The induced continuous ordered weighted geometric operators and their application in group decision making

In [IEEE Trans. Syst., Man, Cybernet.--Part B 29 (1999) 141], a more general class of OWA operators called the induced ordered weighted averaging (IOWA) operators is developed. Later, Yager and Xu [Fuzzy Sets and Syst, 157 (2006) 1393-1402.] introduced the continuous ordered weighted geometric operator(COWG), which is suitable for individual decision making problems taking the form of interval multiplicative preference relation. The aim of this paper is to develop some induced continuous ordered weighted geometric (ICOWG) operators. In particular, we present the reliability induced COWG (R-ICOWG) operator, which applies the ordering of the argument values based upon the reliability of the information sources; and the relative consensus degree induced COWG (RCD-ICOWG) operator, which applies the ordering of the argument values based upon the relative consensus degree of the information sources. Some desirable properties of the ICOWG operators are studied, and then, the ICOWG operators are applied to group decision making with interval multiplicative preference relations.