Summary
In real-life situations experimental data can arise which do not derive from exact measurements or observations, but they correspond to ranges, judgements, perceptions or ratings often involving imprecision and subjectivity. These data are usually formalized with (and treated as) grouped or categorical/qualitative data for which the statistical analysis techniques to be applied are rather limited.
However, many of these data could be alternatively and suitably identified with either interval- or fuzzy number-valued data. This approach offers in fact mathematical languages/scales allowing us to express many imprecise data related either to ranges/fluctuations or to judgements/perceptions/ratings, and to capture the underlying imprecision, subjectivity and variability. Besides capturing the information surrounding the imprecision, subjectivity and variability (which is frequently ignored in dealing with grouped or categorical data), the use of the rich interval and fuzzy scales enables to state distances between data with a meaning similar to that for numerical ones. Moreover, it will possible to develop statistical methods based on these distances and exploiting the added information.
This paper aims to review the key ideas in this approach as well as some of the existing techniques for the statistical analysis.
This paper has been written as a tribute to our beloved friend Marisa Menéndez. She touched us with her friendship and warm hospitality, and we have had the opportunity to share with her many wonderful personal meetings and fruitful scientific discussions. She has been always ready to help us in many respects, and we will always feel indebted to her. Thank you, Marisa, for your affection and care; you will always occupy a very special place in our hearts.
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Corral, N., Gil, M.Á., Gil, P. (2011). Interval and Fuzzy-Valued Approaches to the Statistical Management of Imprecise Data. In: Pardo, L., Balakrishnan, N., Gil, M.Á. (eds) Modern Mathematical Tools and Techniques in Capturing Complexity. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20853-9_31
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