Type-2 Membership Functions Research Articles

PREDICTION SYSTEM FOR THE AMOUNT OF SUGAR PRODUCTION USING ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM

Sugar is one of the staple foods most Indonesians use, so sugar production needs to be done optimally to meet people's needs. This research will design a prediction system for the amount of sugar production in PTPN XI PG Prajekan using the Adaptive Neuro-Fuzzy Inference System (ANFIS) method. ANFIS is a combined method of two systems, namely a fuzzy logic system and an artificial neural network system. This research consists of data collection, ANFIS system design, ANFIS training, ANFIS testing, accuracy calculation, and result analysis. The prediction system for the amount of sugar production is designed to predict the variable which is the amount of sugar production in the year using the input variables (sugarcane harvested area in year ), (amount of sugarcane in year ), (average of yield in year ), and (number of milling days in year ). The experiments in this research used variations of the type of membership function and the number of membership functions. The best model obtained in this research is a model with a difference between two sigmoidal membership functions and a product of two sigmoidal membership functions with a total of 2 membership functions for each input variable. Both models have the same Mean Absolute Percentage Error (MAPE) value, which is 1.79% in the training process and 4.82% in the testing process.

Methodological issues of the fuzzy set theory (generalizing article)

The theory of fuzziness is an important area of modern theoretical and applied mathematics. The methodology of the theory of fuzziness is a doctrine of organizing activities in the field of development and application of the scientific results of this theory. We discuss some methodological issues of the theory of fuzziness, i.e., individual components of the methodology in the area under consideration. The theory of fuzziness is a science of pragmatic (fuzzy) numbers and sets. The ancient Greek philosopher Eubulides showed that the concepts «Heap» and «Bald» cannot be described using natural numbers. E. Borel proposed to define a fuzzy set using a membership function. A fundamentally important step was taken by L. A. Zadeh in 1965. He gave the basic definitions of the algebra of fuzzy sets and introduced the operations of intersection, product, union, sum, negation of fuzzy sets. The main thing he did was demonstration of the possibilities of expanding («doubling») mathematics: by replacing the numbers and sets used in mathematics with their fuzzy counterparts, we obtain new mathematical formulations. In the statistics of non-numerical data, methods of statistical analysis of fuzzy sets have been developed. Interval and triangular fuzzy numbers are often used specific types of membership functions. The theory of fuzzy sets in a certain sense is reduced to the theory of random sets. We think fuzzy and that is the only reason we understand each other. The paradox of the fuzzy theory is that it is impossible to consistently implement the thesis «Everything in the world is fuzzy». For ordinary fuzzy sets, the argument and values of the membership function are crisp. If they are replaced by fuzzy analogues, then their description will require their own clear arguments and membership functions, and so on ad infinitum. System fuzzy interval mathematics proceeds from the need to take into account the fuzziness of the initial data and the prerequisites of the mathematical model. One of the options for its practical implementation is an automated system-cognitive analysis and the intellectual system «Eidos».

Construction of a model for evaluating the efficiency of technology transfer process based on a fuzzy logic approach

The object of research is technology transfer, which covers the mechanism of transfer of technological knowledge and innovations from developers to end users or manufacturers. The problem to be solved is to provide a relevant assessment of the effectiveness of technology transfer by applying modern economic and mathematical models (based on the method of fuzzy logic) to assess the effectiveness of technology transfer under conditions of uncertainty. The main results obtained: a fuzzy-logical model for evaluating the level of the technology transfer efficiency indicator was built; it is performed according to the following algorithm: 1) the involvement of three components of technology transfer – technological, financial, and marketing as input variables of the model, which are calculated on the basis of statistical and financial reporting data, expert surveys; 2) selection of parameters and type of membership function for three input variables and one output variable (integral indicator) and construction of a system of 27 logical rules; 3) determining the efficiency of technology transfer using Mamdani's fuzzy derivation and checking the adequacy of the model. A visualization of the "input-output" surface was performed, which determines the maximum value of the TTPE (TechnologyTransferProjectsEfficiency) indicator, which serves as a summary indicator for the success of technology transfer projects and is observed at high levels of model input variables. The indicator T (technical component of technology transfer efficiency), F (financial component of technology transfer efficiency), and M (marketing component of technology transfer efficiency) was introduced. The scientific results could be applied to determine the optimal ways of technology transfer to industry, to plan strategies for introducing new technological products to the market, taking into account the effectiveness of licensing, partnership, and cooperation processes

