Extracting Decision Rules from Qualitative Data via Sugeno Utility Functionals

Abstract

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 SUF 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 SUF. These max-SUF and min-SUF 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.

Incremental Elicitation of Capacities for the Sugeno Integral with a Maximin Approach

“…We are also interested in methods that support the interpretation of real data, for instance by using if-then rules based on Sugeno integrals. As the Sugeno integral represents a single threshold rule [6], an interesting direction is to adapt our procedure for Sugeno Utility Functionals (SUF) [4].…”

New Directions in Ordinal Evaluation: Sugeno Integrals and Beyond

“…For example, if Φ R is a model of a dataset D, we may want to find an SUF that best fits D. Obtaining S µ,φ = Φ R is not always possible since SUFs are not expressive enough. However, equality can be always achieved using a max-SUF [11]. The method presented in the next section relies on this fact.…”

“…Thus, an interesting question is whether SUFs can serve as an intermediary model that helps guiding the learning process of a rule based model. Indeed, in [11], such a learning algorithm is proposed. Let D be a dataset.…”

“…Shorter rules are easier to interpret and constitute more concise models. In [11] it was presented an empirical study of rule length distributions obtained after steps 1, 2, and 3.…”

“…We will say that a function Φ is equivalent to R if Φ = Φ R . It was shown in [19,11] that: (i) Any SUF S µ,φ is equivalent to a rule set. (ii) Any single rule is equivalent to a SUF.…”