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  • Existing Ways to Formalize Fuzzies in Transport Processes

    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

  • Modern methods and algorithms for solving fuzzy distribution (transport) problems, reflected in foreign literature

    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