On Maximum Guaranteed Payoff in a Fuzzy Matrix Decision-Making Problem with a Fuzzy Set of States

The current study delves into a fuzzy matrix decision-making problem involving fuzzy sets of states. It establishes that a maximum guaranteed payoff constitutes a type-2 fuzzy set defined on the real line. Additionally, it provides the associated type-2 membership function. Moreover, the paper illustrates that the maximum guaranteed payoff type-2 fuzzy set of the decision-making problem can be broken down, based on the secondary membership grades, into a finite collection of fuzzy numbers. Each of these fuzzy numbers represents the maximum guaranteed payoff of the corresponding decision-making problem with a crisp set of states. This set corresponds to a specific cut of the original fuzzy set of states. Some properties of the maximum guaranteed payoff type-2 fuzzy set are investigated, and illustrative examples are provided. Since the problem formulation is symmetrical with respect to alternatives and states of nature, the results obtained can be used in the case of a fuzzy set of alternatives.

Computer-Aided Neuro-fuzzy Algorithm for Prediction of Ginger(Zingiber officinale) Rhizome Drying

Neuro-fuzzy modeling technique has been used for the development of computer-based adaptive process control systems for most postharvest operations instead of convectional mechanistic modeling technique owing to its good prediction without prior knowledge of process operation. Therefore, adaptive neuro-fuzzy inference system (ANFIS) modeling and prediction of ginger (Zingiber officinale) rhizome moisture content in a forced convective tray dryer was investigated in this study. Computer codes for an exhaustive search and grid partitioning were written in the Matlab software environment and used for the analysis of experimental data obtained from the ginger rhizome drying experiment. The data were trained and checked using the grid-partitioning ANFIS method for the development of neuro-fuzzy network for ginger drying prediction. The prediction accuracy of the network was evaluated by varying input and output Membership Function (MF) types. The exhaustive search analysis shows that drying time (DT) has the highest effect on the moisture content, followed by air drying temperature (ADT), air relative humidity (ARH), and air flow velocity (AFV). Moreover, combination of DT and ADT as two interactive variables; and combination DT, ADT and ARH as three interactive variables show highest effect on ginger moisture content removal during the process. Generalized bell (gbell) MF with two MF for each input variable and constant output MF 2 type were obtained as the best ginger drying ANFIS network with corresponding R and MSE of 0.9667 and 0.0971, respectively. Therefore, this study shows the reliability of the ANFIS model for the prediction of ginger rhizome drying in a tray dryer.

Computer-Aided Neuro-fuzzy Algorithm for Prediction of Ginger(Zingiber officinale) Rhizome Drying

Neuro-fuzzy modeling technique has been used for the development of computer-based adaptive process control systems for most postharvest operations instead of convectional mechanistic modeling technique owing to its good prediction without prior knowledge of process operation. Therefore, adaptive neuro-fuzzy inference system (ANFIS) modeling and prediction of ginger (Zingiber officinale) rhizome moisture content in a forced convective tray dryer was investigated in this study. Computer codes for an exhaustive search and grid partitioning were written in the Matlab software environment and used for the analysis of experimental data obtained from the ginger rhizome drying experiment. The data were trained and checked using the grid-partitioning ANFIS method for the development of neuro-fuzzy network for ginger drying prediction. The prediction accuracy of the network was evaluated by varying input and output Membership Function (MF) types. The exhaustive search analysis shows that drying time (DT) has the highest effect on the moisture content, followed by air drying temperature (ADT), air relative humidity (ARH), and air flow velocity (AFV). Moreover, combination of DT and ADT as two interactive variables; and combination DT, ADT and ARH as three interactive variables show highest effect on ginger moisture content removal during the process. Generalized bell (gbell) MF with two MF for each input variable and constant output MF 2 type were obtained as the best ginger drying ANFIS network with corresponding R and MSE of 0.9667 and 0.0971, respectively. Therefore, this study shows the reliability of the ANFIS model for the prediction of ginger rhizome drying in a tray dryer.

