Takagi-Sugeno-Kang fuzzy model to assist with real estate appraisals is described and optimized using evolutionary algorithms. Two approaches were compared in the paper. The first one consisted in learning the rule base and the second one...
moreTakagi-Sugeno-Kang fuzzy model to assist with real estate appraisals is described and optimized using evolutionary algorithms. Two approaches were compared in the paper. The first one consisted in learning the rule base and the second one in combining learning the rule base and tuning the membership functions in one process. Moreover two model variants with three and five triangular and trapezoidal membership functions describing each input variable were tested. Several TSK fuzzy models comprising different number of input variables were evaluated using the MATLAB. The evolutionary algorithms were based on Pittsburgh approach with the real coded chromosomes of constant length comprising whole rule base or both the rule base and all parameters of all membership functions. The experiments were conducted using training and testing sets prepared on the basis of actual 150 sales transactions made in one of Polish cities and located in a residential section. The results obtained were not decisive and further research in this area is needed. The real estate appraisals has become a large research area with considerable literature. Many professional journals such as "Appraisal Journal", "Real Estate Appraiser", "The Appraisal Review and Mortgage Underwriting Journal", "The Journal of Real Estate Research", "Journal of Property Valuation and Investment,", and "International Real Estate Review" specialize on the topic and practice of appraisal methods. Traditionally, three models have dominated the valuation of real estate: the sales comparison approach, the cost approach and the income capitalization approach [1]. More recently, hedonic pricing (multiple regression analysis) have been used to automate the comparison approach [2]. However, both groups of these methods have been criticized. The first group uses subjective judgments, whereas MRA has produced problems that result from the inclusion of outliers. Real data have several sources of error or imprecision generating difficulties to construct precision mass appraisal models. Automated valuation methodologies (AVM) using artificial methods have been offered as a solution for both problems . Automated valuation methodologies undergo many development during the last years. Mass appraisal modelling tries to replicate market behaviour. AVM usually demand patterns for groups of properties. For this reason, they refer to large groups rather than single property. The multiple regression analysis (MRA) remains the most reliable automated valuation method [2], which was successfully applied, among other things, in constructing price indices in Geneva, Switzerland, determining rental values in Bordeaux, France, explaining the market in Tel Aviv, Israel. However, MRA has two known problems. First, the procedure requires, that the appraiser selects the best comparables. Second, it is significantly influenced by the presence of outliers. An interesting direction for research has been the inclusion of the neural networks (NN) inside the AVM models [4], but several criticisms have been raised . The nature of the NN is informal, there is no clear function between the input and the output values. The algorithm learns by training. Inspired in the human brain, they save knowledge in weighted connections. The connections have an initial sum of the weighted inputs and an activation function which gave the output. The most widely used NN is based on multi-layer perceptron with a back propagation scheme of learning. A major drawback on NN is that knowledge is stored only in the weights with no direct significance to the valuation process. One of the most interesting problem in this area is the extraction of fuzzy rules from the trained NN. Some have argued that NN are better than MRA if the data set is large and if the right parameters are found. The mean absolute error resulted from NN model was lower (from 3,9 to 6.9%) than the mean absolute error from the regression model (from 7.5 to 11.3%) [1], [3]. However, several authors arrived at the same conclusion how outcomes vary with different NN models. Results from show that NN models give inconsistent results and long run times, which lead to reject this technique from mass appraisal. Analysis of the current directions in research shows that the most prominent types of AVM are fuzzy systems and genetic fuzzy rule-based systems . Fuzzy models have emerged as an effective tool, when the data are both quantitative and qualitative. They could be applied