| Herrera-Viedma[17] et al presented a method to construct a consistent fuzzy preference relation and a consistent multiplicative preference relation from a set of n-1preference values{p12,p23,…,pn-1n}.For the lack of acceptable compati bility can lead to unsatisfied decision making with multiplicative preference relati on, so we know in the group decision making with the multiplicative preference relations, the compatibility degree of the multiplicative preference relation given by the expert is a very important problem. Thus, in this article when aggregati on the completed multiplicative preference relations by experts in group decision making, we use the method presented by E. Herrera-Viedma et al.[17] to constr uct the compatibility degree and the compatibility index. And we also present a new induced ordered weighted geometric operator (IOWG) to deal with group de cision making problems. Combined with the operator we will do some research about group of decision making problems as follows:First, we present a new induced ordered weighted geometric operator for gr oup decision-making with multiplicative preference relation. And some properties of the new IOWG operators in group decision making with multiplicative prefere nce relations is also given. In the end of this section, a numerical example was used to illustrative the developed procedure and the theorems.Then, we provide a method to estimate missing values for incomplete multiplicative preference relation and the sufficient condition to estimate all missing values. We also give two methods to deal with the group decision making of incomplete multiplicative preference relations and the weights of the multiplicative preference relation given by the experts are known. An illustrative example is also discussed in the end of this section. |