Proposal of a Framework for Evaluating the Importance of Production and Maintenance Integration Supported by the Use of Ordinal Linguistic Fuzzy Modeling

Over the years, the integration of Production Management and Maintenance Management has gained significant attention from the scientific community due to its benefits for the company. When searching through the states of the art and practice, it is possible to understand that one of the main challenges for the integration is the lack of systematic, methodological, and scientific approaches and evaluation systems that lead companies into a successful implementation and a clear understanding of the benefits and drawbacks of the process. This paper introduces an original framework that conducts the processes of evaluation, weighting, and aggregation of set of novel indicators proposed by the authors. The main output of the proposal is an integral index that allows us to qualify, in a linguistic domain, the importance of the Production and Maintenance Management integration. At the same time, the proposed framework includes a methodology to evaluate the consensus of the experts, based on the use of linguistic terms with a membership function of the triangular type, which attempts to overcome some deficiencies of previous models identified by the authors in a detailed and complex analysis of the scientific literature. The proposed framework is applied in a plant of the Cuban mechanical industry. The results of this application are clearly presented and discussed, allowing us to verify and validate the proposal while also contributing to its ease of understanding and ultimately to the successful integration of the production and maintenance tasks in the given company.

НЕЙРОНЕЧЕТКИЙ КЛАССИФИКАТОР ОЦЕНКИ УРОВНЯ ЗНАНИЙ ОБУЧАЮЩИХСЯ

This article is devoted to the solution of the problem of constructing a neuro-fuzzy classifier for assessing the level of students' knowledge. Currently, intelligent systems for assessing complex technical, biophysical and socio-economic systems have undergone rapid development and are often based on the use of neural networks, fuzzy logic methods and procedures for forming rule bases based on data analysis. In this work, a neuro-fuzzy classifier was used to assess the level of students' knowledge. The User Knowledge Modeling dataset for training the fuzzy neural network was obtained from the open source Machine Learning Repository. The number of copies in the dataset is 403, and the number of attributes for classification is 5. Four gradations are distinguished for the level of students' knowledge - very low, low, medium and high. This corresponds to the Russian assessment system: unsatisfactory, satisfactory, good and excellent. In the Deductor environment, a preliminary analysis of data quality, work with outliers and extreme values, checking for duplicates and contradictions, as well as correlation analysis of input and output parameters were carried out. After processing, the data were randomly divided into training and test samples in the ratio of 70% and 30%, respectively. To build a neuro-fuzzy model, the ANFIS editor from the MATLAB application package was used. The fuzzy inference system contained 5 input variables with 3 fuzzy gradations and 1 output variable. As a result of training, 128 fuzzy rules corresponding to the model structure were formed. When building a neuro-fuzzy classifier, fuzzy neural networks with various combinations of the training method, type of membership function of the input and output parameters were used. The lowest value of the root mean square error, equal to 0.16, was achieved in the model with the following parameters: training method - back propagation of the error, membership function of the input variables - double Gaussian, membership function of the output variable - constant. To assess the adequacy of the neuro-fuzzy model, errors of the first and second kind were calculated. The error of the first kind on the test data was 0%, the error of the second kind - 4.6%. The accuracy of the neuro-fuzzy model was 95.6% and was higher than when using other methods of data mining: neural network, decision tree, linear and logistic regression. Thus, the constructed neuro-fuzzy model showed high accuracy in assessing students' knowledge and can be effectively used in the educational process to solve the task.

АНАЛИЗ МОДЕЛЕЙ АДАПТИВНЫХ НЕЙРО-НЕЧЕТКИХ СИСТЕМ

The article deals with the study of basic methods for models of adaptive neuro-fuzzy systems. Based on the analysis, the strengths of neural networks and fuzzy logic were found, that became powerful tools for solving complex modeling and forecasting issues. There is studying and analyzing the adaptive neural network, which is a class of neural networks that have the ability to change their structure and parameters in the process of learning and adaptation to new data and conditions and besides the article studies the Gaussian membership function, also known as the normal membership function or the Gauss-type membership function, which is a valuable tool in the f ield of fuzzy logic and fuzzy systems. The paper provides as well an analysis of the generalized Bell membership function, also known as the Bell type membership function or Bell function, which plays an important role in the field of fuzzy logic and fuzzy systems. Furthermore it analyzes the Tsukamoto model, which is one of the main models of fuzzy logic. The author opted to choose the Co-Active Neuro-Fuzzy Inference System model, which is an adaptive neuro-fuzzy system that combines neural networks and fuzzy logic for processing data with uncertainty and fuzziness. With the further implementation of the combined model based on the abovelisted models based on the STL of the C++ language, thus the neural network model is obtained, the model with versatility, that is achieved by using a combination of those models. That will facilitate its easy modification and adaptation to various tasks.

