Perception-based functions in qualitative forecasting

Perception-based function (PBF) is a fuzzy function obtained as a result of reconstruction of human judgments given by a sequence of rules R_k: If T is T_k then S is S_k, where T_k are perception-based intervals defined on the domain of independent variable T, and S_k are perception-based shape patterns of variable S on interval T_k. Intervals T_k can be expressed by words like Between N and M, Approximately M, Middle of the Day, End of the Week, etc. Shape patterns S_k can be expressed linguistically, e.g., as follows: Very Large, Increasing, Quickly Decreasing and Slightly Concave, etc. PBF differs from the Mamdani fuzzy model which defines a crisp function usually obtained as a result of tuning of function parameters in the presence of training crisp data. PBF is used for reconstruction of human judgments when testing data are absent or scarce. Such reconstruction is based mainly on scaling and granulation of human knowledge. PBF can be used in Computing with Words and Perceptions for qualitative evaluation of relations between variables. In this chapter we discuss application of PBF to qualitative forecasting of a new product life cycle. We consider new parametric patterns used for modeling convex- concave shapes of PBF and propose a method of reconstruction of PBF with these shape patterns. These patterns can be used also for time series segmentation in perception-based time series data mining.