Increasing the Safety of Flights with the Use of Mathematical Model Based on Status Functions

  • Irina VeshnevaEmail author
  • Aleksander Bolshakov
  • Aleksei Kulik
Conference paper
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 199)


The article deals with application of complex-valued status functions for development of the method of mathematical modeling of flights to ensure their safety based on the prevention of flight accidents. The application of the proposed method on the basis of status functions is shown using a precedent matrix of flight accidents. The method contains the steps corresponding to the Mamdani algorithm for the following purposes: the formation of the rules base, fuzzification, aggregation, activation, accumulation. Notable is the use of orthonormal basis of complex-valued status functions instead of membership functions, which changes the implementation at each stage. The configuration of flight operations safety management system is used on the input of which the information is received about the condition of the crew, instruments for measuring external factors and airborne equipment. The main parameters of the aircraft flight safety assessment are identified by formalization of expert information and the values of linguistic variables are formulated with their use. Orthonormal status functions were formed for which interpretation rules are presented. For activation we used status functions, which makes it possible to create a rule for the double evaluation of object and phenomenon when creating rules database. Analogues of minimax operations are used for accumulation with a demonstration of the form of these functions for different values of factors. Comparison of the proposed method with analogues is given (algorithms of Mamdani, Tsukamoto, Larsen and Sugeno).


Status functions Membership functions Mamdani algorithm Flight safety Mathematical model 


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Authors and Affiliations

  1. 1.Saratov State UniversitySaratovRussian Federation
  2. 2.Peter the Great St. Petersburg Polytechnic UniversitySaint PetersburgRussian Federation
  3. 3.Yuri Gagarin State Technical University of SaratovSaratovRussian Federation

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