Ultrasound assisted phytochemical extraction of red cabbage by using deep eutectic solvent: Modelling using ANFIS and optimization by genetic algorithms

The present investigation studied the effect of process parameters on the extraction of phytochemicals from red cabbage by the application of ultrasonication and temperature. The solvent selected for the study was deep eutectic solvent (DES) prepared by choline chloride and citric acid. The ultrasound assisted extraction process was modeled using adaptive neuro-fuzzy inference system (ANFIS) algorithm and integrated with the genetic algorithm for optimization purposes. The independent variables that influenced the responses (total phenolic content, antioxidant activity, total anthocyanin activity, and total flavonoid content) were ultrasonication power, temperature, molar ratio of DES, and water content of DES. Each ANFIS model was formed by the training of three Gaussian-type membership functions (MF) for each input, trained by a hybrid algorithm with 500 epochs and linear type MF for output MF. The ANFIS model predicted each response close to the experimental data which is evident by the statistical parameters (R2>0.953 and RMSE <1.165). The integrated hybrid ANFIS-GA algorithm predicted the optimized condition for the process parameters of ultrasound assisted extraction of phytochemicals from red cabbage was found to be 252.114 W for ultrasonication power, 52.715 °C of temperature, 2.0677:1 of molar ratio of DES and 25.947 % of water content in DES solvent with maximum extraction content of responses, with fitness value 3.352. The relative deviation between the experimental and ANFIS predicted values for total phenolic content, antioxidant activity, total anthocyanin activity, and total flavonoid content was found to be 1.849 %, 3.495 %, 2.801 %, and 4.661 % respectively.

Multi-Objective De Novo Programming with Type-2 Fuzzy Objective for Optimal System Design

De Novo Programming, which is also known as Optimal System Design, regulates the resource amount of constraints depending upon the budget. Mostly, this process is managed using traditional methods, fuzzy methods and hybrid methods. When considered from this point of view, there is no certain method for the solution of De Novo Programming problems. An approach for solving the Multi-Objective De Novo Programming has been recommended using Type-2 Fuzzy Sets in this research. Without exceeding the budget in the recommended approach, Type-2 membership function for each objective function has been defined applying positive and negative ideal solutions. The solution phase of this approach, called Multi-Objective De Novo Programming with Type-2 Fuzzy Objective, has been shown step by step on the illustrative problem. Then, this illustrative problem has been solved with regards to five different approaches in the literature and the results have been compared.

Modeling of Fuzzy Systems Based on the Competitive Neural Network

This paper presents a method to dynamically model Type-1 fuzzy inference systems using a Competitive Neural Network. The aim is to exploit the potential of Competitive Neural Networks and fuzzy logic systems to generate an intelligent hybrid model with the ability to group and classify any dataset. The approach uses the Competitive Neural Network to cluster the dataset and the fuzzy model to perform the classification. It is important to note that the fuzzy inference system is generated automatically from the classes and centroids obtained with the Competitive Neural Network, namely, all the parameters of the membership functions are adapted according to the values of the input data. In the approach, two fuzzy inference systems, Sugeno and Mamdani, are proposed. Additionally, variations of these models are presented using three types of membership functions, including Trapezoidal, Triangular, and Gaussian functions. The proposed models are applied to three classification datasets: Wine, Iris, and Wisconsin Breast Cancer (WDBC). The simulations and results present higher classification accuracy when implementing the Sugeno fuzzy inference system compared to the Mamdani system, and in both models (Mamdani and Sugeno), better results are obtained when the Gaussian membership function is used.

