The induced fuzzy integral aggregation operator

We discuss the fuzzy integral. The centrality of the ordering operation, based upon the arguments to be aggregated, is pointed out. We then extend the fuzzy integral aggregation operator by allowing the ordering operation to be based upon values other then those being aggregated. This leads to the induced fuzzy integral aggregation operator. We look at this new operator and study its properties. We show its relationship to a formulation called limited fuzzy integral aggregation. It is shown how this new induced fuzzy integral operator provides a natural framework for the implementation of nearest neighbor rules. Throughout this work, use is made only of the ordinal aspects of the information used. (C) 2002 Wiley Periodicals, Inc.