CONSTRUCTION OF A MATHEMATICAL MODEL FOR FINDING A DANCE STUDIO IN THE FORM OF A LOGICAL NETWORK USING FINITE PREDICATE ALGEBRA

Abstract

The article is devoted to the research and implementation of methods and tools of finite predicate algebra for conducting a systematic analysis of the subject area, exemplified by the formalization of the task of finding a dance studio based on selected parameters.. Specifically, the process of choosing a studio depends on a number of parameters: the type of subscription based on the number of sessions, groups, specific dance style, the professionalism of the instructor, the location and proximity to certain types of transport, and the price. The goal of the work is to increase the processing speed of knowledge in the task of finding the optimal subscription by decomposing the initial multi-parameter relationship into a composition of binary ones. The methodology is based on the tools and methods of finite predicate algebra. The application of predicate decomposition in the method of constructing logical networks ensures parallel knowledge processing, thereby increasing query processing speed, while formalization through finite predicates provides universality in describing any subject area. Thus, the complex multi-parameter relationship was decomposed into a composition of binary relations, described in the language of predicate algebra, considering a detailed analysis of the subject area and further decompositions. The scientific novelty lies in the constructed mathematical model of the task of finding a dance studio, represented as a predicate depending on ten variables. This predicate is characterized by the composition of thirteen binary predicates, which are presented in the article as bipartite graphs and formulas of the corresponding predicates. The predicate of the model is a composition of all the constructed binary predicates. The practical significance is determined by the logical network built on the basis of the mathematical model, which allows transitioning from a "many-to-many" relationship to "one-to-one" relationships and parallelizing the information processing. The result of the work is the constructed logical network for the task of finding the optimal dance studio subscription based on specific input parameters, which facilitates the solution of synthesis, analysis, and comparison tasks.