State estimation for sound environment system by using Bayesian filter based on fuzzy observation

The specific signal in a sound environment is measured in decibel scale and often contains the fuzziness due to several causes. Furthermore, there exists usually a background noise in addition to the specific signal. In this study, a Bayesian filter for estimating the specific signal, based on the observed data containing the fuzziness and the effects of a background noise with non-Gaussian type, is proposed. More specifically, the energy variables satisfying the additive property of the specific signal and background noise are first considered. Next, after introducing an expansion expression of the probability density function based on a log-normal distribution and a new type of membership function, which are suitable for the nonlinear relationship between the energy variable and the measurement in decibel scale, by applying probability measure of fuzzy events, a state estimation method is theoretically derived. The proposed theory is applied to the actual observation data in a sound environment, and its usefulness is experimentally confirmed.

An Experimental Private Small Hydropower Plant Investments Selection Classification System

Investment selection problems and models are crucial for humans, communities, and states. Private small hydroelectric power/ hydropower plant investments (PSHPPIs) selection problem is a unique one in those problems and models. Many available scientific methods can be implemented on this research topic. One methods group is type-2 Mamdani’s type fuzzy inference systems (FISs). This study presents an experimental one-node general type-2 4-zslices Mamdani’s type FIS model for PSHPPIs selection. There are 3 input variables (total estimated electricity generation: M1, total estimated cost: M2, change in the average runoff: M3), 1 output variable (O1: selected/unselected, selection classification of PSHPPIs), and 49 rules. M1 is designed in 5 triangular and trapezoidal general type-2 4-zslices fuzzy membership functions (MFs), M2 in 5 triangular and trapezoidal general type-2 4-zslices fuzzy MFs, M3 in 5 Gaussian type-2 4-zslices fuzzy MFs, and O1 in 2 Gaussian type-2 4-zslices fuzzy MFs. All modeling details are finalized by a human-expert decision process. JuzzyOnline V2.0, a browser-based platform of Juzzy (a Java-based library: Juzzy toolkit), is used for all FIS modeling and calculation activities. Five PSHPPI options assumed to be in their very early investment stages in Turkiye are evaluated in an experimental application. It is clear that an improved, tuned, and fine-tuned version of this model will help private investors to take more convenient/satisfying actions/decisions in a very short evaluation period in their PSHPPIs decision processes. An automatic investment selection classification system can be built in an appropriate development period after experiencing many methods and models. This study is one of the open-science humanoid robot, robot and platform development activities entitled Global Power Robots and Platforms: GPRP/GPRAP (Global Power Plants Developers: GP2D/G2PD/GPPD, Global Power Plants Engineers: GP2E/G2PE/ GPPE, Global Power Plants Owners: GP2O/G2PO/GPOO, Global Power Prediction Systems: GP2S/G2PS/GPPS), Global Profile Analyses Systems, and Global Social Network Analyses Systems.

On a value of a matrix game with fuzzy sets of player strategies

The present paper investigates a fuzzy matrix game with fuzzy sets of player strategies. We construct a game value with the help of Zadeh's extension principle in combination with an approach to fuzzy matrix games worked out by Liu and Kao. We prove that the FSs of players strategies in a fuzzy matrix game generate a game value in the form of a type-2 fuzzy set (T2FS) on the real line. Furthermore, the corresponding type-2 membership function is given. It is shown that the T2FS of the game value can be decomposed according to the secondary membership grades into a finite collection of fuzzy numbers. Each of them is the value of the corresponding fuzzy matrix game for crisp sets of player strategies. These sets are the corresponding cuts of the original fuzzy sets of player strategies. Illustrative examples are given.

A Review of Fuzzy Logic Method Development in Hydraulic and Pneumatic Systems

Fuzzy logic has been developed since the 1960s. Research related to fuzzy logic application in hydraulics and pneumatics is mainly aimed at energy demand reduction and improvement in operational characteristics. This article summarizes the recent achievements in hydraulic and pneumatic fuzzy logic system design. First, the main application areas have been identified, including control and fault diagnosis. The control systems were additionally grouped according to the main objects of study, such as pumps, actuators, proportional valves, etc. Then, the results of the recent research were presented, and the main features of the designed fuzzy logic units were summarized for each group. Particular attention was paid to types of membership functions used for fuzzification and defuzzification, numbers of fuzzy sets defined for input and output signals, types of fuzzy operators, the applied inference algorithm and the defuzzification method. Based on the analysis of the listed parameters, conclusions were formulated regarding advantages, main issues and difficulties, as well as recommended directions for further development.

