Extracting Decision Rules from Qualitative Data via Sugeno Utility Functionals
Sugeno integrals are qualitative aggregation functions. They are used in multiple criteria decision making and decision under uncertainty, for computing global evaluations of items, based on local evaluations. The combination of a Sugeno integral with unary order preserving functions on each criterion is called a Sugeno utility functionals (SUF). A noteworthy property of SUFs is that they represent multi-threshold decision rules, while Sugeno integrals represent single-threshold ones. However, not all sets of multi-threshold rules can be represented by a single SUF. In this paper, we consider functions defined as the minimum or the maximum of several SUFs. These max-SUFs and min-SUFs can represent all functions that can be described by a set of multi-threshold rules, i.e., all order-preserving functions on finite scales. We study their potential advantages as a compact representation of a big set of rules, as well as an intermediary step for extracting rules from empirical datasets.
KeywordsSugeno integral Sugeno utility functional Piecewise unary function Decision rules Qualitative representation
This work has been partially supported by the Labex ANR-11-LABX-0040-CIMI (Centre International de Mathématiques et d’Infor-matique) in the setting of the program ANR-11-IDEX-0002-02, subproject ISIPA (Interpolation, Sugeno Integral, Proportional Analogy).
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