Supply chain performance evaluation model for integrated circuit industry based on fuzzy analytic hierarchy process and fuzzy neural network

3.2.1 Process method

tThe FAHP combines the advantages of the traditional AHP and fuzzy logic to deal with the uncertainty of decision-makers by using a fuzzy numerical value. Constructing a fuzzy consistency judgment matrix and fuzzy priority calculation can make the decision-making process more flexible and adapt to the complex real scene. The FAHP effectively deals with the fuzziness in human judgment and converts the results into a clear decision basis through de-fuzzification technology, to help decision-makers make more reasonable and reliable choices.

The key to the FAHP is to construct a fuzzy consistency judgment matrix, which considers the possible fuzziness that decision-makers may have when judging the relationships between levels. Hierarchical analysis (AHP) is a systematic decision analysis method. It forms a multi-level analytical structure model by dividing the complex decision problem into different constituent factors and combining factors at different levels according to the correlation between factors. In addition, the implementation process of the FAHP is relatively simple and fast, allowing decision-makers to complete the entire analysis process more quickly and make effective decisions. The detailed steps are depicted in Figure 3:

Figure 3

Flow chart of FAHP. Source: Created by the authors.

3.2.2 Definition of fuzzy judgment matrix

3.2.3 Weight calculation

Once the feature vector W is computed, it is crucial not to directly employ it, as doing so could result in considerable errors and contravene the scientific principles underlying the model construction. In the hierarchical analysis (AHP), although the eigenvector W represents the relative importance weight between the factors, there may be errors in directly using the original calculated eigenvectors. This is because the judgment matrix is constructed based on the subjective judgment of the decision maker and may be inconsistent. The direct use of unverified and corrected feature vectors as weights may introduce bias and affect the scientificity and accuracy of the final decision.

Therefore, preprocessing is also necessary to ensure that it meets ∑ i = 1 n W i = 1 requirements, using this approach ensures the accurate acquisition of weight data for each indicator. Numerous methods exist for determining eigenvectors, including geometric averaging, arithmetic averaging, and eigenvalue methods, among others.

3.2.4 Consistency check

The process of selecting evaluation indicators initially relies on methods like expert consultation and online research, thus inherently containing a notable degree of human subjectivity. At present, the process of selecting the evaluation index of the fuzzy level analysis method relies more on the systematic construction strategy and rigorous logical analysis. It combines the professional knowledge and experience judgment of experts and also uses quantitative models to deal with uncertainty and ambiguity, weakening the influence of a single subjective judgment. This process emphasizes the scientific classification and hierarchical division of the evaluation indicators and handles the complex evaluation relationship through fuzzy mathematical theory to ensure that the evaluation process is more objective, scientific, and comprehensive. Therefore, after obtaining λ max , consistency testing is required to reduce errors and improve the accuracy of the results [19]. The specific inspection method is as follows.

Calculate the consistency index CI as follows:

Calculate the consistency ratio CR as follows:

When the CR falls below 0.1, falling within the acceptable range defined by academic standards, it indicates that the construction of the matrix adheres to the principles and is suitable for practical research applications. Naturally, a smaller CR signifies a higher level of consistency between the judgment matrix and the decision objective.

3.3.1 Introduction to FNNs

Fuzzy theory and artificial neural networks are two active parts in the fields of artificial intelligence and intelligent computing in recent years. The effective combination of fuzzy theory and artificial neural networks can complement each other and leverage their respective advantages [20,21]. Fuzzy theory is good at handling uncertainty and fuzzy information, while artificial neural networks are good at learning complex nonlinear mapping relationships. After combination, it can not only process fuzzy data efficiently but also optimize the decision-making process through self-learning to improve the adaptability and intelligence level of the system, to show stronger ability and flexibility in the decision-making of complex problems. In essence, the FNN stands out as a superior theoretical framework that seamlessly integrates fuzzy theory with artificial neural networks, leveraging the strengths of both methodologies.

3.3.2 Takagi–Sugeno (T–S) model for fuzzy systems

Many literatures show that there are two kinds of fuzzy models widely used in fuzzy systems at present: (1) Mamdani model representation is the standard model representation of fuzzy systems, and the consequent of Mamdani model fuzzy rules is a fuzzy set of outputs; (2) The T–S model of fuzzy systems represents that, compared to the Mamdani model, the fuzzy rule consequence of the T–S model is a function of input language variables and a linear combination or constant of output variables. Among them, when it is a linear combination, it is the first-order T–S model representation; when it is a constant, it represents the zero-order T–S model [22]. For the purpose of better comparative research with FNN models, the authors select the T–S model of fuzzy systems to establish a FNN model for evaluating the risk of industrialization of patent technology in universities. Here the network structure and learning algorithm of T–S model in fuzzy systems are briefly introduced.

