The fuzzy approach to statistical analysis
For the last decades, research studies have been developed in which a coalition of Fuzzy Sets Theory and Statistics has been established with different purposes. These namely are: (i) to introduce new data analysis problems in which the objective involves either fuzzy relationships or fuzzy terms; (ii) to establish well-formalized models for elements combining randomness and fuzziness; (iii) to develop uni- and multivariate statistical methodologies to handle fuzzy-valued data; and (iv) to incorporate fuzzy sets to help in solving traditional statistical problems with non-fuzzy data. In spite of a growing literature concerning the development and application of fuzzy techniques in statistical analysis, the need is felt for a more systematic insight into the potentialities of cross fertilization between Statistics and Fuzzy Logic. In line with the synergistic spirit of Soft Computing, some instances of the existing research activities on the topic are recalled. Particular attention is paid to summarize the papers gathered in this Special Issue, ranging from the position paper on the theoretical management of uncertainty by the father of Fuzzy Logic to a wide diversity of topics concerning foundational/methodological/applied aspects of the integration of Fuzzy Sets and Statistics.
fuzzy approaches statistical analysis fuzzy sets uncertainty fuzzy numbers information statistical reasoning