Mapping of ordinal feature values to numerical values through fuzzy clustering

Objects are represented by feature values, and the feature values are in general numerical, ordinal or nominal. The feature values of an ordinal type are totally ordered labels, and the labels can be considered as fuzzy sets. The formulation of proper fuzzy sets for the labels is important for the systems to deal with the objects of mixed feature types. When a proper ordinal-numerical mapping of the ordinal feature of interest is given, fuzzy sets for the labels of the ordinal feature can easily be formulated. In this paper, we present an algorithm to obtain an ordinal-numerical mapping of an ordinal feature of interest from a given object set in which objects have the ordinal feature values, in the way that the obtained mapping reflects the information structure in the object set. The proposed algorithm starts with an initial ordinal-numerical mapping, and iteratively obtains a fuzzy partition matrix with the ordinal-numerical mapping and computes a new ordinal numerical mapping from the fuzzy partition matrix. In this way both of them become improved gradually. The information structure, i.e., the fuzzy partition matrix, stored in the given object set is eventually reflected in the ordinal numerical mapping. We also show the validity of the proposed algorithm through experiments with synthetic object sets.