Correspondence analysis with fuzzy data: The fuzzy eigenvalue problem

Authors:
Y. Theodorou;C. Drossos;P. Alevizos
Affiliations:
Department of Electronics, Technological Educational Institute of Lamia, GR-35100 Lamia, Greece;Department of Mathematics, University of Patras, GR-265 00 Patras, Greece;Department of Mathematics, University of Patras, GR-265 00 Patras, Greece
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

This paper constitutes a first step towards an extension of correspondence analysis with fuzzy data (FCA). At this stage, our main objective is to lay down the algebraic foundations for this fuzzy extension of the usual correspondence analysis. A two-step method is introduced to convert the fuzzy eigenvalue problem to an ordinary one. We consider a fuzzy matrix as the set of its cuts. Each such cut is an interval-valued matrix viewed as a line-segment in the matrix space. In this way, line-segments of cut-matrices are transformed into intervals of eigenvalues. Therefore, the two-step method is essentially a reduction of the fuzzy eigenvalue problem to an ordinary one. We illustrate the FCA-fuzzy eigenvalue problem with a simple numerical example. We hope upon the completion of this project in near future, to be able to supply the necessary tools for the end user of the correspondence analysis with fuzzy data.