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APPLICATION OF THE FUZZY-SET THEORY TO ASSESS THE KNOWLEDGE OF ELECTRIC POWER INDUSTRY SPECIALISTS
V.Kh. Nasibov R.R. Alizade I.Y. Mastaliyev A.M. Ramazanli
Azerbaijan Scientific-Research and Design-Prospecting Power Engineering Institute nvaleh@mail.ru , rena_alizade@mail.ru , ismayil_inf@mail.ru , ahmet.ramazanli@gmail.com
Abstract
In most cases, the assessment of the knowledge of electric power industry workers is carried out according to a test scheme, where the correct answer is selected from the list of answers. All questions have the same difficulty and only the single correct answer gives a certain score [1]. The article developed a universal model for assessing the knowledge of electric power industry workers, where using the theory of fuzzy logic and fuzzy inference, both the complexity of questions and the possibility of a partial correct answer are taken into account.
Keywords: Knowledge Assessment, Training, Fuzzy Knowledge Base
I. Introduction
Articles Personnel training, advanced training of electric power industry workers is a necessary task to improve the efficiency and safety of the operation of electric power facilities. Refresher courses for employees, which should be held at least once every 3-5 years, are necessary for employees and the head of energy enterprises in the electric power industry. Terms should be determined by the internal regulations of the enterprise, as well as the requirements of standards. Refresher courses are held; electricians, technologists, power engineers and heads of departments. Upon completion of advanced training courses, knowledge is tested by conducting an appropriate exam, where a test scheme of answers to the questions posed is mainly implemented. Only one correct answer is selected from the submitted answers, all other answers are considered incorrect. With this approach to testing knowledge, the complexity of the questions is not taken into account, and the possibility of a partial correct answer is also excluded.
The need to take into account the complexity of questions and a partial correct answer makes it possible to use the theory of fuzzy sets and fuzzy inference to assess the level of preparedness of electric power industry workers [2].
II. Knowledge assessment
To account for the complexity of the questions, the questions are divided into four groups: relatively easy questions, normal questions, questions of medium difficulty and difficult questions. The weight coefficients of correct answers are ranked according to the level of difficulty of the questions. The partial correct answer for groups of normal and questions of average difficulty has
a smaller total in the resulting assessment of knowledge than the partial correct answer for complex questions. To obtain a quantitative value of knowledge assessment based on linguistic information, one can use the provisions of the theory of fuzzy sets and fuzzy logic [3].
Figure 1: Fuzzy inference circuit
The fuzzy model contains the following blocks: a fuzzifier that converts a fixed vector of influencing factors X into a vector of fuzzy sets X ~ required to perform fuzzy inference;
Y = f (X)
fuzzy knowledge base containing information about dependence in the form of linguistic rules of the "IF-THEN" type;
a fuzzy inference machine that, based on the rules of the knowledge base, determines the value of the output variable in the form of a fuzzy set Y corresponding to the fuzzy values of the
input variables X ;
a defuzzifier that converts the output fuzzy set Y into a clear number Y. The Mathlab program contains the Fuzzy Logic Toolbox package, which implements two types of fuzzy models, the Mamdani and Sugeno types. For our case, a Mamdani-type fuzzy model is preferable.
In the Mamdani-type model, the relationship between inputs X=(x1, x2, ... xn) and output Y is determined by a fuzzy knowledge base of the following format:
if (xi = a\,j\) and (x2 = a2,ji) and...and (xn = an,jX) or (xi = ai,j2) and (X2 = a2,j2) and..-and (xn = anJ2 )
or (x1 = a1,jk- ) and (x2 = a2,jk ■ ) and^and (xn = an,jk - )
which evaluates the variable Xt in the line with the number
conjunctions in which the output y evaluated by linguistic term dj;
That
y = dj, i = 1, m, Where
aijp - linguistic term, jp (p = 1, kj) kj - number of rows -
V.Kh. Nasibov, R.R. Alizade, I.Y. Mastaliyev, A.M. Ramazanli RT&A, No 1 (77) SHORT VERSION OF ARTICLE TITLE_Volume 19, March 2024
m- the number of terms used for the linguistic evaluation of the output variable y.
All linguistic terms in the knowledge base are represented as fuzzy sets defined by the
corresponding membership functions:
VjP(xi) - input membership function xt fuzzy term a^p, i = l,n,j = l,m,p = 1, kj, those.
= ¡Mjp(xi)/xi, xi ^[xi'xi]
a
jp
X;
Hdj(y) - output membership function y fuzzy term dj, j = 1, m, those.
y
di =iMd, (y)/y, y 6[yy]
y
Degree input vector accessories X* = (x*,x?*,... xjj) fuzzy terms dj from the fuzzy knowledge base is determined by the following system of fuzzy logical equations:
Md, (x*) = ^ ^ [Mjp(x*)], j =1 m,
p=\,kj i =1,n
Where V (A) -operation from the s-norm (t-norm), i.e. from a set of implementations of logical operations OR (AND). The following implementations are most often used: for the OR operation -finding the maximum, for the AND operation - finding the minimum.
The fuzzy set y corresponding input vector X*, is defined as follows:
f- ' _ \imp(Md, (x* W (y))/ y
y = agg
j=1,m ^
Where
imp - implication, usually implemented as a minimum finding operation; agg - aggregation of fuzzy sets, which is most often implemented by the operation of finding the maximum.
