Fuzziness in data analysis: Towards accuracy and robustness

Abstract

The first aim is to emphasize the use of fuzziness in data analysis to capture information that has been traditionally disregarded with a cost in the precision of the conclusions. Fuzziness can be considered in the data analysis process at various stages, but the main target in this paper will be fuzziness in the data. Depending on the nature of the fuzzy data or the aim to which they are handled, different approaches should be applied. We attempt to contribute to the clarification of such a difference while focusing on the so-called ontic approach in contrast to the epistemic approach. The second aim is to underline the need of considering robust methods to reduce the misleading impact of outliers in fuzzy data analysis. We propose trimming as a general and intuitive method to discard outliers. We exemplify this approach with the case of the ontic fuzzy trimmed mean/variance and highlight the differences with the epistemic case. All the discussions and developments are illustrated by means of a case-study concerning the perception of lengths of men and women.