A Fuzzy Expert System for Auction Reserve Prices

The paper focuses on the issue of a reliable reserve price: important both for the sellers as for the purchaser. A too high reserve price may discourage the bidding process, but a price too low may damage the sellers. The analysis of the problem shows its high complexity. We suggest an objective methodology of constructing the evaluation of art works, based on a multi-attributes valuation system using a fuzzy expert system. The start point is the use of FM matrix similar to the Boston matrix to assign the work to one of four main categories of authors and art goods: stars, blue chips, portfolios and dogs, questions. For each one of the categories, the second step is the decision tree design. At the basis of these designs there is the belief that four are the main categories of variables, which carry at the final evaluation: artistic values, hedonic values, sociological economic macro-factors, micro-economic factors. These four are not independent variables. So the simple decision trees with four branches become very involved till at the final building which has more then thirty independent variables like the artistic values relate to the artist, to the work, to the artistic current, etc.The paper is a preliminary effort to apply the Fuzzy Sets Theory to the multi-attributes valuation of art goods. This theory provides a systematic framework to deal with qualitative concepts that can be translated in to quantitative parameters in a complex system of variables only by “fuzzy” relations, because of the intrinsic lack of precision and of uncertainty about the causal relation between sets of the inputs and of outputs. Experts give the ranges of values imputed to the linguistic variables, by reference to the statistics of the past auctions in the international market. The system structure identifies the fuzzy logic inference flow from the input variables to the output variables. The fuzzy inference takes place in rule blocks, which contain the linguistic control rules. The outputs of these rule blocks are linguistic variables. The defuzzification in the output interfaces usually translates them into crisp variables. In this case we propose as output a fuzzy evaluation that produces an interval of values between the minimum and the maximum. At the moment the paper is of methodological nature and does not aim to offer empirical results, but we are working with experts to new improvements and to a really running of the system.