Fuzzy Medoids Based on an  \(L^{1}\) -Type Distance

The first robust central tendency measures for fuzzy number-valued data introduced in the literature were extensions of the notion of median in the real-valued settings. In particular, they were defined as the fuzzy numbers that minimize the mean distance to the sample fuzzy number-valued observations. In order to solve the minimization problem, only \(L^1\) -type metrics were considered in the fuzzy-valued settings, and the corresponding measures were proven to present some interesting properties. However, these approaches do not necessarily keep the shape of the sample data, and they do not have to coincide with a sample observation like it happens in real-valued scenarios. The aim is to propose new location measures (fuzzy medoids) by restricting the previous minimization problem to the set of fuzzy observations. Their practical interest is highlighted by means of a real-life example.