The lack of information about the conditions for the implementation of transport processes does not allow building mathematical models that operate with extremely accurate input data. Therefore, methods are being developed that formalize input uncertainties for constructing mathematical models of transport processes. To describe uncertainties, along with static, stochastic and interval approaches, methods based on fuzzy sets are actively used. The generalization of the belonging of the element, presented by Zadeh, allowed blurring the boundaries of the set. The blurring of the boundaries of the sets allows one to formalize insufficiently complete, in an informational sense, judgments and facts for the purpose of the subsequent use of this information in the construction of mathematical models. To identify formal approaches to working with uncertainties, an analysis of foreign periodicals in recent years has been carried out and two well-known approaches have been identified. The first is based on the theory of fuzzy sets - the generalized concept of belonging of an element to a set, leading to blurring of the boundaries of the set. The second approach involves describing fuzziness using a hierarchy - a family of ordered crisp sets [1]. Within the framework of the first approach, the authors have identified five ways of formalization. The first includes fuzzy sets (numbers) with different n-gonal forms of the membership function. The second consists of intuitionistic fuzzy sets (numbers) with n-gonal membership functions. The third contains heterogeneous fuzzy sets of type 2. The fourth represents non-standard fuzzy sets (oscillating, Pythagorean, etc.). The fifth method is a combination of spaced fuzzy numbers, intuitionistic spaced fuzzy numbers, and the like. References are given to sources containing a description of formalization methods and their application in solving some fuzzy transport problems, possible directions of research on the considered topics are formulated.

Keywords: fuzzy transport routing problem, optimization, fuzzy methods, fuzzy numbers, fuzzy sets, heuristic algorithms, hybrid algorithms, transport processes

The article discusses the work of foreign authors in the field of solving fuzzy distribution (transport) problems. To solve such problems in real conditions, it is rather difficult to formalize all parameters in the form of definite numbers, therefore, the field of solving fuzzy distribution (transport) problems attracts wide attention of scientists and experts, provoking numerous successful studies. To solve distribution (transport) problems, when considering the current state of foreign literature, the main approaches have been identified, consisting in the use of pentagonal, hexagonal, octagonal fuzzy numbers, ranking, intuitive fuzzy environment, as well as the Pythagorean approach. Now it is becoming more and more important to use inaccurate data in real transportation problems. The listed approaches to solving distribution (transport) problems give a certain effect in comparison with the existing ones, therefore it is necessary to investigate solutions of fuzzy distribution problems using modern approaches and methods.

Keywords: fuzzy transport routing problem, optimization, fuzzy methods, fuzzy numbers, heuristic algorithms, hybrid algorithms

Presents an adaptive algorithm for solving the data flow of minimum cost in a static and a dynamic formulation. In the dynamic formulation of the problem change the matrix describing the network. An important component of the algorithm is to use the ideas of co-evolution, the choice of models of evolution (micro-, macro-, meta-evolution), adaptation to the external environment, hierarchical management of genetic and evolutionary search, local search solutions and the use of all modified by genetic operators based on greedy strategies and search methods. Given the example of the recommended data flow based on a known formula the definition of fuzzy proximity µx(b) variable b to the specified value. The adjustment of the process data under the recommended settings implemented with the help of machines adaptation. A distinctive feature of the algorithm is the use of machines adapted for determining the need for and the method of modifying intermediate solutions, as well as for a decision about modifying the previously obtained solutions.

Keywords: data flow, adaptation, evolution, optimization, evolutionary search

One of the components of the optimization problem is a set of constraints describing the basic requirements for solutions. So as to find a solution that fully satisfies all the wishes of the experts, it is not always possible, the search area extends through analysis of semi-feasible solutions. The adjustment of the system constraints may contribute to changes in the structure and appropriateness of the decisions. The paper shows the ways to form a generalized membership functions of vague constraints of optimization problems based on the logics of Reichenbach and Lukasiewicz. It is known that for the same design procedures in some cases it is necessary to obtain accurate solutions, while others just get approximate solutions. Therefore, we analyzed the features of membership functions obtained using these logics. It is shown that by implication deny rules to allow logic-based Reichenbach membership function takes values equal to one if the value of the function allow rule is one, or if the value of the function deny rule is zero. By implication deny rules in allowing based on Lukasiewicz logic membership function takes values equal to one if the value of the function allow rule is greater than the value of the function deny rules. Therefore, it can be argued that when designing systems with increased reliability (precision) is more expedient to use the function implications for Reichenbach deny rules in a permissive compared with the same implication by Lukasiewicz. The implication deny rules to allow for the Lukasiewicz appropriate to use when designing subsystems that perform secondary functions that are not systemically forming, etc.

Keywords: adaptation, fuzzy system, the implication, intellectual method, membership function, optimization, logic, Reichenbach, Lukasiewicz logic

In article the problem of development of algorithm of bionic search for tasks about an extreme way on the column is considered. Now development of effective methods and algorithms for problems of this type is carried out many years, being on - former an actual problem. Development of bionic algorithms on the basis of evolutionary strategy is perspective, especially at the solution of labor-consuming problems of optimization. It is possible to carry to advantages: possibility of performance of evolutionary and genetic search, and also that OH consists in parallel generation of sets of quasioptimum alternative decisions with possible "migration" of decisions between these sets. Realization of the general strategy of adaptation of the size of population by use of sequence of a sieve of Eratosfen, allowing to adapt for characteristics of bionic search is offered.

Keywords: evolution, bionic algorithm, task about an extreme way, adaptation