Interval-Valued Fuzzy Galois Connections: Algebraic Requirements and Concept Lattice Construction

Issue title: Methodologies for Intelligent Systems

Article type: Research Article

Authors: Djouadi, Yassine | Prade, Henri

Affiliations: Department of Computer Science, University of Tizi-Ouzou, BP 17, RP, Tizi-Ouzou, Algeria. E-mail: ydjouadi@mail.ummto.dz | IRIT, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 09, France. E-mail: prade@irit.fr

Abstract: Fuzzy formal concept analysis is concernedwith formal contexts expressing scalar-valued fuzzy relationships between objects and their properties. Existing fuzzy approaches assume that the relationship between a given object and a given property is a matter of degree in a scale L (generally [0,1]). However, the extent to which "object o has property a" may be sometimes hard to assess precisely. Then it is convenient to use a sub-interval from the scale L rather than a precise value. Such formal contexts naturally lead to interval-valued fuzzy formal concepts. The aim of the paper is twofold. We provide a sound minimal set of algebraic requirements for interval-valued implications in order to fulfill the fuzzy closure properties of the resulting Galois connection. Secondly, a new approach based on a generalization of Gödel implication is proposed for building the complete lattice of all interval-valued fuzzy formal concepts.

Keywords: Formal concept analysis, Interval-valued fuzzy formal contexts, Algebraic closure operators, Extended Gödel implication, Concepts lattice construction

DOI: 10.3233/FI-2010-244

Journal: Fundamenta Informaticae, vol. 99, no. 2, pp. 169-186, 2010