1. An Interval Approach to Discover Knowledge from Multiple Fuzzy Estimations Vagan Terziyan * & **, Seppo Puuronen **, Helen Kaikova * *Department of Artificial Intelligence and Information Systems, Kharkov State Technical University of Radioelectronics, UKRAINE e-mail: vagan@kture.cit-ua.net, vagan@jytko.jyu.fi **Department of Computer Science and Information Systems, University of Jyvaskyla, FINLAND, e-mail: sepi@jytko.jyu.fi GRWS’98 - The 5-th Open German-Russian Workshop on Pattern Recognition and Image Understanding, Herrsching, Germany, 21-25 September, 1998

2. Herrsching, GRWS’98 Host Triangle of Friendship

3. Metaintelligence Laboratory: Research Topics Knowledge and metaknowledge engineering; Multiple experts; Context in Artificial Intelligence; Data Mining and Knowledge Discovery; Temporal Reasoning; Metamathematics; Semantic Balance and Medical Applications; Distance Education and Virtual Universities.

4. Contents Context in Pattern Recognition Interval estimation Decontextualization with two intervals Decontextualization with several intervals Trends of uncertainty Interval estimation with several trends

5. Context in Pattern Recognition Context 1 Context 2 Context 3 Context 4 Decontextualization pattern recognition result

6. Decontextualization of Noise in Pattern Recognition with Multiple Estimations Decontextualization pattern noise estimations recognized pattern 1 2 3 4 1 2 3 4 result

7. The Problem of Interval Estimation Measurements (as well as expert opinions) are not absolutely accurate. The measurement result is expected to lie in the interval around the actual value. The inaccuracy leads to the need to estimate the resulting inaccuracy of data processing. When experts are used to estimate the value of some parameter, intervals are commonly used to describe degrees of belief.

8. Noise of an Interval Estimation In many real life cases there is also some noise which does not allow direct measurement of parameters. The noise can be considered as an undesirable effect (context) to the evaluation of a parameter. Different measurement instruments as well as different experts possess different resistance against the influence of noise. Using measurements from several different instruments as well as estimations from multiple experts we try to discover the effect caused by noise and thus be able to derive the decontextualized measurement result.

9. Basic Assumption The estimation of some parameter x given by more accurate knowledge source (i.e. source guarantees smaller upper bound of measurement error) is supposed to be closer to the actual value of parameter x (i.e. source is more resistant against a noise of estimation). The assumption allows us to derive different trends in cases when there are multiple estimations that result to shorter estimation intervals.

10. R1R1 R2R2 R res real pattern recognized pattern Physical Interpretation of Decontextualization Uncertainty is like a “resistance” for precise recognition of a pattern

11. Conclusion If you have several opinions (estimations, recognition results, solutions etc.) with different value of uncertainty you can select the most precise one, however it seems more reasonable to order opinions from the worst to the best one and try to recognize a trend of uncertainty which helps you to derive opinion more precise than the best one.