Type-2 Membership Functions Research Articles

Load Forecasting Through Estimated Parametrized Based Fuzzy Inference System in Smart Grids

For optimal utilization of power generation resources, load forecasting plays a vital role in balancing the load flow in a power distribution network. There are several drawbacks associated with existing forecasting techniques for load flow balancing. Neural network (NN) based forecasting techniques are unable to consider the actual states of a power system, while weighted least squares state estimation (WLS) fails to counter nonlinearity in the demand profile. In this article, a hybrid approach is proposed for short term load forecasting. The hybrid technique, comprised of a WLS, NN, and adaptive neuro-fuzzy inference system (ANFIS), is termed WLANFIS. ANFIS itself is the combination of an NN and fuzzy logic. It takes a refined data set obtained through NN and WLS, which helps in determining the optimal number and types of membership functions. It also helps in determining the effective fuzzy set ranges for an individual membership function that is used by the fuzzy system. WLS provides estimated states in the real-world scenario while the NN models the nonlinearity in the demand profile and is tested on IEEE 14 and 30 bus systems as well on real-world data sets. Results show that the proposed algorithm has a higher generalization capability and provides accurate forecasting results even in the case of medium-term load forecasting. It outperforms other methodologies by achieving a mean absolute percentage error as low as 2.66%.

FUZZY INFERENCE SYSTEMS BASE ON POLYNOMIALCONSEQUENTS OF FUZZY RULES

Various fuzzy inference systems that operate on the basis of polynomial consequents of fuzzy rules. As well as inference methods for such systems, in particular, Takagi-Sugeno fuzzy inference systems, their differences from other popular fuzzy systems, such as Mamdani systems, etc., are considered. The attention is focused on the features of the functioning of such systems both in the construction of elementary fuzzy systems. The Systems for which the calculation of the general logical conclusion involves intermediate levels of logical inference with many hierarchically interconnected blocks of fuzzy rules. Fuzzy sets of type 2 are considered, the membership index of which is a fuzzy term of the first type. This allows you to take into account the secondary fuzziness of linguistic concepts in the design of intelligent systems based on fuzzy inference. Fuzzy systems of the second type based on Takagi-Sugeno systems and the iterative Karnik-Mendel algorithm are considered to obtain a logical conclusion for fuzzy systems with the interval membership functions of the second type in the antecedents of fuzzy rules. The proposed procedure for lowering the order of fuzzy rules for higher-order Takagi-Sugeno fuzzy systems is described and justified. A fuzzy inference method for higher-order fuzzy systems based on the partition of a set of input variables is proposed. It is proposed to build a separate block of fuzzy rules for each of the input subspaces in the presence of a common polynomial. Which is a higher-order consequent, that reduces the total number of fuzzy rules in blocks.

Type-2 Duality Trapezoidal Fuzzy Fractional Transportation Problem using Fuzzy Optimization Techniques

The authors focused goal programming technique for solving type-2 duality fuzzy fractional transportation problem by using interval-valued triangular intuitionistic fuzzy numbers. The proposed method solves three types of models in which variables are taken as type-2 fuzzy variables which have spring up to the fuzzy fractional transportation problem. In these models, duality is applied and a particular type of non-linear membership functions are used to resolve duality fractional transportation problem including fuzzy parameters. A numerical example for examining the performance of the proposed model is envisaged here.

PERAMALAN BEBAN LISTRIK JANGKA PENDEK MENGGUNAKAN METODE ADAPTIVE NEURO FUZZY INFERENCE SYSTEM (ANFIS) DI GARDU INDUK NUSA DUA BALI

Electric load in Nusa Dua Bali has increased from 2013-2017 by an average of 11.83%. The increase in electric load requires the electrical energy service provider to be able to adjust the electricity demand and be able to increase its reliability, The effort that can be done is to predict the electric load. Electric load forecasting can be done by various methods, ANFISo (Adaptiveo Neuroo Fuzzyo Inferenceo Systemo) is one method that is often used in forecasting electrical loads. ANFIS is able to explain the reasoning process and do data learning. The data used are the electric load, temperature, humidity and time, the data was chosen because changes in temperature and humidity affect people's habitual patterns in using air conditioners (electric load patterns). The electric load pattern is trained 100 times using ANFIS with the type of membership function is trimf, and [3 3 3 3] is the number of membership function. The indicator to determining the accuracy of the electrical load forecasting pattern results with the real electric load pattern used the MAPE (Mean Absolute Percentage Error) value, which the MAPE standard value that good is less than 10%. The test results from this study produced a MAPE value of 6.98%.

