In this paper, we execute some computer simulation experiments to demonstrate the reliability of interior-outer-set mode. The experiments are done for the normal distribution, exponential stribution 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 is 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.

In this paper, we use the interior-outer-set model to calculate the risk of crop flood and order farming alternatives for Huarong County, China, where only a small sample of eight observations is available.Any risk assessment from the data must be imprecise. The risk calculated by this suggested model is a particular case among imprecise probabilities, called possibility-probability distribution.We discuss in detail how to order alternatives based on a possibility-probability distribution.The result shows, aside subjective assessment, the fuzzy risk can also be calculated.The comparison shows that the ordering based on a calculated fuzzy risk is better than one based on a histogram estimate.

The method of the information distribution is used to produce a more intelligent architecture, called primary information matrix. Then, without any assumption, we can construct a fuzzy relation matrixf or fuzzy inference. To display the advantage of the new framework, in this paper, we use it to study the relationship between epicentre intensity, I0, and earthquake magnitude, M. The result shows that the new model is better than the traditional regression model.

. Mit der neuen Methode kann die kleine Anzahl sich wie eine groK {ere Anzahl auswirken, so da{ wir ein genaueres Ergebnis erhalten. Rechnersimulationen zeigen, daβ die Leistungsfáhigkeit der neuen Methode ungefaK hr 28% höher liegt als die Histogram-mmethode.

In this paper, we use the information matrix technique to extract fuzzy if-then rules from data including noise. Witha normal diffusion function, we change all crisp observations of a given sample into fuzzy sets to make an information matrix. We extract rules according to the centroids of the rows of an information matrix. These rules are integrated into an additive fuzzy system with the same rule weight. Such fuzzy systems can be used as adaptive function approximators. Simulations show that this method is very effective compared with the conventional least-squares method and neural network. The best advantage of the suggested method is that, it may be the simplest way to extract fuzzy if-then rules from data.