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14 December 1999 Assessing the accuracy of soft thematic maps using fuzzy set-based error matrices
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Within the soft classification context, the vagueness conveyed by the grades of membership in classes leads us to conceive classification statements as less exclusive than in conventional hard classification, and to compare them in the light of more relaxed, flexible conditions, which results in degrees of matching. This paper proposes a new evaluation method which uses fuzzy set theory to extend the applicability of the traditional error matrix method to the evaluation of soft classifiers. It is designed to cope with those situations in which classification and/or reference data are expressed in multimembership form and the grades of membership represent different levels of approximation to intrinsically vague classes. To verify the applicability of the method we conducted a remote sensing study on a highly complex real scene of the Venice lagoon (Italy). Alternative evaluation procedures, such as the traditional confusion matrix and the Standard errors of estimate, have been developed for this application in order to demonstrate the value and the advantages of the proposed measures as compared with other approaches.
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Elisabetta Binaghi, Pietro Alessandro Brivio, Pier Paolo Ghezzi, and Anna Rampini "Assessing the accuracy of soft thematic maps using fuzzy set-based error matrices", Proc. SPIE 3871, Image and Signal Processing for Remote Sensing V, (14 December 1999);

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