Modeling of systems using heterogeneous data

A mathematically tractable methodology is proposed for system modeling based on heterogeneous data, these are jointly numeric and linguistic data. It is illustrated how the data in question can be represented as interval supported fuzzy sets, namely fuzzy interval numbers (FINs), with either positive or negative membership functions. Emphasis is given to a specific scheme for regression on heterogeneous data based on a suitable representation of the data. A rule´s antecedent is a conjunction of FINs, whereas a rule´s consequent could be either a FIN or a linear input-output relation. Therefore, the utility of the proposed regression scheme is in the direction of cross-fertilizing “system modeling in the sense of Mamdani” with “system modeling in the sense of Tagaki-Sugeno”. The capacity for regression is demonstrated in a few examples