The diagnosis of the fuzzy-rules can be compared to the

expected diagnosis (verification of degree of danger) and the diagnosis given by the KN (see Tab. 2). The first comparison corresponds to the correctness of the fuzzy-rules, while the latter indicates the explanation capability of fuzzy-rules relating to the KN. The reason why the explanation capability is not clearly better than the correctness of the diagnosis can not be given at this time. Further examples have to be explored to see whether the reasons of this result are based on the fuge-method or on type of the problem treated.

The fuzzy-rules generated by the fuge-method use, according to the experts of the SFISAR, the most relevant parameters for the different classes of the avalanche danger. Nevertheless the rules formulate only general conformities with natural laws and allow no deeper insights into the physical dependences of the avalanche forecasting problem. Nevertheless the generalization capabilities of the fuzzy-rules can be observed for higher classes of the avalanche danger (4, 5 and 6). This classes are represented in the dataset of totaly 1210 days only through 50 days. Using only the relevant parameters the fuzzy-rules perform better than the KN for this days.

Compared to other forecasting systems ALUDES shows about the same performance as the best statistical based systems used so far. An advantage of the system that includes a Kohonen Net is the robustness and ability to work with incomplete data. Further, an explanation in natural language terms for a diagnosis can be given in about 60% of the cases using fuzzy-rules.

5. Conclusions

The new approach showed to be a powerful method to the problem of avalanche forecasting. ALUDES is a reliable support system for the decision process which directly evaluates the degree of avalanche danger for a given region.

sets (# cases) % correct % to low % to high

learn set (1210) 80 10 10
test set (mean
of 3 sets of 151
days)
69 17 14

TABLE 1. Performance of the KN.

diagnosis of
fuzzy-rules
compared to ...
% correct % to low % to high

... verification 58 16 26
... KN diagnosis 61 13 26

TABLE 2. Performance of the fuzzy-rules.

Using the fuge-method, it is possible to extract (symbolic) knowledge in form of fuzzy-rules out of a connectionist system that uses sub-symbolic knowledge. The generated fuzzy-rules are able to explain the behavior of the KN used in ALUDES in 61% of the cases. So the lack of transparency of neural networks can partially be overcome.
Comparing the diagnosis of a KN and the diagnosis of fuzzy-rules generated out of this KN it is possible to improve the performance of a hybrid expert system through combining the different diagnosis in a blackboard.
The new fuge-method presented above may be used as a knowledge acquisition tool based on Kohonen Networks and therefore may also be used to build an explanation component for hybrid expert systems using Kohonen Networks.

Acknowledgments

This research was supported by the ?Swiss Federal Institute for Snow and Avalanche Research? (SFISAR) and the ?Swiss National Science Foundation? (SNSF).
Special thanks also to Prof. Dr. A. Ultsch from the University of Marburg/Lahn (D) for his cooperation in this project.

References

[1] Jaccard, C.: Die Rolle des Eidg. Instituts f?r Schneeund Lawinenforschung f?r das Gebirge. In Schweiz. Z. Forstwes., 5:357-365. 141, 1990.

[2] Schweizer, J., F?hn, P.M.B.: Avalanche forecasting - an expert system approach. In Proceedings Int. Snow Science Workshop (in press), Snowbird USA, Oct. 1994.

[3] Ultsch, A.: Konnektionistische Modelle und ihre Integration mit wissenbasierten Systemen. Forschungsbericht Nr. 396, Universit?t Dortmund, FB Informatik, Feb. 1991.

[4] Palm, G., Ultsch, A., Goser, K., R?ckert, U.: Knowledge Processing in Neural Architecture, Delgado-Fraias, J.G., Moore, W.R. (eds) : VLSI for Neural Networks and Artificial Intelligence, Plenum Publ., New York 1993.

[5] Kohonen, T.: Self-Organization and Associative Memory, Springer Series in Information Sciences, 1989 (3rd ed.).

[6] Ultsch, A.: Automatische Wissensakquisition f?r Fuzzy-Expertensysteme aus selbstorganisierenden Netzen. Forschungsbericht Nr. 404, Universit?t Dortmund, FB Informatik, Okt. 1991.