Granular computing with closeness and negligibility relations

Authors:
Didier Dubois;Allel Hadj-Ali;Henri Prade
Affiliations:
I.R.I.T., Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France;Institut d'Informatique, Université Mouloud Mammeri 15000 Tizi-Ouzou, Algeria;I.R.I.T., Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
Venue:
Data mining, rough sets and granular computing
Year:
2002

Citing 6
Cited 1

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Abstract

One of the simplest examples of information granulation is the use by humans of approximate equalities when reasoning with orders of magnitude. The paper proposes a symbolic approach for handling orders of magnitude in terms of a closeness relation and an associated negligibility relation. At the semantic level, these relations are represented by means of fuzzy sets and are parametered. A reduced set of rules, where the parameters are formally combined, embodies all the knowledge for reasoning on the basis of pieces of information in terms of orders of magnitude. These rules describe how closeness and negligibility relations can be composed and how they behave with respect to addition and product. The problem of handling qualitative probabilities in uncertain reasoning is then investigated in that perspective.