Using Orders of Magnitude and Nominal Variables to Construct Fuzzy Partitions

The application of qualitative reasoning to learning algorithms can provide these models with the capability of automate common-sense and expert reasoning. Learning algorithms aim at automatically gathering the relevant information from a set of patterns and turn it into useful knowledge. That information usually comes from different sources and displays subjectivity and ambiguity, especially as far as qualitative data is concerned. This paper analyses the unsupervised learning capability of the LAMDA (learning algorithm for multivariate data analysis) algorithm. The LAMDA algorithm relies on the generalising capability of fuzzy connectives obtained as the interpolation of a t-norm and its dual t-conorm and permits the use of qualitative variables. Qualitative variables defined on orders of magnitude scales or on nominal scales are used to reduce the search space. A mathematical property of the hybrid connectives used is imposed to guarantee coherence in the obtained classification. The results obtained are applied to support decision making in a marketing problem: identifying customer behaviour.