Building a Logical Network for Solving the Problem of Car Rental by Means Algebra of Finite Predicates

Abstract

The article is devoted to the research of the tools of algebra of finite predicates for the system analysis and formalization of the task of automating car rental according to the selected parameters. In particular, the process of optimal car selection depends on the following parameters: car class, brand, availability of driver, type of trip and its duration, fuel type, tariff type, as well as season and weather conditions. Each of these criteria has its own area of definition, where you need to take into account all the relationships and influences between the values of the entered variables (criteria). The aim of the work is to increase the speed of data processing in the problem of car rental by dividing the input multi-place ratio into a binary composition. The technique is based on the means and methods of algebra of finite predicates. Introduction of the predicate of object recognition in the specified subject area allowed to formally describe data of any type, and the applied method of construction of logical networks provides increase in speed of information processing due to parallelization of processing processes. Thus, a complex multi-place relation was divided into a composition of binary relations described in the language of predicate algebra, taking into account the detailed system analysis of the subject area. A scientific novelty is the constructed mathematical model of the car rental problem, which is represented by a predicate that depends on thirteen variables. This predicate is characterized by a system of twelve binary relations, which are represented in the article by dual graphs and formulas of the corresponding predicates. The model predicate is a composition of all constructed binary predicates. The practical significance is due to the logical network built on the basis of a mathematical model, which allows from the relationship "many to many" to move to the relationship "to each other" and parallelize the process of information processing. The result is a logical network of car rental problems, which works iteratively until it receives stable results in two consecutive steps and allows you to solve problems of analysis and synthesis for car rental according to selected parameters.