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  • Determination dominating set intuitionistic fuzzy graph

    In this paper, the concept of minimal intuitionistic dominating vertex subset of intuitionistic fuzzy graph was considered, and on its basis the notion of a domination set as an invariant of the intuitionistic fuzzy graph was considered. A method and an algorithm for finding all minimal intuitionistic dominating vertex subset and domination set were proposed. This method is the generalization of Maghout’s method for fuzzy graphs. The example of finding the domination set of the intuitionistic fuzzy graph was considered as well. The considered method and algorithm can be used to find other invariants, in particular, externally stable set, intuitionistic base and antibase of the intuitionistic fuzzy graphs.

    Keywords: intuitionistic fuzzy set, degree of belonging, degree of non-belonging, fuzzy relation, intuitionistic fuzzy graph, intuitionistic fuzzy graph of the first kind, domination set, algorithm, disjunctive member, adjacency matrix

  • Solution of the problem of forming a distribution system under conditions of uncertainty

    The distribution center is one of the main elements of the distribution system, which forms the structure of the movement of resources. It is responsible for ensuring the efficient allocation of the flow of resources. The effective location of the distribution center allows you to reduce the cost of allocating resources to 30%. The method of solving the problem of effectively securing demand zones for a particular distribution center is proposed in this article. The uncertainty of the initial parameters is taken into account when solving this problem. The result of solving the problem of determining the effective location of distribution centers is a set of fuzzy intervals. These intervals determine the coordinates of the location depending on the parameters of the task, namely, the demand of consumers, the capacity of distribution centers, the distance between the resource consumers and the center. The location of the distribution center will be determined not by a specific numerical value, but by a fuzzy interval that will determine the region of the best location. A software application is developed that allows you to specify parameters in a fuzzy interval form, on the basis of which the results of solving the problem are formed. The cost of delivering resources to consumers changes significantly with the change in the number and location of distribution centers, so the issue of rational distribution and the number of centers is important. This task becomes especially relevant when a new distribution system is being designed, or the existing system is being modernized.

    Keywords: distribution centers, the demand, the uncertainty of the initial parameters of the fuzzy intervals, potential interactions, grouping

  • Determination of the chromatic set of fuzzy temporal graph

    In this paper, the concept of chromatic set of fuzzy temporal graph is introduced. Chromatic set of fuzzy temporal graph is a generalization of one side of a fuzzy, but on the other hand - temporal graphs. The degree of connectivity vertices changes in discrete time in a fuzzy temporal graph. Most of isomorphic transformations of fuzzy temporal graph change their external representation without changing its signature. In this regard, matters relating to the consideration of temporal invariants of fuzzy graphs. Example of finding chromatic sets of fuzzy temporal graph is considered here.

    Keywords: Fuzzy temporal graph, fuzzy partial graph, graph coloring, chromatic set, the degree of separability

  • Developing of the algorithm of maximum flow of minimum cost finding in a fuzzy dynamic network

    The article considers the problem of maximum flow of minimum cost finding in fuzzy dynamic transportation network. The relevance of the problem is in its wide practical application on the rail, air, sea and other roads in finding of routes of minimum cost. The feature of the problem statement is that fuzzy nature of the network parameters, such as arc capacities and costs is taken into account. It allows us to make decisions more sensitive to environmental changes. The dependence of network parameters from flow departure is also considered, that allows to introduce the notion "dynamic" network as opposed to "stationary-dynamic", examined in the literature. The algorithm for solving the described problem in fuzzy conditions is proposed. To illustrate the algorithm a numerical example is presented.

    Keywords: dynamic network, maximum flow of minimum cost, fuzzy numbers, arc capacity, transit time