Diagnostyka, 20xx, Vol XX, No X e-issn

INTRODUCTION

In recent years, there has been a rapid development of data transmission networks, each of which, being a complex organizational and technical system, must ensure the high-quality functioning of all its elements and the network as a whole.
The data transmission network, as an object of diagnostics, can be represented as a mathematical model that includes input (external influences), output (reactions to external influences) and internal (state) variables. Dependencies between the input, output and internal variables of the object, written functionally, can be put in correspondence with the space of technical states inherent in this object.[11]
The use of traditional mathematical methods in solving problems related to the technical diagnostics of data transmission networks is ineffective when the initial information about the state of network elements is completely absent or is statistically incomplete.[10]
A promising direction in the development of diagnostic methods and tools are methods based on fuzzy logic or fuzzy sets, which can significantly simplify the description of the model of control and diagnostic objects.

3. 
   METHODOLOGY
   

The process of diagnosing data transmission networks includes such stages as collecting initial information, identifying a defect, and localizing a defect. At the same time, the initial information includes information about defects received from users, information about non-standard situations during maintenance, and other data collected by maintenance personnel, which, for simplicity, can be called symptoms. Then, in the general case, the simplified algorithm for the operation of an automated remote diagnostic system will correspond to the following. Initially, initial information is entered into the diagnostic system in the form of subjective symptoms. The system identifies the most significant among them, taking into account the proximity of symptoms to one of the defects, using the knowledge embedded in it during creation, and then collects more detailed information about the symptoms associated with a probable defect, and issues a conclusion. As knowledge in this case, general relationships between defects and symptoms are needed, in addition, some measure of such a relationship is needed, both for a defect from the point of view of a symptom, and for a symptom from the point of view of a defect.[14]

Given the above, when implementing the system, it is initially necessary to establish theses for adapting knowledge to fuzzy conclusions. To do this, denote by D={D₁, …, D_m} and S={S₁, …, S_n} respectively, the set of all defects and the set of all symptoms. Then we introduce the following linguistic variables:

• 
  Ai _{_} – “there is a defect D _i ”;
  
• 
  B _j – “Symptom S _j is determined_”;
  
• 
  R _ij – “defect D _i according to its
  

characteristics corresponds to the symptom S _j ".
These linguistic variables can take the following values from the term-set CON , which characterize their degree of reliability (truth):

• 
  un - "unknown";
  
• 
  vt - "very true";
  
• 
  rt - "quite true";
  
• 
  pt - "probably true";
  
• 
  pf - "probably false";
  
• 
  rf - "quite false";
  
• 
  vf - "very false."
  

Each of these values is described by the membership function, which characterizes the degree of certainty of a particular statement, and takes a value from the interval [0; 1].

The linguistic variable R_ij is a reflection of the knowledge of an expert (or experts) about the correspondence of the observed symptoms to defects in the data transmission network. The set of all values R_ij can be represented as a matrix M from m rows and n columns: