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In the Internet era, soccer teaching has gotten rid of the previous theoretical teaching mode and paid more attention to the use of video and multimedia for network teaching. In this paper, from the perspective of a fuzzy mathematical algorithm, the mathematical set algorithm is used to construct a fuzzy matrix through algorithm mapping, calculate the NMI value of the equivalent algorithm and the comprehensive rating weights of U1-U10 in the evaluation elements of soccer network teaching, and derive the fuzzy transformation value of the rating result of soccer network teaching platform as 83.7895. The probability distribution value is inferred to be 45.8% on average by creating the affiliation function and then calculating the search accuracy, platform recall, and teaching F1 metrics of the Zadeh mathematical operator. After calculating the weighted average value of B=87.6617 for the Zadeh mathematical operator through the metrics, an empirical analysis of the feasibility of invoking the fuzzy mathematical algorithm in the soccer teaching web platform was conducted. The results showed that the total number of students who wanted to continue using the platform was 36,530, accounting for 91.33% of the total number of students, indicating that the use of fuzzy mathematical algorithms to participate in the teaching of the online platform is significantly better than the traditional teaching model and is conducive to improving the effectiveness of student autonomy.

The implementation of content-based image retrieval (CBIR) mainly depends on two key technologies: image feature extraction and image feature matching. In this paper, we extract the color features based on Global Color Histogram (GCH) and texture features based on Gray Level Co-occurrence Matrix (GLCM). In order to obtain the effective and representative features of the image, we adopt the fuzzy mathematical algorithm in the process of color feature extraction and texture feature extraction respectively. And we combine the fuzzy color feature vector with the fuzzy texture feature vector to form the comprehensive fuzzy feature vector of the image according to a certain way. Image feature matching mainly depends on the similarity between two image feature vectors. In this paper, we propose a novel similarity measure method based on k-Nearest Neighbors (kNN) and fuzzy mathematical algorithm (SBkNNF). Finding out the k nearest neighborhood images of the query image from the image data set according to an appropriate similarity measure method. Using the k similarity values between the query image and its k neighborhood images to constitute the new k-dimensional fuzzy feature vector corresponding to the query image. And using the k similarity values between the retrieved image and the k neighborhood images of the query image to constitute the new k-dimensional fuzzy feature vector corresponding to the retrieved image. Calculating the similarity between the two k-dimensional fuzzy feature vector according to a certain fuzzy similarity algorithm to measure the similarity between the query image and the retrieved image. Extensive experiments are carried out on three data sets: WANG data set, Corel-5k data set and Corel-10k data set. The experimental results show that the outperforming retrieval performance of our proposed CBIR system with the other CBIR systems.

In the structure of ANFIS, there are two different parameter groups: premise and consequence. Training ANFIS means determination of these parameters using an optimization algorithm. In the first ANFIS model developed by Jang, a hybrid learning approach was proposed for training. In this approach, while premise parameters are determined by using gradient descent (GD), consequence parameters are found out with least squares estimation (LSE) method. Since ANFIS has been developed, it is used in modelling and identification of numerous systems and successful results have been achieved. The selection of optimization method utilized in training is very important to get effective results with ANFIS. It is seen that derivate based (GD, LSE etc.) and non-derivative based (heuristic algorithms such us GA, PSO, ABC etc.) algorithms are used in ANFIS training. Nevertheless, it has been observed that there is a trend toward heuristic based ANFIS training algorithms for better performance recently. At the same time, it seems to be proposed in derivative and heuristic based hybrid algorithms. Within the scope of this study, the heuristic and hybrid approaches utilized in ANFIS training are examined in order to guide researchers in their study. In addition, the final status in ANFIS training is evaluated and it is aimed to shed light on further studies related to ANFIS training.

This paper presents a comparative study between the firefly algorithm (FA) and the galactic swarm optimization (GSO) method, where the performance of both methods is observed and tested in the optimization of a fuzzy controller for path tracking of an autonomous mobile robot. The main contribution of this work is finding the best method that generates an optimal vector of values for the membership function optimization of the fuzzy controller. This with the goal of improving the performance of the controller and thus the trajectory generated by the autonomous robot is closer to the desired trajectory. It should be noted that the fuzzy controller that is optimized is an interval type-2 fuzzy controller, which has a greater capability for managing uncertainty than a type-1 fuzzy controller. In this case, the limiting membership functions in the interval type-2 fuzzy sets are themselves type-1 fuzzy sets that define the footprint of uncertainty. Type-2 fuzzy controllers have been shown in previous works to handle better the control of robotic systems under noisy and dynamic conditions and this is why their optimal design is very important. Simulation results show that GSO outperforms FA in the optimal design of interval type-2 fuzzy controllers.

