Mathematical Methods and Information Technologies in Banking

Abstract

The article explores decision-making information technologies in the banking sector utilizing mathematical methods. It delves into the optimal management decision-making tasks and presents a classification of decision support methods used within the banking industry. The study considers methods from fuzzy logic theory and inductive modeling, along with approaches to linguistic terms and the creation of fuzzy knowledge sets for decision-making and choice problems in banking. To simplify complex decision-making problems, strategies such as problem decomposition into simpler subsets, altering the model’s structural hierarchy, aggregation, and identifying reference situations with predetermined solutions are employed. A fuzzy model of the subject matter is developed, focusing on the phasization of variables–identifying linguistic assessments of variables and the membership functions necessary for their formalization. The introduction of rule weights in the fuzzy knowledge base reflects varying levels of confidence in the data, emphasizing the expert’s trust in each selected rule for decision-making. The formation of a general fuzzy knowledge base is detailed. The study validates the efficiency of utilizing neural network learning methods to adjust the parameters of a fuzzy model based on real data. This approach automates the process, significantly reducing both development time and costs while optimizing system parameters. This feature is particularly critical for economic problem-solving, notably in banking support activities, where the rapid pace of changes necessitates constant adaptation of membership functions to the dynamic conditions of the banking system.