An ILOWG operator based group decision making method and its application to evaluate the supplier criteria

The aim of this work is to present some cases of the induced linguistic ordered weighted geometry (ILOWG) operators and study their desired properties, which are very suitable to deal with group decision making (GDM) problems involving multiplicative linguistic preference relations. First, the concepts of compatibility index (CI) for two multiplicative linguistic preference relations are defined. Then, we provide some ILOWG operators to aggregate multiplicative linguistic preference relations in GDM problems. In particular, we present the compatibility index ILOWG (CI-ILOWG) operator, which induces the order of argument values by utilizing the compatibility index of experts; and the importance ILOWG (I-ILOWG) operator, which induces the order of argument values based on the importance index of the experts. Next, the reciprocity, consistency and compatibility properties of the collective multiplicative linguistic preference relations obtained by these cases of ILOWG operators are verified. Finally, the aggregation of individual judgements (AIJ) and the aggregation of individual priorities (AIP) provide the same priorities of alternatives by utilizing the row geometric mean method (RGMM) as a prioritization procedure and the ILOWG operators as an aggregation procedure. Our results show that if all the individual decision makers have an acceptable consensus degree, then the collective preference relation is also of an acceptable consensus degree. Moreover, the compatibility index induced linguistic ordered weighted geometric mean complex judgement matrix (CI-ILOWGCJM) guarantees that the group compatibility degree is at least as good as the arithmetic mean of all the individual compatibility degrees. Accordingly, a theoretic basis has been developed for the application of these cases of ILOWG operators in linguistic group decision making. Finally, a numerical example for evaluating criteria of supply selection is given to illustrate the application of the results.