Construct The Probability Distribution Method Under The Conditions Of Cognitive Uncertainty

In engineering design optimization (DO) of large-scale and complex systems, it is important to handle epistemic uncertainty which exists in design parameters and stages of DO. Using possibility theory to deal with this kind of uncertainty, one of the vital points is constructing reasonable possibility distribution. In many cases, epistemic uncertainty is caused by the situation of data insufficiency and/or information incompleteness. In possibility distribution construction, on the one hand, the constructed possibility distribution should be accurate enough to describe the true distribution; one the other hand, the constructing method should be applicable to the situation of limited data/information. Moreover, the construction method should be able to cater for the case of multi-variable.This paper conducts research that addresses the above-mentioned requirements of possibility distribution constructing method, i.e., the maximal specificity, the ability to handle small sample size, and the case of multi-variable. The main research work of this paper can be summarized as follows:Firstly, base on the concept of joint distribution in probability theory, this paper extends the possibility distribution to the two-dimensional and multi-dimensional cases under the finite set situation.Secondly, this paper proposes a maximal-specificity-based possibility distribution (MSBPD) method to reduce the information loss during probability-possibility transformation. Considering the maximal specificity principle, an assessment method is proposed to assess possibility distribution constructing method's degree of maximal specificity. The assessment method illustrates that of the proposed MSBPD method has good performance in terms of degree of maximal specificity.To cater for the situation of data insufficiency, which often exists DO practice, this paper proposes a possibility distribution constructing method which can be applied to the case of small sample size based on probability-possibility transformation by introducing Sison-Glaz's simultaneous confidence intervals. The consistency with the true probability distribution and the coverage probability of the proposed method are testified, and an example is given.