The fuzzy rule consequence of the T–S model is a linear combination of input variables, i.e., Rj ; If x 1 is A 1 j , x 2 is A 2 j , and x n is A n j , then

Equation (9) illustrates that the output of a fuzzy system is derived from the weighted average of the outputs generated by each rule.

where α → j = α j ∑ i = 1 m α i ( α j represents the applicability of each rule).

3.3.3 Learning algorithms for FNNs

We can first determine the fuzzy number of input components based on actual situations and expert knowledge. Under these conditions, the FNN parameters that need to be learned include not only the connection weight p ji ′ ( j = 1 , 2 , … , m ; i = 1 , 2 , … , n ; l = 1 , 2 , … , r ) of the posterior networkbut the parameter values of the membership functions for each node in the second layer of the antecedent network also need to be determined [23].

Let the error function be as follows:

where t i and y i represent the expected output and actual output, respectively. Below is the learning algorithm for parameter p ji 1 . Similar to the derivation of the BP algorithm, according to the chain rule and Delta learning rule, there are the following equations:

where j = 1 , 2 , … , m ; i = 1 , 2 , … , n ; l = 1 , 2 , … , r .

Taking the Gaussian membership function as an example, this study explores the learning problem of its center σ ij .

It is evident that the simplified structure closely resembles the architecture of the FNN based on the standard model. When the connection weight y ij = W ij of the last layer is set, the results obtained by the standard model (Mamdani model) of the fuzzy system can be borrowed, as shown in equations (15)–(18).

where if the cancellation operation is used, then it is an input to the rule node; otherwise, it is not. Finally, the following equations are obtained:

where β > 0 is the learning rate, i = 1 , 2 , … , n ; j = 1,2 , … , m

For the neural network model introduced above, when given an input, only a small number of elements in the α = [ α 1 , α 2 , … , α m ] T of the third layer of the antecedent network are greater than 0, and most of the other elements are either 0 or close to 0. Therefore, in the above network, the mapping from input x to membership vector a is very similar to the nonlinear mapping of the radial basis function neural network [24].

3.4.1 Learning rate

The learning rate dictates the extent of adjustment in weights induced by each training session. By sequentially setting the learning rate parameters net.trainParam.lr = 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, and 0.1 in the programming language, the FNN model is repeatedly debugged and trained after setting the corresponding learning rate value each time. In this experiment, the value of the learning rate is determined by step-by-step testing and evaluation of different learning rates. The selection of these parameters is based on common machine learning practices and is designed to cover a range of low to high learning rates to observe the impact of each learning rate on the model’s training performance. The training data are shown in Table 4 and Figure 4.

Figure 4

Error corresponding to the number of hidden layer nodes. Source: Created by the authors.

As shown in Figure 4, it can be observed that the training performance of the FNN model at different learning rates shows obvious differences. First of all, although a lower learning rate (such as 0.01) can achieve a lower mean square error, more training steps are required, which indicates that the learning process is slower. With the increase in the learning rate, the training steps are significantly reduced, indicating that the convergence speed is accelerated, but at the same time, the mean square error begins to fluctuate, especially when the learning rate is too high (such as 0.1), the mean square error increases significantly. This may be due to the unstable training process caused by the excessive learning rate, and it is difficult for the model to converge to the optimal solution. On further analysis, we found that there is an optimal learning rate interval. In this interval, the model can not only maintain a fast convergence speed but also obtain a relatively low mean square error. When the learning rate is 0.01, the corresponding mean square error value is the smallest; therefore, the learning rate is determined to be 0.01.

3.4.2 Training function

The authors used the commonly used training functions to train the constructed network model. To improve the accuracy of the model, the comparison of the mean-variance, correlation coefficients, and training steps before and after model calibration are shown in Table 5.

