For multiple attribute group
decision making problems, in which the attribute values are normal
distribution interval numbers and the attribute weight information
is incomplete, some new aggregation operators are defined, such as the
normal distribution interval number weighted arithmetic averaging(NDINWAA) operator, the normal distribution interval number
ordered weighted averaging(NDINOWA) operator and the normal
distribution interval number hybrid weighted
averaging(NDINHA) operator. Then an approach is developed for
solving multiple attribute group decision making based on normal
distribution interval number with incomplete information. In this
method, normal distribution interval number attribute values are
aggregated by the NDINWAA operator and the NDINHA operator, some
optimal models are constructed to determine the optimal attribute
weights by using the variance of normal distribution interval
number attribute values, and ranking of alternatives is performed by
using expectation-variance principle. Finally, an example shows
the effectiveness of this method.