Statistics with Fuzzy Data by Using Random Fuzzy Sets
Maria A. Gil
Estadistica e I.O. y D.M., Universidad de Oviedo, Oviedo, Asturias, Spain

Data obtained from the sampling of a random experiment are often supposed to be numerical and exactly known/perceived. However, this assumption does not fit some practical situations, especially those concerning judgments, perceptions or ratings involving imprecision and subjectivity.

Data of this type are usually modeled and treated as categorical/qualitative ones, and statistical techniques dealing with them are in some senses rather limited. Many of these data could be alternatively modeled and handled in a suitable, intuitive and easy-to-use way as fuzzy-valued ones. This alternative approach enables, on one hand, capturing the underlying imprecision, subjectivity and variability and, on the other hand, stating distances between data with a meaning similar to that for numerical ones.

By using the notion of random fuzzy sets (or fuzzy random variables in Puri and Ralescu's sense) a statistical methodology based on these distances can be developed; actually, several techniques have been already formalized most of them in connection with the fuzzy-valued mean values of random fuzzy sets. The added value of this methodology lies in the fact that it exploits the information associated with the imprecision, subjectivity and variability captured by the use of the fuzzy scale. Furthermore, combining this methodology with the so-called fuzzy representation of a real-valued random variable will provide us with an appealing and competitive approach to develop inferential statistics on the distribution of random variables.

An introduction to the key ideas and tools will be summarized in the talk.

Keywords: Distance between fuzzy data; Fuzzy data; Random fuzzy set; Statistical methodology

Biography: María Angeles Gil has a degree in Mathematics from the University of Valladolid (1976) and a PhD in Mathematics from the University of Oviedo (1979). Since 1976 she joined the University of Oviedo through different positions and since 1992 she is Professor of Statistics and Operations Research at this university.

She has published around 200 papers (in journals, book series and conference proceedings), edited some special issues of international journals and some books. She is chairing the Research Group SMIRE ( and is a permanent member of the Advisory Committee for the SMPS series of conferences. She participates in the European COST Action IC0702: SoftStat, where she is chairing Working Group C. She is Co-Chair of the Specialized Group on “Fuzzy Statistical Analysis” of the ERCIM Working Group “Fuzzy Statistical Analysis”. All these activities are closely related to Data Analysis with Imprecise Information/Methods.