A Qualitative Approach for symbolic Data Manipulation under Uncertainty
Résumé
In decision making problems, the experts knowledge has different natures: numerical, interval-valued, symbolic, linguistic, ... In other terms, the information is heterogeneous. In this article, a qualitative (also symbolic and linguistic) approach for knowledge representation is presented. It is the continuation of studies in a given many-valued logic. First of all, a qualitative approach to manipulate uncertainty is presented as an alternative to classic probabilities. After having defined the linguistic counterpart of the symbolic framework, Generalized Symbolic Modifiers are defined to modify symbolic data usually expressed with linguistic terms. In the context, qualitative data are represented by degrees on a totally ordered scale. As fuzzy modifiers that act on kernels and supports of membership functions, several kinds of symbolic modifiers acting on scales and degrees are proposed. The other object of this work is data combination, especially when data don't have the same importance. The combination operator, called the Symbolic Weighted Median, deals with weights and proposes a representative answer depending on an initial piece of data. One interesting point is that this new median is constructed on the Generalized Symbolic Modifiers.