This article discusses a variant of a High-speed Fuzzy Inference Machine Learning Device Based on Single-Layer Area Ratio Defuzzifier. The developed mathematical model is presented, the steps by which this system operates are described. The results of modeling in Simulink are also presented and show a 1.5x increase in training speed. In an era of rapidly advancing technology, traditional binary logic systems often fall short when dealing with the complexity and uncertainty of real-world scenarios [1], [2], [3], [4]. Fuzzy logic systems, which mimic human reasoning by handling partial truths and uncertainties, have emerged as a powerful alternative. By integrating machine learning techniques, these systems are now capable of adapting and improving their performance over time, creating a dynamic approach to problem-solving. This article explores the foundations of fuzzy logic systems with learning capabilities, their advantages, and their growing applications across various fields, from robotics to data analysis [5], [6].
The main purpose of the developed High-speed Fuzzy Inference Machine Learning Device is to implement the system learning function and improve computing performance. This is achieved by adding feedback from the training unit to the defuzzification unit, which allows for the training of the fuzzy logic device [7], [8]. Some operations in the defuzzification unit were also excluded, which reduced the computational performance time of the defuzzification process to 180 ns.
The result of a high-speed fuzzy logic inference machine learning device based on a single-layer defuzzifier of the area ratio method is the generation and transformation of input data into a single specified crisp value at the output of the fuzzy logic system. This type of device can be used for image classification or thermocouple control tasks [9], [10].
Also, an ontological model of neuro-fuzzy learning based on the area ratio method was developed: = ⟨
2 6 5 2 ⟩
, , , ,
in=1 im=1 def =1 l=1
(
The working principle of the high-speed fuzzy inference machine learning device (Fig. 1) based on the single-layer area ratio defuzzifier consists of five steps [ 11], [12]. The values of two variables «A» and «B» are generated in block 1 – Control Signal Generator Block (CSGB). Then the variable «A» goes to block 2 – First Input Variable Fuzzification Block (FIVFB), and the variable «B» is transferred to block 3 – Second Input Variable Fuzzification Block (SIVFB). In FIVFB 2, the first three triangular functions «A1», «A2», «A3» are generated in First, Second and Third Triangular Function Formation Blocks (FTFFB, STFFB, TTFFB) respectively. In SIVFB 3, the second three triangular functions «B1», «B2», «B3» are generated in FTFFB, STFFB, TTFFB too. Each of the triangular membership functions has a form similar to Fig. 3. The triangular functions «A1», «A2», «A3», «B1», «B2», «B3» are transferred to block 4 – Implication Block (IB), where they are subject to implication. As a result, at the output of IB 4, five variables «M1», «M2», «M3», «M4», «M5» are transferred to block 5 – Defuzzification Block (DefB). In DefB 5, the defuzzification process takes place, during which the resulting variable «MAR2» is calculated. And after receiving MAR2, the calculations go to block 6 – Learning Block (LB).
The calculation of the resulting variable "MAR2" (Fig.1) in the high-speed fuzzy inference machine learning device based on the single-layer area ratio defuzzifier [ 13], [14] is carried out by the steps described below.
Step 1. Generation of input variables by counters (Fig.2):
= 1 × 1 +
= 2 × 2 +
(
Step 2. The formation of the triangular membership function (Fig.3 and Fig.4) is calculated using the formula: ⎧⎨ −− , if x < s < y
−− , if y < s < z
⎩ 0, else
where s is input value A or B coming from the block 1 (Fig.3 and Fig.4), x, y, z are membership function
labels. Their value stored in blocks 2.1÷2.5 and 3.1÷3.5. The variables for «x», «y», and «z» are selected
depending on the required type of membership function. In our case, a triangular membership function
is used, which is shown in Fig.3. An example of their calculation is presented above Eq.(
The implementation of Eq.(
Step 3. Functions «A1», «A2», «A3», «B1», «B2», «B3» come from the outputs of the FIVFB, SIVFB blocks to the inputs of the IB block. The implication process [15], [16] (Fig.6) of the input variables is calculated according to the established fuzzy rules: 1 = min(1, 1) 2 = max(min(1, 2), min(2, 1)) a) b) 3 = max(min(1, 3), min(2, 2), min(3, 1)) 4 = max(min(2, 3), min(3, 2)) 5 = min(3, 3) (7) (8) (9)
The output values of the block are M1, M2, M3, M4, M5 (Fig.7), and the variable M1 is calculated in block 4.1, M2 is calculated in block 4.10, M3 is calculated in block 4.11, M4 is calculated in block 4.12, M5 is calculated in block 4.9.
Step 4. The defuzzification process (Fig.8). Determining the output value after defuzzification based on the area ratio method according to Eq.10: × (max − min) + min ︂] (10) where is value transmitted from the IB block 4, n is number of output fuzzy membership functions (n = 5) (Fig.7), +1 is weighting factor (default 1), is maximum value of the output function (block 5.4), is minimun value of the output function (block 5.5) (Fig.7 and Fig.8: = 250, = 210).
To find the diference between
and , input values and are fed to the inputs of subtraction block SUB 5.7. To calculate Eq.10 ten-digit values and are fed to the input of the subtractor SUB 5.7. The output value of the subtractor SUB 5.7, which determines the value of the domain of definition of the output membership function, is fed to the input of the multiplier MUL 5.6, and D, obtained at the output of the divider DIV 5.3, is fed to the second input of the multiplier MUL 5.6. The output of the multiplier MUL 5.6 is connected to the input of the adder ADD2 5.8. The value is fed to the second input of the adder ADD2 5.8. At the output of the adder ADD2 5.8, the output ten-bit value is calculated after defuzzification based on the area ratio method "MAR2" [17].
Step 5. The training process (Fig.9). The output value after learning is determined according to the formula:
Learn+1 = Learn + ([MAR2 − target] ×
Mult), until MAR2 − target| ≤ (11) where Mult is learning rate (default 0.04), T is threshold coeficient (default 0.01) (Fig.9, block 6.2), is expected output value after defuzzification.
The above mathematical model was simulated in the Simulink software for modeling, simulation and analysis of multidomain dynamic systems. The results of the training process simulation are shown in
The developed method is described, the ontological and mathematical model of High-speed Fuzzy Inference Machine Learning Device Based on Single-Layer Area Ratio Defuzzifier is presented. In addition, the proposed system was simulated in Simulink and compared with the performance of the center-of-gravity defuzzifier and the multilayer modification of the area ratio method.
Thus, the high-speed fuzzy inference machine learning device based on the single-layer area ratio defuzzifier allows determining a single value after defuzzification, provides increased performance by simplifying the defuzzifier structure, and allows training the fuzzy inference system to the target value.
The work was prepared as part of the implementation of the RSF project No. 24-21-00055. The authors are grateful to the Foundation for their support.
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