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.

In some variants of the supervised classification setting, the domains of the attributes and the set of classes are totally ordered sets. The task of learning a classifier that is nondecreasing w.r.t. each attribute is called monotonic classification. Several kinds of models can be used in this task; in this paper, we focus on decision rules. We propose a method for learning a set of decision rules that optimally fits the training data while favoring short rules over long ones. We give new results on the representation of sets of if-then rules by extensions of Sugeno integrals to distinct attribute domains, where local utility functions are used to map attribute domains to a common totally ordered scale. We study whether such qualitative extensions of Sugeno integral provide compact representations of large sets of decision rules.

We define a pattern structure whose objects are elements of a supporting ontology. In this framework, descriptions constitute trees, made of triples subject-predicate-object, and for which we provide a meaningful similarity operator. The specificity of the descriptions depends on a hyperparameter corresponding to their depth. This formalism is compatible with ontologies formulated in the language of RDF and RDFS and aims to set up a framework based on pattern structures for knowledge discovery in the web of data.