An Overview on the Statistical Central Tendency for Fuzzy Data Sets

Abstract

When Statistics deals with data which cannot be expressed in a numerical scale, the scale of fuzzy values (in particular, the scale of fuzzy numbers) often becomes a suitable tool to express such data. In this way, many ratings, opinions, judgements, etc. mostly coming from human valuations can be appropriately described in terms of fuzzy data. To summarize the central tendency of a fuzzy dataset, some measures have been suggested in the literature. This paper aims to review some of the main ones, and examine their properties in a comparative way. A real-life example illustrates their application. Furthermore, the paper shows the statistical robustness (both through the finite sample breakdown point and a simulation study) and the empirical “precision” of the fuzzy number-valued sample measures. Finally, some related developments and future directions are pointed out.