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

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S1	S2	S3	S4
S5
D1	vt	vt	pf	pf	vf
D2	rf	rf	vt	vf	vt
D3	pt	vt	vf	rt	pt

In addition, the following rule base is implemented in the system (Figure 2):


RUL₁: "IF B₁=vt AND B₂=vt AND B₃=pf AND B₄=pf AND B₅=vf TO A₁=vt "
RUL₂: "IF B₁=rf AND B₂=rf AND B₃=vt AND B₄=vf AND B₅=vt TO A₂=vt "
RUL₃: "IF B₁=pt AND B₂=vt AND B₃=vf AND B₄=rt AND B₅=pt Maintenance A₃=vt "
RUL₄: "IF B₁=vt AND B₂=vt AND B₃=vt AND B₄=vt AND B₅=vt TO A₁=pf »
RUL₅ : "IF B₁=vt AND B₂=vt AND B₃=vt AND B₄=vt AND B₅=vt TO A₂=rt "
RUL₆: "IF B₁=pt. AND B_{2_}=pt. AND B₃=pt. AND B₄=pt. AND B₅=pt. Maintenance A₃=pt. "
RUL₇: "IF B₁=pt. AND B_{2_}=pt AND B₃=pt AND B₄=pt AND B₅=pt TO A₁=rt "
RUL₈: "IF B₁=pt AND B_{2_}=pt AND B₃=pt AND B₄=pt AND B₅=pt TO A₂=pt "
RUL₉ : "IF B₁=vt AND B₂=vt AND B₃=vt AND B₄=vt AND B₅=vt Maintenance A₃=rt "
Consider the case when a message containing B₂=rt. Since there was no information about the presence of other symptoms, then B₁=un, B_{3_}=un, B_{4_}=un , B_{5 _}=un. Therefore, we can consider only that part of the rules in which B₂=rt.
On fig. Figures 3-6 show fuzzy inference surfaces for assessing defect cases for fuzzy models A₁, A₂, A₃.
At the first stage, the input values (ie B₂ values ) are compared with the rule base implemented in the system. This comparison is equivalent to the operation of intersection of fuzzy sets. Based on this comparison, a modified membership function for A₁, A₂ and A₃ is determined in accordance with each of the rules. Further, to find the generalized membership functions A₁, A₂ and A₃, the operation of combining fuzzy sets is applied. After finding the generalized membership functions A₁, A₂ and A₃, the centroid method determines the quantitative values of A₁, A₂ and A₃ , the largest of which (in this case A₁ ) will correspond to the type of defect in the system (i.e. D₁ ).[13]




Fig. 1. Graph of membership functions of linguistic variables.

Fig. 2. Rules of fuzzy knowledge bases of fuzzy logical models.

Fig. 3 Fragments of computational experiments.

Fig.4 Fuzzy inference surface for case A₁.

Fig. 5 Fuzzy inference surface for case A_2.
Fig.6 Fuzzy inference surface for case A_3.
Conclusions
Thus, the increasing requirements for the reliability of data transmission networks necessitate the creation and implementation of promising methods and diagnostic tools. The given technique for estimating the classes of states of alleged defects in a data transmission network under conditions of incomplete information allows us to successfully solve the problem of diagnosing data transmission networks by applying the apparatus of fuzzy set theory.
Analytical expressions that determine the characteristics of fuzzy set elements for a data transmission network and the rules for making a decision about the type of defect, as well as methods for constructing membership functions of fuzzy sets and implementing rule bases, are the basis for building a system for diagnosing data transmission networks based on fuzzy set theory.
The use of the apparatus of fuzzy set theory makes it possible to create fairly simple diagnostic algorithms based on expert knowledge, taking into account both the objective characteristics of data transmission networks and the subjective states of service personnel, which is not possible using traditional diagnostic methods and algorithms.[6]


REFERENCES

[1] Bestugin A.R., Bogdanova A.F., Stogov G.V. Monitoring and diagnostics of telecommunication networks - St. Petersburg: Politekhnika, 2003. 174 p.: Il. Ivanova A.B. Quality control in telecommunications and communications - Moscow 2001

[2] Garanin M.V., Zhuravlev V.I., Kunegin S.V. Systems and networks of information transmission. - M.: Radio and communication, 2001.
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[4] Aripov M.N. Juraev R.Kh., Jabbarov S.Yu. Technical diagnostics of digital systems. Textbook Tashkent 2006 p.82.
[5] Zade L.A. Linguistic approach to the analysis of complex systems, 1975 г.
[ 6] Borisov A.N., Krumberg O.A., Fedorov I.P. Decision making based on fuzzy models: examples of use. - Riga, "Knowledge", 1999 г.
[7] Vilkas E.J., Maiminas E.Z. Solutions: theory, information, modeling. - M., Radio and communication, 1991 г.
Kofman A. Introduction to the theory of fuzzy sets. - M., Radio and communication, 1992 г.
[8] Treano T., Asai K., Sugeno M. Applied fuzzy systems. - M., Mir, 1997 г.
[9] Leonenkov A. Fuzzy modelling in MATLAB and fuzzyTECH 2011
[10] Sugano M. Fuzzy measures and fuzzy integrals. – Amsterdam, North-Holland Publishing Company , 1997.
[11] Djurayev, R. Kh, Sh Yu Jabborov, and I. I. Omonov. "Analysis of the open queuing system model of diagnostics of data transmission network elements." ITN&T-2022: 48.
[12] Djurayev, R. Kh, Sh Yu Jabborov, and I. I. Omonov. "Analysis of methods for calculating reference signatures in digital devices." (2021).
[13] Gutten M, Brncal P, Sebok M, Kucera M, Korenciak D. Analysis of insulating parameters of oil transformer by time and frequency methods. Diagnostyka. 2020;21(4):51-56. doi:10.29354/diag/128607.
[14] Varbanets RA, Zalozh VI, Shakhov AV, Savelieva IV, Piterska VM. Determination of top dead centre location based on the marine diesel engine indicator diagram analysis. Diagnostyka. 2020;21(1):51-60. doi:10.29354/diag/116585.

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