A Demonstration of Reliability of the Interior-outer-set Model*

Abstract

In this paper, we execute some computer simulation experiments to demonstrate the reliability of the interior-outer-set model. The experiments are done for the normal distribution, exponential distribution and Poisson distribution. The simulation results show that the interior-outer-set model is more reasonable than the histogram model because the errors from the interior-outer-set model are smaller. The most important issue is that the possibility–probability distribution (PPD) (calculated by using the interior-outer-set model) coordinates the practical situation; it is impossible to assign a unique probability value for an event with incomplete information.

Keywords:

• Fuzzy probability
• possibility
• information distribution
• expected value
• computer simulation

Notes

Chongfu Huang is a full professor of Beijing Normal University. He received his B.A.Sc. in Mathematics from Yunnan University, Kunming, China; M.A.Sc. in Earthquake Engineering from Institute of Engineering Mechanics, Harbin, China; Ph.D. in Applied Mathematics from Beijing Normal University. From 1993 to 1995 he worked in the Beijing University of Aeronautics and Astronautics as a postdoctoral research fellow. He worked in The Chinese University of Hong Kong as a research associate, in the Science University of Tokyo as an associate professor in 1996. As a visiting professor, he worked in the University of Ghent, Belgium, in 1997 and in the University of Nebraska at Omaha, USA, in 2000. From the 2000 to 2001, he was a Mercator professor and worked in the University of Dortmund, Germany. From 1982, he worked to introduce fuzzy mathematics methods to earthquake engineering, risk analysis of natural disaster and to do research on the characteristics of fuzzy information. He has developed the information distribution method into the principle of information diffusion. His current research interests include fuzzy information processing, fuzzy risk, fuzzy neural networks, computer simulation, soft computing, computational intelligence, earthquake and flood. His researches have been supported by the Chinese Earthquake Science Foundation, the Chinese Aeronautical Science Foundation, the National Natural Science Foundation of China, the Croucher Foundation of Hong Kong, UNDP of United Nations, the Fund for Scientific Research – Flanders of Belgium, the National Science Foundation of USA and the Mercator Visiting Professorship of the German Research Society DFG.

Project Supported by National Natural Science Foundation of China, No. 40371002.