Color Filter Polishing Optimization Using ANFIS With Sliding-Level Particle Swarm Optimizer

An adaptive network-based fuzzy inference system (ANFIS) with a sliding-level particle swarm optimization (SL-PSO) is proposed for optimizing parameters of a chemical-mechanical process for polishing a color filter (CMP-CF). The SL-PSO is used not only to find the best membership function types, but also to optimize the premise and consequent parameters for ANFIS. The important process parameters for CMP-CF included the initial time, polishing time, polishing pad weight (down force), slurry chemicals, and rotation speed. The output targets were red pixels, green pixels, blue pixels, and the surface roughness. First, the performance of the SL-PSO was tested with 18 continuous global numerical optimization problems, including six unimodal functions, seven multimodal functions, and five complex rotated and shifted functions. Nonparametric Wilcoxon tests were also used in multiple-problem analysis for simultaneous comparison of various algorithms over a problem set. The computational experiments showed that the proposed SL-PSO approach outperforms PSO-based methods reported in the literature. Finally, the proposed SL-PSO method was used to optimize CMP-CF parameters. The experimental results showed that the ANFIS with SL-PSO outperforms the conventional ANFIS method and conventional back propagation neural network in terms of prediction accuracy. A practical industrial application in a CF manufacturer showed that the ANFIS with SL-PSO obtained superior results compared to the previous method and immediately enhanced production efficiency. Together, these experimental results indicate that the proposed ANFIS with SL-PSO is a reliable method for optimizing CMP-CF processes.

Soft Computing Techniques for the Prediction of Hybrid Composites

Soft computing techniques such as Artificial Neural Networks and Fuzzy logic are widely used in application of manufacturing technology. Surface roughness plays a vital role for quality of the product using machining parameters. Soft computing techniques are applied to predict the surface roughness in an economical manner. In this paper, prediction of surface roughness is evaluated using ANFIS [Adaptive Neuro-Fuzzy Inference System] methodology for the cutting parameters of end-milling process for machining the halloysite nanotubes (HNTs) with aluminium reinforced epoxy hybrid composite material. Experimental datas are used to analyse the relationship between the input parameter such as depth of cut (d), cutting speed (S), feed-rate (f) and output parameters as surface roughness. Datas are classified into training and testing with different types of membership functions. The observed results accurately predict the output which was not used in training and it is almost very close to the actual output obtained in the experimental work. Moreover it was found that gbellmf is helpful for better prediction with minimum error.

Development of an algorithm to train artificial neural networks for intelligent decision support systems

The algorithm to train artificial neural networks for intelligent decision support systems has been constructed. A distinctive feature of the proposed algorithm is that it conducts training not only for synaptic weights of an artificial neural network, but also for the type and parameters of membership function. In case of inability to ensure the assigned quality of functioning of artificial neural networks due to training of parameters of artificial neural network, the architecture of artificial neural networks is trained. The choice of the architecture, type and parameters of membership function occurs taking into consideration the computation resources of the facility and taking into consideration the type and the amount of information entering the input of an artificial neural network. In addition, when using the proposed algorithm, there is no accumulation of an error of artificial neural networks training as a result of processing the information entering the input of artificial neural networks.Development of the proposed algorithm was predetermined by the need to train artificial neural networks for intelligent decision support systems in order to process more information given the unambiguity of decisions being made. The research results revealed that the specified training algorithm provides on average 16–23 % higher the efficiency of training artificial neural networks training that is on average by 16–23 % higher and does not accumulate errors in the course of training. The specified algorithm will make it possible to conduct training of artificial neural networks; to determine effective measures to enhance the efficiency of functioning of artificial neural networks. The developed algorithm will also enable the improvement of the efficiency of functioning of artificial neural networks due to training the parameters and the architecture of artificial neural networks. The proposed algorithm reduces the use of computational resources of decision support systems. The application of the developed algorithm makes it possible to work out the measures aimed at improving the effectiveness of training artificial neural networks and to increase the efficiency of information processing

Type 1 versus type 2 fuzzy logic speed controllers for brushless dc motors

<span lang="EN-US">This work presented two fuzzy logic (FL) schemes for speed-controlled brushless DC motors. The first controller is a Type 1 FL controller (T1FLC), whereas the second controller is an interval Type 2 FL controller (IT2FLC). The two proposed controllers were compared in terms of system dynamics and performance. For a fair comparison, the same type and number of membership functions were used for both controllers. The effectiveness of the structures of the two FL controllers was verified through simulation in MATLAB/SIMULINK environment. Simulation result showed that IT2FLC exhibited better performance than T1FLC.</span>

