index (GCI) for interval multiplicative reciprocal matrices is defined and its properties are studied. The relation between the GCI and the consistency index (CI) of interval multiplicative reciprocal matrices is further shown. Second, the GCI of interval multiplicative reciprocal matrices is utilized to propose a new induced ordered weighted geometric averaging (IOWGA) operator, which is named as the GCI-IOWGA operator. It permits the aggregation of interval multiplicative reciprocal matrices in such a way that more important weight is given to that with more consistency. The properties of the collective interval multiplicative reciprocal matrix are further studied. Third, the sensitivity analysis of the associated exponential weight vector with respect to the parameter is made. Finally, two numerical examples are carried out to illustrate the developed model and compare with the existing methods.