Evaluating the classification accuracy of fuzzy thematic maps with a simple parametric measure

In thematic maps, information is traditionally represented in a one-pixel-one-class method, which assumes each pixel in the map can be assigned unambiguously to a single class. The introduction of fuzzy classifications overcomes the traditional limitations on the mutually exclusive nature of map classes assigning varying levels of class membership for individual map pixels. However, the accuracy of fuzzy classifications is difficult to evaluate as conventional measures of classification accuracy are appropriate only for conventional one-pixel-one-class representations. This is a major barrier to the wider adoption of fuzzy classifications. In this paper, a parametric generalization of Morisita's index, first proposed in the ecological literature, is introduced whose members have varying sensitivities to the presence of rare and abundant thematic map classes. Due to its simplicity, the proposed index may be used to summarize the classification accuracy of fuzzy thematic maps obtained by softening the output of a maximum likelihood classification.