THE SITUATION OF UNCERTAINTY THAT ARISES IN THE PROBLEMS OF SEMANTICS AND WAYS TO SOLVE IT

Various types of uncertainties that arise when solving semantics problems are considered. Decision theory investigates this situation involving incomplete input, current, and fuzzy information. But uncertainty in the problems of semantics has other manifestations. Its solution is carried out in different ways depending on its types. The problems of this class are related to recognition and when establishing the essence of certain objects, measures of similarity are introduced, which are a subjective assessment. For different measures, the values of the objective functions may differ due to the ambiguity of the result obtained for these functions or the chosen degree of similarity measures, and may not satisfy the purpose of the study. When choosing the result there is a situation of uncertainty. But with some measures of similarity, you can find a global solution. Such problems are divided into subclasses of solvable problems. Since the problems of semantics are reduced to combinatorial optimization problems, in which the argument of the objective function is combinatorial configurations, the situation of uncertainty may be related to the special structure of the set of combinatorial configurations. To solve it, it is necessary to enter several objective functions or to conduct optimization according to several criteria, which are reduced to a weighted criterion (linear convolution). Finding the optimal solution is carried out by self-tuning algorithms taking into account the constant and variable criteria, which are introduced in the process of solving the problem. That is, in the process of the algorithm generates additional current information (quality criteria), which affects the prediction of future results. The situation of uncertainty is manifested both due to developed fuzzy rules of information processing and evaluation and ambiguity in the choice of the optimal solution for several criteria in multicriteria optimization. To get out of this situation, self-tuning algorithms are developed, using the introduction of formal parameters in the process of solving the problem, which generates auxiliary current information that can not be specified in the input data. Also, subclasses of solvable problems are used to solve the situation of uncertainty, the reference library is structured to reduce unsolvable problems to solvable ones.

Combinatorial configurations, fractals, fractal dimension of combinatorial sets

Combinatorial configurations and their sets are considered. The definitions of these objects are given, recurrent combinatorial operators are introduced, with the help of which they are formed, and rules are formulated according to which their sets are ordered. The property of periodicity, which takes place in the generation of combinatorial configurations, is described. It follows from the recurrent way of their formation and ordering. The fractal structure of combinatorial sets is formed due to the described rules, in which the property of periodicity is used. Analysis of these structures shows that they are self-similar, both finite and infinite, which is characteristic of fractals. Their fractal dimension is introduced, which follows from the rules of generating combinatorial configurations and corresponds to the number of these objects in their set.

Using Periodicity Properties to Generate the Combinatorial Configurations

Identifying patterns of the ordering of a certain combinatorial set allows to develop of simple procedures for its generation for an arbitrary value and to strictly prove that this set contains all non-identical combinatorial configurations. A characteristic feature of combinatorial sets is their formation from the base set according to given rules. For this purpose, it is enough to enter the basic set from which elements their formation is carried out, type of these objects and the system of rules of their generation.

Formation of orthogonal latin squares by index structuring of n-set multiplication tables

Objective. Formation of structurally perfect orthogonal Latin squares by the method of index ordering of the multiplication table elements of n-sets based on the multiplication table. Methods. Orthogonal Latin squares are formed by the method of index structuring of n-set multiplication tables. Results. A method is proposed for constructing structurally perfect orthogonal Latin squares of pairs of indexed finite sets of odd dimension, based on the index ordering of an nxn-array of elements in the multiplication table. A distinctive feature of the proposed method for constructing structurally perfect orthogonal squares from elements of two indexed sets of the same dimension is the use by the authors of the method of permutations of elements of the original nxn-matrix configurations, with the formation of index-ordered or index-structured combinatorial configurations. Conclusion. The use of the method for constructing a family of orthogonal Latin squares for pairs of indexed finite sets of the same odd dimension by the elements forming their multiplication table by the method of index structuring based on the principle of functional dependency of the index values on pairs of set elements and index values on pairs of elements from its environment allows creating a specific class orthogonal configuration, which, in terms of element indices, easily demonstrates their orthogonality.