Discussion on Normalization Methods of Interval Weights

This paper is collecting the classic and newly normalization methods, finding deficiency of existing normalization methods for interval weights, and introducing a new normalization methods for interval weights. When we normalize the interval weights, it is very important and necessary to check whether, after normalizing, the location of interval centers as well as the length of interval weights keep the same proportion as those of original interval weights. It is found that, in some newly normalization methods, they violate these goodness criteria. In current work, for interval weights, we propose a new normalization method that reserves both proportions of the distances from interval centers to the origin and of interval lengths, and also eliminates the redundancy from the original given interval weights. This new method can be widely applied in information fusion and decision making in environments with uncertainty.