A Note on OWA Operator Based on the Normal Distribution

The most important thing in using the OWA operator is to determine OWA weights. In this paper, we first discussed the OWA weights in depth based on the normal distribution from the results in Ref. 1. Then, we pointed out that the probability density function used in Ref. 1 was not a standard probability density of the normal distribution though the same results as us can be deduced from it. We redefined the weights based on the normal distribution, and explained that different standard deviation sigma could bring different aggregation result. Motivated by the idea of maximum entropy, we developed a new method by the satisfied entropy to determine the satisfied OWA weights based on the normal distribution, and proposed a conjecture about the relationship between the standard deviation sigma and the entropy of OWA weights. Finally we used an experiment to illustrate our viewpoint and compared the results with those in Ref. 1.