GENERAL PRINCIPLES OF CONSTRUCTION OF SYSTEMS OF INDEXATION OF ELEMENTS OF FINITE SETS

Abstract

Objectives Definition of general principles for constructing indexing systems for elements of finite sets.Method. Building a model of the indexing process. Definition of general rules for assigning attributes - indices to elements of sets.Result. The general principle of constructing indexing systems for elements of sets and their aggregates is proposed. The basis of the proposed indexing principle is the mandatory presence of functional relationships between the values of the element indices. The main sign of differences in indexing systems is the difference in functional dependencies between the values of the indices of the environment elements. Indexing systems determine the structural properties of sets and their aggregates. A change in indexing systems predetermines a change in structure. This allows one to form sets, sets with different structures from elements of the initial configurations, and change their structural properties.Conclusion. A general principle is proposed for constructing systems for indexing elements of sets and their aggregates, based on which are functional dependencies between element indices. Changes in the used functional dependencies between the element indices, as shown in the work, allows one to form combinatorial configurations with different structural properties. The indexing system is a set of rules for assigning to the elements sets of attributes - indices, ensuring their visibility and communication with the environment and determining their structural properties. At the heart of the construction of any structures and indexing systems are some common basic principles for their construction. They are illustrated based on the indexing systems used in classical algebra. Based on the results of a study of the principles of constructing indexing systems, a generalized model of indexing systems is proposed. As a general principle, which is a general principle of constructing indexing systems, a system of functional dependencies between the values of the indices of an element of sets and the values of the indices of the elements of its environment is proposed as a model.

Keywords

• indexing systems
• principle of functional dependence
• structural properties of sets