Title: Fuzzy sets, fuzzy logic and aggregation operators: recent developments in artificial intelligence applications

Abstract: Since their emergence in the 1960s, Fuzzy Logic and Fuzzy Set Theory have been the basis for a rich field of research dedicated to addressing the imprecision inherent in human knowledge. This field has been receiving attention from researchers who have made it an active and heated area of research, both in theoretical and practical aspects. In the theoretical field, the topic of aggregation functions stands out, which define how to merge information and can assume classical and generalized forms. In our research group, formed by national and international researchers, significant progress has been made in defining generalizations of the Choquet integral as a means of merging information.

Among the methods developed based on the concepts of Fuzzy Logic and Fuzzy Sets, which have gained popularity and relevance in applications, the Fuzzy Reasoning Systems and Fuzzy Clustering stand out, which can benefit from the use of aggregation functions and their generalizations.

In this talk, after introducing some basic concepts related to the aggregation function and generalizations of the Choquet integral, we will discuss two of the most important applications of these concepts in classical methods of artificial intelligence and fuzzy systems that resulted from the group's research. The first application is in Fuzzy Rules Based Systems for classification, in which information fusion is used in the fuzzy reasoning method. The second, Clustering in Data Streams, uses concepts of extensible functions to calculate similarities between fuzzy clusters.