Search with fuzzy numbers

The application of knowledge which can be considered only incompletely and imprecisely and the combination of this knowledge by means of evaluation functions results in uncertain values. In many search algorithms, this uncertainty simply is ignored by using only the resulting (crisp) value. It is assumed that the consideration of this uncertainty in search algorithms will give better results. The paper presents methods and an application which allow one to represent and to process uncertainty and imprecision. A new application of fuzzy numbers in relation to search algorithms and heuristics is proposed. The evaluation functions do not supply a simple crisp value, but a fuzzy number representing the uncertainty of the evaluation of the problem state. The consequences of applying fuzzy numbers for search algorithms are discussed (a new back-up paradigm, new priority relations between alternative possibilities evaluated by fuzzy numbers). First results and experiences in using this search algorithm in a chess program are finally given