III. Fuzzy inference models
Clear output value y, corresponding to the input vector X*, is determined as a result of defuzzification of the fuzzy set y. The most commonly used defuzzification is the center of gravity method:
The choice of the membership function affects the accuracy of the fuzzy inference model. Figures 2-9 show various membership functions for input and output variables [4-6].
Figure 2 shows the function of input variables (answers to all four groups of questions by complexity) in the form of a triangle. The optimal output membership function is shown in Figure 3, in which the adequacy of the result to the rules corresponds to 88.3%.
Figure 2: Linear membership function for the input
According to the rules (Rules), the program compared the data with the forms of relations and received the results. The triangular membership function results were compared with the rules and it was observed that the result was about 88.3% correct.
Figure 3: Linear membership function for the output
Figure 4 shows the membership function of the inputs in the form of a trapezoid, and Figure 5 corresponds to the membership function of the output in the form of a triangle. Such a choice of the output membership function leads to a high indicator of the adequacy of the output to the rules - 91%.
Figure 4: Trapezoidal membership function for the input
Figure 5: Trapezoidal membership function for the output
One of the most commonly used membership functions is the Gbell function (a Gaussian type function). The graphs of the membership functions for the inputs and for the output are shown in Figures 6 and 7, respectively, the result is 88.1% adequate.
0 10 20 30 40 50 60 70 80 90 100
input wraua-HMr
Figure 6: Gaussian membership function for the input
Figure 7: Gaussian membership function for the output
Numerous studies on the choice of membership functions for inputs and outputs have shown that the maximum adequacy is achieved when using Gauss-Linear functions, which is formed by combining the Gauss and limf functions (Gauss and limf), which are shown in Figure 7 and 8. For these membership functions, the adequacy of the output to the rules is 97.7%.
Mwnborship function plots
Figure 8: Gauss-Linear membership function for the input
Figure 9: Gauss-Linear membership function for the output
Table 1 shows a comparison of the adequacy of the output to the rules for various membership functions. As can be seen from Table 1, the maximum adequacy of the model is achieved when using membership functions of the Gauss-Linear type [7-9].
Table 1: Percentages, based on the rules of the membership functions
Membership Function Accuracy percentages
Triangular 88.3
Trapezoid 91.0
Gaussian 88.1
Gauss Linear 97.7
Table 2 presents a fragment of the learning rules (knowledge base) of the fuzzy inference model for assessing the level of preparedness of electric power industry workers.
Table 2: Fragment of model training rules
Examples Hard Medium 2 Medium 1 Easy Result (with rules) Result (Gbell-mf)
Examples 1 85 85 75 65 A A(84.84)
Examples 2 85 75 85 55 A A(84.84)
Examples 3 75 85 35 45 B B(64.94)
Examples 4 65 55 65 45 B B(64.94)
Examples 5 65 35 75 55 C C(55.06)
Examples 6 15 25 85 65 C D(37.87)
Examples 7 45 35 25 35 D D(35.10)
Examples 8 15 25 45 95 D D(27.86)
Examples 9 15 25 15 55 E E(13.23)
Examples 10 5 15 65 55 E E(13.23)
With the selected answers to questions from four blocks, you can get the corresponding score, as shown in Figure 10. Here, the first column shows the score for difficult questions, the fourth for easy questions, and the last column the resulting score.
Answers on questions
Resulting score
Hard
Medium 2
Medium 1
Easy
Evaluation
->■ Grades
Figure 10: a) Evaluation by points
Figure 10: b) Evaluation by points
IV. Discussion
1. A universal method for assessing the level of preparedness of electric power industry workers has been developed, where, using the theory of fuzzy logic and fuzzy inference, one can take into account the complexity of questions, as well as the possibility of a partial correct answer.
2. By choosing membership functions for the inputs and outputs of functions of the Gauss-Linear type, you can achieve the maximum adequacy of the fuzzy inference model - 97.7%.
References
[1] Jianchang Lu & Yinchun Lvy, Research of Electric Power Enterprise Knowledge Workers' Incentive Based on Fuzzy Model. Procedia Engineering, Volume 16, 2011
[2] Ling Li Talking about the Electric Power Enterprise Knowledge Staff Management Advantages and Challenges. J. China power education, 2006
[3] Fuzzy Logic Toolbox™ User's Guide Matlab.
[4] Nadia Rousseau, Carl Beaudoin, Corina Borri-Anadon & oth. Enquête nationale sur les services éducatifs complémentaires à la formation professionnelle. Rapport de recherche
https://www.researchgate.net/publication/344671920 Enquete nationale sur les services edu catifs complementaires a la formation professionnelle Rapport de recherche
[5] Zhiyong Xu, Xudong Zhang, Ming Zeng, Fan Yan Application of ANP-based Multilevel Fuzzy Comprehensive Evaluation Methods to Post-evaluation for Grid Construction Projects. J. East China Electric Power, 2009
[6] Mei-Hsiang Wang & Tarng-Yao Yang Investigating the success of knowledge management: An empirical study of small- and medium-sized enterprises. Asia Pacific Management Review Volume 21, Issue 2, June 2016
[7] I. Chan & C.K. Chao Knowledge management in small and medium-sized enterprises. Communications of the ACM, 51 (4), 2008
[8] J.C. Anderson & D.W. Gerbing Structural equation modeling in practice: a review and recommended two-step approach. Psychological Bulletin, 103 (3), 1988
[9] R.E. Bohn Measuring and managing technological knowledge. Sloan Management Review, 36 (1), 1994
