Fuzzy Sets in Data Analysis: From Statistical Foundations to Machine Learning

Basic ideas and formal concepts from fuzzy sets and fuzzy logic have been used successfully in various branches of science and engineering. This paper elaborates on the use of fuzzy sets in the broad field of data analysis and statistical sciences, including modern manifestations such as data mining and machine learning. In the fuzzy logic community, this branch of research has recently gained in importance, especially due to the emergence of data science as a new scientific discipline, and the increasing relevance of machine learning as a key methodology of modern artificial intelligence. This development has been accompanied by an internal shift from largely knowledge-based to strongly data-driven fuzzy modeling and systems design. Reflecting on the historical dimension and evolution of the area, we discuss the role of fuzzy logic in data analysis and related fields, highlight existing contributions of fuzzy sets in these fields, and outline interesting directions for future work.