4.1.1 Model validation

To verify the feasibility and effectiveness of the performance evaluation model for CM company’s ordinary integrated circuit product suppliers after completing design and revision training, the following steps and MATLAB programming statements are used to validate the model. Use the normalized data from three suppliers, S16, S17, and S18, as the test matrix for the inspection samples and import it into MATLAB. Historical performance data for these suppliers are collected through CM’s supplier management system. To create a comprehensive performance benchmark, data from industry reports, historical best performance indicators, and expert opinion are also combined. This ensures that the evaluation criteria are not only relevant to CM companies but also reflect industry standards. The hypothesis is that the FNN model can accurately evaluate supplier performance and reflect the real performance differences among suppliers based on standardized operational data. Recall the already trained FNN model for simulation. The cross-validation strategy was adopted to verify the results, and the training set and the test set were randomly divided several times. The comparison between the specific output results and the expected results is shown in Table 6 and Figure 5.

Figure 5

Model validation error. Source: Created by the authors.

From the model validation results in the table above and Figure 5, it can be seen that the error value output after running the validation sample is relatively small.

4.1.2 Application of the model

The supply chain management department of CM Company have used various types of integrated circuit products in the engineering construction process. In this section, we will use the established and debugged FNN model to select one type of integrated circuit product, namely, a butterfly integrated circuit, for the application of supplier performance evaluation. We will use the relevant data of various suppliers of butterfly integrated circuit products from CM Company from 2022 to 2023 and normalize them as the input matrix. Subsequently, we input these data into the model and run an FNN simulation to evaluate supplier performance. After the operation, we will obtain the performance evaluation results of ten suppliers of butterfly integrated circuit products and compare them with the actual supplier management requirements. The results are shown in Table 7.

According to the supplier grading management method of CM Company, suppliers with higher comprehensive scores can participate in the evaluation of excellent suppliers every year. The proportion of participation depends on different product settings. Among them, suppliers DS1, DS8, and DS9 with a comprehensive performance score greater than 0.8 are considered relatively excellent suppliers. This indicates that the model effectively identifies suppliers with better performance.

4.2.1 Improving the level of informatization and intelligence in supply chain management

The advantage of using FNN models for supplier performance evaluation is that they have good adaptability and generalization ability, and can be trained through historically accumulated sample data to scientifically and reasonably evaluate supplier performance [22,24]. However, considering that when general telecommunication companies choose to use FNNs, evaluators engaged in supplier management may not be able to quickly grasp the theoretical and practical knowledge of relevant models. Improper model parameter settings often lead to inaccurate evaluation results.

4.2.2 Correct and reasonable use of evaluation models and indicator data

In modern supply chain management theory, regardless of which performance evaluation indicators or methods are selected to evaluate suppliers, the primary prerequisite must be based on the supplier’s true original indicator data. Therefore, when using FNNs to construct evaluation models for various product suppliers in telecommunication operators, it is necessary to rationally judge whether the supplier in that category is suitable to use evaluation methods based on FNNs; Second, it is necessary to consider whether objective and accurate basic indicator data can be obtained in a timely and effective manner. For the performance evaluation of CM Company’s suppliers, it is important to start from the perspective of management system and supervision and to require and improve the objectivity, fairness, and consistency of evaluation indicators among many provincial companies. Obtaining the original basic data of true supplier evaluation indicators is an important prerequisite for conducting subsequent model simulation fairness. Otherwise, evaluation models constructed based on incorrect indicator data are worthless. Otherwise, relying too much on evaluation methods and models can often lead to losses outweighing gains. Not only does the efficiency of supplier management work not improve, but the value of data analysis applications cannot be highlighted.

4.2.3 Looking at supplier performance evaluation methods from a development perspective

There are multiple methods to evaluate supplier performance. The author chooses to use an FNN model to evaluate the performance of CM company’s integrated circuit product suppliers, which is a relatively ideal, feasible, and highly operational evaluation method. On the one hand, due to the significant fluctuations in the upstream fiber preform and other raw material market for integrated circuit products, the tight supply of raw materials leads to a shortage of supply and an oversupply of raw materials, CM Company’s classification and positioning of integrated circuit product suppliers should be different. At the same time, the selection of indicators in the evaluation model and the weight of various indicators in factor analysis will undergo significant changes. On the other hand, due to the different positions of the same type of product in different telecommunication operator enterprises, mobile communication operators and tower companies also have different classifications and positioning of the integrated circuit products and suppliers. The construction of a supplier performance evaluation index system should be combined with the actual situation of enterprise supply chain management work, realistic, constantly adjusted, improved, and optimized, facilitating the construction of a reasonable evaluation model that adapts to the characteristics of the enterprise and product types. In summary, supplier performance evaluation is not static but should be adjusted promptly based on the internal and external market environment and the development goals of the enterprise.