Professor Dan Ralescu from the University of Cincinnati, USA, visited Research Center for Accounting and stayed from April 1 to April 20, 2025, to obtain cooperation for the 2025 regular project "Research on the application of artificial intelligence technology to solve corporate CUC Research Institute issues" of the Accounting Education Research Institute of the Comprehensive Research Center. Professor Ralescu is from Romania and is currently a Professor at the Department of Mathematical Sciences at the University of Cincinnati. His specialty is the mathematical treatment of fuzzy logic, which is different from ordinary mathematical logic. While it is clear whether an element belongs to a normal set (in the framework of fuzzy logic, this is called a crisp set), in fuzzy logic, the boundaries of set concepts are made ambiguous, and concepts such as "tall" and "young" are expressed in language. For example, if Taro Shodai is 170 cm tall and 20 years old, it can be expressed that he belongs to "about half" of the set of "tall" people and "almost" belongs to the set of "young" people. This ambiguity is expressed by the degree of membership in a fuzzy set. Both probability and membership can take values between 0 and 1, but fuzzy sets handle it differently than probability.
Professor Ralescu's lecture introduced his research on fuzzy logic, entitled "Statistics without numbers." This way of thinking is deeply related to recent artificial intelligence research, and he introduced it in conjunction with the research center's projects.

The outline of the lecture is as follows:

: Many statistical data are imprecise due to factors such as measurement errors, computational errors, and insufficient information. In such cases, the data are better represented as intervals or fuzzy sets rather than as single numerical values. Existing methods for analyzing interval-valued data include regression analysis in interval metric spaces and symbolic data analysis, which has been proposed in a more general setting. In this presentation, we propose a normal hierarchical model for random sets, specifically random intervals. Furthermore, we develop a minimum contrast estimator (MCE) for the model parameters and show that it is consistent and asymptotically normally distributed. We then support our theoretical results with simulation studies.