We describe in this paper a proposed enhancement of the bat algorithm (BA) using interval type-2 fuzzy logic for dynamically adapting the BA parameters. The BA is a metaheuristic algorithm inspired by the behavior of micro bats that use the echolocation feature for hunting their prey, and this algorithm has been recently applied to different optimization problems obtaining good results. We propose a new method for dynamic parameter adaptation in the BA using interval type-2 fuzzy logic, where an especially design fuzzy system is responsible for determining the optimal values for the parameters of the algorithm. Simulations results on a set of benchmark mathematical functions with the interval type-2 fuzzy bat algorithm outperform the traditional bat algorithm and a type-1 fuzzy variant of BA. The proposed integration of the type-2 fuzzy system into the BA has the goal of improving the performance of BA for the future applicability of the algorithm in more complex optimization problems where higher levels of uncertainty need to be handled, like in the optimization of fuzzy controllers.

In recent, various metaheuristic algorithms have shown significant results in control engineering problems; moreover, fuzzy sets (FSs) and theories were frequently used for dynamic parameter adaption in metaheuristic algorithms. The primary reason for this is that fuzzy inference system (FISs) can be designed using human knowledge, allowing for intelligent dynamic adaptations of metaheuristic parameters. To accomplish these tasks, we proposed shadowed type-2 fuzzy inference systems (ST2FISs) for two metaheuristic algorithms, namely cuckoo search (CS) and flower pollination (FP). Furthermore, with the advent of shadowed type-2 fuzzy logic, the abilities of uncertainty handling offer an appealing improved performance for dynamic parameter adaptation in metaheuristic methods; moreover, the use of ST2FISs has been shown in recent works to provide better results than type-1 fuzzy inference systems (T1FISs). As a result, ST2FISs are proposed for adjusting the Lèvy flight (P) and switching probability (P′) parameters in the original cuckoo search (CS) and flower pollination (FP) algorithms, respectively. Our approach investigated trapezoidal types of membership functions (MFs), such as ST2FSs. The proposed method was used to optimize the precursors and implications of a two-tank non-interacting conical frustum tank level (TTNCFTL) process using an interval type-2 fuzzy controller (IT2FLC). To ensure that the implementation is efficient compared with the original CS and FP algorithms, simulation results were obtained without and then with uncertainty in the main actuator (CV1) and system component (leak) at the bottom of frustum tank two of the TTNCFLT process. In addition, the statistical z-test and non-parametric Friedman test are performed to analyze and deliver the findings for the best metaheuristic algorithm. The reported findings highlight the benefits of employing this approach over traditional general type-2 fuzzy inference systems since we get superior performance in the majority of cases while using minimal computational resources.

Multi-state components, common cause failures (CCFs) and data uncertainty are the general problems for reliability analysis of complex engineering systems. In this paper, a method incorporating fuzzy probability and Bayesian network (BN) into multi-state systems (MSSs) with CCFs is proposed. In particular, basic theories of multi-state BN and fuzzy probability are developed. Moreover, a model integrating CCFs with BN has also been illustrated. In order to incorporate fuzzy probability into MSSs reliability evaluation considering common parent node generated by CCFs, fuzzy probability has to be translated into accurate probability through defuzzification and normalization methods which are both elaborated. In addition, quantitative analysis based on BN is carried out. In this paper, feed system of boring spindle in computer numerical control machine is analyzed as an example to validate the feasibility of the proposed method. It can improve the ability of BN on reliability evaluation of complex system with uncertainty issues.

This paper presents a new fuzzy bee colony optimization method to find the optimal distribution of the membership functions in the design of fuzzy controllers for complex nonlinear plants. We used interval type-2 and type-1 fuzzy logic systems in dynamically adapting the alpha and beta parameter values of the bee colony optimization algorithm (BCO). Simulation results with a type-1 fuzzy logic controller for benchmark control plants are presented. The advantage of using interval type-2 fuzzy logic systems for dynamic adjustment of parameters in BCO applied in fuzzy controller design is verified with two benchmark problems. We considered different levels and types of noise in the simulations to analyze the approach of interval type-2 fuzzy logic systems to find the best values of alpha and beta for BCO when applied in the design of fuzzy controllers.

Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.

In IaaS (infrastructure as a service) cloud environment, users are provisioned with virtual machines (VMs). To allocate resources for users dynamically and effectively, accurate resource demands predicting is essential. For this purpose, this paper proposes a self-adaptive prediction method using ensemble model and subtractive-fuzzy clustering based fuzzy neural network (ESFCFNN). We analyze the characters of user preferences and demands. Then the architecture of the prediction model is constructed. We adopt some base predictors to compose the ensemble model. Then the structure and learning algorithm of fuzzy neural network is researched. To obtain the number of fuzzy rules and the initial value of the premise and consequent parameters, this paper proposes the fuzzy c-means combined with subtractive clustering algorithm, that is, the subtractive-fuzzy clustering. Finally, we adopt different criteria to evaluate the proposed method. The experiment results show that the method is accurate and effective in predicting the resource demands.