On Nash Equilibria in a Finite Game for Fuzzy Sets of Strategies

The present paper investigates a finite game with fuzzy sets of player strategies. It is proven that Nash equilibria constitute a type-2 fuzzy set defined on the universal set of strategy profiles. Furthermore, the corresponding type-2 membership function is provided. This paper demonstrates that the Nash equilibria type-2 fuzzy set of the game can be decomposed based on the secondary membership grades into a finite collection of crisp sets. Each of these crisp sets represents the Nash equilibria set of the corresponding game with crisp sets of player strategies. A characteristic feature of the proposed decomposition approach is its independence from the chosen method for calculating the Nash equilibria in crisp subgames. Some properties of game equilibria T2FSs are studied. These sets correspond to specific partitions or cuts of the original fuzzy sets of player strategies. An illustrative example is also included for clarity.

Event-Triggered Positive Filter Design for Positive Polynomial Fuzzy Systems via Premise Integration and Membership-Function-Dependent Methods

This paper focuses on the design of the positive fuzzy filter with event-triggered mechanism for positive polynomial fuzzy-model-based (PPFMB) system. The main objective is to design a positive and stable fuzzy filter which makes the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula> performance index of the estimated output signal as good as possible with limited networked bandwidth resources. Since the positive constraints exist in the positive systems, while the disturbance signal of the output signal and the transmission delay in the event-triggered mechanism are taken into account in this research, the augmented system is rebuilt by introducing the weight coefficient of disturbance signal, and a novel linear copositive Lyapunov function (LCLF) is proposed. In order to adapt to the analysis framework based on linear Lyapunov function, a novel linear event-triggered condition is proposed. Furthermore, to handle the mismatched premise variables caused by the event-triggered mechanism, the premise variable associated with event-triggered instants are integrated into the interval of continuous premise variable with the help of the novel event-triggered condition, which means that the original multi-dimensional type-1 membership functions (MFs) are transformed into single-dimensional interval type-2 MFs. Then, an interval type-2 membership-function-dependent (IT2MFD) method is employed to introduce MFs information into the resultant conditions, so that more optimized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula> performance index is obtained. Finally, an example with simulation results is given to verify the effectiveness of all the fuzzy filter design strategies proposed in this paper for optimizing performance index.

Control of the temperature regime of the process of bacterial oxidation on the basis of fuzzy logic

The work is devoted to modeling the temperature control system for the process of bacterial oxidation of refractory gold-bearing sulfide ores. The simulation was performed using the Fuzzy Logic Toolbox editor in the MATLAB software package. The substantiation of the set of input and output variables, the type of membership functions was carried out, the base of rules for the inference engine was formed. The main stages of modeling are described and the results are analyzed. The use of trapezoidal membership functions is substantiated.

Optimization for Interval Type-2 Polynomial Fuzzy Systems: A Deep Reinforcement Learning Approach

It is known that the interval type-2 (IT2) fuzzy controllers are superior compared to their type-1 counterparts in terms of robustness, flexibility, etc. However, how to conduct the type reduction optimally with the consideration of system stability under the fuzzy-model-based (FMB) control framework is still an open problem. To address this issue, we present a new approach through the membership-function-dependent (MFD) and deep reinforcement learning (DRL) approaches. In the proposed approach, the reduction of IT2 membership functions of the fuzzy controller is completing during optimizing the control performance. Another fundamental issue is that the stability conditions must hold subject to different type-reduction methods. It is tedious and impractical to resolve the stability conditions according to different type-reduction methods, which could lead to infinite possibility. It is more practical to guarantee the holding of stability conditions during type-reduction rather than resolving the stability conditions, the MFD approach is proposed with the imperfect premise matching (IPM) concept. Thanks to the unique merit of the MFD approach, the stability conditions according to all the different embedded type-1 membership functions within the footprint of uncertainty (FOU) are guaranteed to be valid. During the control processes, the state transitions associated with properly engineered cost/reward function can be used to approximately calculate the deterministic policy gradient to optimize the acting policy and then to improve the control performance through determining the grade of IT2 membership functions of the fuzzy controller. The detailed simulation example is provided to verify the merits of the proposed approach.