Regression on Heterogeneous Fuzzy Data

A novel formalism is presented, which enables the processing of heterogeneous data including numeric-, interval-valued-, or fuzzydata. The data in question are represented herein as interval-supported fuzzy sets with suitable membership functions. The term Fuzzy Interval Number (FIN) denotes one of the aforementioned types of data. A FIN can have either a positive or a negative membership function. We show a number of mathematical tools/properties in the set of FIN’s including, a partial ordering relation, a distance function, an addition and a multiplication operation; hence we can talk of FIN-arithmetic. The presented formalism is used to carry out regression on FIN’s. Potential applications of regression on FIN’s include reduction in the number of rules in a fuzzy system, generalization of fuzzy rules, etc. Two examples demonstrate the merits of the presented formalism.