Extending microaggregation procedures using defuzzification methods for categorical variables

Defuzzification is one of the fundamental steps in the development of fuzzy knowledge based systems. Given a fuzzy set μ over the reference set X, defuzzification applied to μ returns an element of X. While a large number of methods exist for the case of X being a numerical scale, only few methods are applicable when X corresponds to a categorical scale. Aggregation procedures have been extensively used in defuzzification in numerical scales. This is so because defuzzification has been studied as equivalent to the computation of an expected value. In this work we present the reversal approach, we study defuzzification procedures for their application to aggregation. We focus on the development of defuzzification methods for the case of X being an ordinal scale. This is, X is a set of finite values in which a total order is defined. Our ultimate goal is to apply these methods to microaggregation (a Statistical Disclosure Risk).