Some properties of the induced continuous ordered weighted geometric operators in group decision making

In Computers and Industrial Engineering 56 (2009) 1545–1552, an induced continuous ordered weighted geometric (ICOWG) operator is presented to deal with group decision making (GDM) problems with interval multiplicative preference relations. But, we still do not know whether the ICOWG operator can improve the consensus among a group of decision makers. The aim of this paper is to study some desired properties of the ICOWG operator in GDM problems. Firstly, the concept of Compatibility Degree and Compatibility Index (CI) is defined. We then present the Compatibility Index induced COWG (CI-ICOWG) operator to aggregate interval multiplicative preference relations, which induces the order of argument values based on the Compatibility Index of decision makers (DMs). The main novelty of the CI-ICOWG operator is that it aggregates individual preference relation in such a way that more importance is placed on the most compatibility one. Thus, the CI-ICOWG operator can guarantee that the Compatibility Degree is at least as good as the arithmetic mean of all the individual Compatibility Degrees. Additionally, if the leading decision maker’s interval multiplicative preference relation P and each of interval multiplicative preference relations Rð1Þ; Rð2Þ; . . . ; RðmÞ are of acceptable compatibility, then P and the collective judgement matrix (CJM) of Rð1Þ; Rð2Þ; . . . ; RðmÞ are of acceptable compatibility. Finally, an illustrative numerical example is used to verify the developed approaches.