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Manipulation of qualitative degrees to handle uncertainty: formal models and applications

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Abstract

In this article, qualitative, symbolic and linguistic models for knowledge representation are presented as well as their applications. Such models are useful in decision making problems when information from the experts' knowledge is expressed through different heterogeneous types such as numerical, interval-valued, symbolic, linguistic, … The whole work proposed here takes place in a given many-valued logic. First, as an alternative to classic probabilities, a method using qualitative degrees is described and an application in supervised learning is proposed. Then we study the transformation of these degrees when they are subjected to a modification: thus we present the Generalized Symbolic Modifiers. These tools are defined as manipulations computed on a pair (degree, scale). They are grouped together into several families and thus offer many possibilities to handle uncertainty. An application in colorimetrics is described and shows the feasibility of the approach. The last point addressed in this article is the data combination. An operator called the Symbolic Weighted Median gives a summary of several qualitative degrees with associated weights. One particularity is that this median is constructed on the Generalized Symbolic Modifiers. Finally we explain how the Symbolic Weighted Median is exploited in the internal mechanism of the application in colorimetrics.

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Authors and Affiliations

  1. Labo IA, University Paris 8, 2, rue de la Liberté, 93526, SAINT-DENIS Cedex 2, France

    Isis Truck & Herman Akdag

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  1. Isis Truck
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  2. Herman Akdag
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Isis Truck did research in the MODECO Group in Reims (France) and received her PhD in computer science from the University of Reims in 2002. She joined the LIASD (Laboratoire d'Intelligence Artificielle de Saint-Denis) at the University Paris 8 in 2003 as an Assistant Professor. Her research interests are in the field of knowledge representation under uncertainty, especially by way of fuzzy logic and many-valued logic. She is also interested in music and computer science and participates in projects in this field.

Herman Akdag (ing. INSA LYON) obtained his PhD in computer science from the University of Paris 6 (France) in 1980, and his Professorship Diploma HDR from the same university in 1992. He is a full professor at the University of Reims. His research interests include knowledge representation, uncertainty management, fuzzy logic, machine learning and data mining. Currently, he is a researcher in artificial intelligence (LOFTI team) at the LIP6 laboratory. He is also the head of the research group MODECO at the University of Reims.

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Truck, I., Akdag, H. Manipulation of qualitative degrees to handle uncertainty: formal models and applications. Knowl Inf Syst 9, 385–411 (2006). https://doi.org/10.1007/s10115-005-0228-3

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