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• USING FUZZY GRAPH INVARIANTS FOR THE STABILITY ANALYSIS OF COMPLEX TRANSPORT SYSTEMS

  I.N. Rozenberg , I.А. Dubchak

  136-145

  2025-12-30

  Abstract ▼

  This article examines the issues of assessing the sustainability of transport and logistics systems (TLS) under conditions of uncertainty, which play a key role in ensuring the effective functioning of supply chains. The sustainability of systems is analyzed in the context of their ability to adapt to external and internal influences, such as economic fluctuations, changes in demand, natural disasters and technological failures. In this paper, it is proposed to use fuzzy graph invariants, namely, a fuzzy dominating set, to assess and analyze the sustainability of transport and logistics systems under uncertainty. It is shown that a fuzzy dominating set allows solving the problem of placing distribution hubs in a transport and logistics system. Examples of finding fuzzy dominating sets for fuzzy and fuzzy temporal graphs as the models of transport and logistic system are presented. Fuzzy temporal graphs also allow for more adequate modeling and analysis of systems in cases where the time parameter is one of the important factors. The practical significance of the study lies in the possibility of designing a more reliable and adaptive TLS capable of functioning effectively under conditions of uncertainty. The results can be used to optimize logistics processes, reduce costs and increase the sustainability of supply chains. The findings also open prospects for further research in the field of integrating artificial intelligence methods and big data analysis in transport system management. Further research is proposed to be directed at integrating flow optimization methods considering time factors and developing digital twins of TLS.

• METHOD AND ALGORITHM FOR OPERATION PLANNING BASED ON FUZZY FINITE AUTOMATA MODEL

  М. V. Knyazeva, А. V. Bozhenyuk, I.N. Rozenberg

  2022-05-26

  Abstract ▼

  In this paper the planning and scheduling problem as an important optimization problem in
  many transportation and robotic applications is discussed. To solve planning problems, the main
  approaches are based on optimization methods, sampling-based methods, and usually such kinds
  of problems are NP-hard and high dimensional. In this work, the method for planning and scheduling
  based on the fuzzy finite state machine model is developed. Fuzzy graph presentation of the
  scheduling problem and operation planning is given. The paper presents two approaches to the
  formulation of the planning problem with limited resources and temporal variables: state-oriented
  (with transitions between states), temporal ordering-oriented (on a time scale). Temporal modeling
  for planning problems implies a qualitative approach to managing the distribution of operations
  or topological ordering, as well as a quantitative approach to handling imprecise durationsrelationships between operations in multiple parameters. The concepts of fuzzy intervals and fuzzy
  relations are introduced for planning operations on a graph. A planning algorithm based on the
  theory of automata and temporal modeling under uncertainty has been developed. Using this formalism,
  a path planning problem is solved by successively altering a state using various operations
  until a solution is found. The idea of temporal-ordered partial schedule associated with the
  planning state of the system is discussed. A model of a finite automaton for a planning system under
  conditions of uncertainty is proposed. A method and algorithm for scheduling operations
  based on a non-deterministic finite automaton and an enumeration scheme have been developed.
  The non-deterministic computation for a scheduling problem is a decision tree whose root corresponds
  to the beginning of the scheduling process, and each branch point in the tree corresponds
  to a computation point at which the machine has multiple choices. And the finite state machine
  model (automata) for the planning system under uncertainty is suggested.

• ALGORITHM FOR DETERMINING A STRONGLY CONNECTED FUZZY SET OF A PERIODIC FUZZY GRAPH

  P. О. Nikashina

  2026-02-27

  Abstract ▼

  The article discusses a method for determining the strong connectivity of a periodic fuzzy graph (PFG), which can be used to make decisions in emergency situations such as evacuation. The concept of a fuzzy set of strong connectivity is introduced. The main attention is paid to the development of a method for finding a fuzzy set of strong connectivity, which makes it possible to determine the degree of reachability between the vertices of a graph in a certain number of time cycles. The paper begins with a review of existing approaches to connectivity analysis in fuzzy graphs, emphasizing the need to consider time and fuzzy parameters. The main part of the paper is devoted to the description of key concepts and definitions related to periodic fuzzy graphs. The concepts of fuzzy path, time and degree of reachability, as well as fuzzy set of reachability are introduced. An algorithm for finding a fuzzy set of reachability based on the wave method is proposed, which allows determining the degree and time of reachability between graph vertices. Next, the concept of fuzzy set of strong connectivity PFG is introduced and an algorithm for its determination is proposed. As an example, a specific PFG is considered for which the fuzzy set of strong connectivity is calculated. The proposed method can be useful for choosing a movement strategy during evacuation, especially in conditions where the territory model is represented by a periodic fuzzy graph. In the future, it is planned to explore issues related to finding a discrete-time reachability between vertices with a given degree of reachability

• THE PROBLEM OF CHOOSING A DUMPING FACTOR IN THE EFFECTIVE CONTROL MODEL FOR DIRECTED WEIGHTED SIGNED GRAPHS

  A.N. Tselykh, V.S. Vasilev, L.A. Tselykh

  2020-07-20

  Abstract ▼

  The paper deals with the problem of choosing a dumping factor in the effective control model
  based on maximizing the transfer of impacts for fuzzy cognitive models represented by directed
  weighted signed graphs. To transfer influence, a management model is used that implements the
  development of the system. An effective control algorithm is based on solving the optimization
  problem of finding a vector of external influences that maximizes the accumulated increase in
  increments of vertex indicators. The optimal control effect is considered to be a control that provides
  the maximum ratio of the square of the norm of the response vector of the system to the
  square of the norm of the control vector. The dumping factor of this model controls the comparative
  scale of the direct and indirect influence of all intrafactor relationships of the system as a
  whole. The purpose of the study is to determine such areas of acceptable values for the obtained
  solutions, in which (i) the condition of consistency of the result is met; (ii) the change of vertex
  ranks is slow. By the sequence of results, we mean satisfaction with the rules of the system as a
  whole. These rules can be expressed in imposing restrictions on the status of vertices, on the sign
  of impacts and responses. Set the damping factor, called the resonance, where resonance occurs a
  surge in the value of the objective function the problem of maximization of the impact when there
  is no alignment between the resonant response and caused its effect. The choice of the dumping
  factor affects the value of the target function of the impact maximization problem and the vector of
  effective management on which this solution is achieved. The value of the resonant damping coefficient
  can be interpreted as the limit of the possible controllability of the system, i.e. limit the
  potential impact on the system without harming it. The proposed solution is evaluated based on the
  degree of stability of the rank of model nodes depending on the influence of changes in the damping
  coefficient, the algorithmization of determining the range of its acceptable values and the
  shape of the resonance within the values of the damping coefficient.