Interval Type-2 Fuzzy Restricted Boltzmann Machine

Restricted Boltzmann machine (RBM) is an energy-based artificial neural network (ANN), applied in several applications like image processing, topic modeling, classification, regression, and pattern recognition. The fuzzy version of RBM is a new approach in this field, with parameters considered as fuzzy numbers. In this article, a fuzzy RBM is extended through interval type-2 membership functions, named the interval type-2 fuzzy RBM (IT2FRBM). The additional uncertainties in the structures of the membership functions are embedded in this model. This is formulated as a maximum likelihood problem which allows the parameters of the type-2 fuzzy numbers to be learned. The capabilities of this proposed approach as a discriminative or generative model are assessed. The robustness of this method against noise is analyzed. The results indicate that this IT2FRBM outperforms RBM and its different fuzzy versions.

Adaptive neuro-fuzzy approach to sodium chlorate cell modeling to predict cell pH for energy-efficient chlorate production

Sodium chlorate production is a highly energy-intensive electro-chemical process. The current efficiency is as low as 66.66% if the pH of the process is not controlled. Hence for energy-efficient sodium chlorate production, it is very important to predict the pH of the cell electrolyte. Though the analytical model of the chlorate cell is available, they are not suitable for pH prediction, as it requires a large number of parameters, which are not easily measurable. This study presents an adaptive neuro-fuzzy inference system model for predicting the pH of sodium chlorate cell from real plant data. This model uses fewer and easily measurable parameters for modeling such as flow rates of brine, HCl, NaOH, cell electrolyte temperature, DC load current, and pH of feed input. An analysis of the accuracy of six models with different combinations of these input parameters is conducted with different model settings for the type of membership functions, epoch number, and number of data sets. The model accuracy is evaluated and compared for six models using the statistical indicators, root mean square error (RMSE), and coefficient of determination (R2). Based on the results obtained, the ANFIS model with HCl flow rate, NaOH flow rate, cell electrolyte temperature, DC load current, and pH of feed as input parameter, is accurate in predicting pH with RMSE 0.1290 and R2 0.8816 at testing stage. The good agreement between the measured pH and estimated pH confirms that the model can be further used to design the controller.

On multi-level quadratic fractional programming problem with modified fuzzy goal programming approach

The present paper addresses an extended algorithm for the solution of multi-level quadratic fractional programming problem(ML-QFPP) based on fuzzy goal programming (FGP) approach. In this algorithm, suitable linear and nonlinear membership functions for the fuzzily described numerator and denominator of the quadratic objective functions of all levels as well as the control vectors of higher levels are respectively defined using individual optimal solutions. Then usual fuzzy goal programming approach is applied for the achievement of highest degree of each of the membership goal by minimising the negative deviational variables. The proposed algorithm is an extension of modified FGP approach for ML-QFPPs and a simple algorithm to obtain compromise optimal solution of ML-QFPPs with all major types of nonlinear membership functions. Comparative analysis over the variation in the types of membership functions is also carried out with numerical example to show suitability of different membership functions in the proposed algorithm.

Application of adaptive neuro-fuzzy inference system (ANFIS) for slope and pillar stability assessment

This study seeks to apply ANFIS model for stability assessment of surface and underground excavation. Two cases of stability assessment for highway slope and underground rib-pillar mining were performed. This paper presents more than one practical approaches in ANFIS simulation for slope and pillar stability assessment. The most important factors to achieve good performance of ANFIS in this study are types of membership function, number of membership function and number of input variable. The results show that the simulation based on those important factors can reach proper error checking. Considering error checking of the model, type and number of MF simulations can show the best result by comparing more than one simulation. Excellent performance of the 4 (four) input variables in slope case and 3 (three) input variables in pillar case provides valuable information for stability assessment using ANFIS.

Takagi-Sugeno fuzzy PID controllers: mathematical models and stability analysis with multiple fuzzy sets

This paper deals with nonlinear Takagi-Sugeno (TS) fuzzy PID controllers with multiple fuzzy sets. Two models of fuzzy PID controllers are proposed using algebraic product (AP) triangular norm, bounded sum (BS)/maximum (Max) triangular co-norm and centre of gravity (CoG) defuzzifier. The inputs are fuzzified by three or more fuzzy sets with trapezoidal/triangular type membership functions. A new rule base is proposed consisting of four rules which reduce the number of tunable parameters. The models of the fuzzy PID controllers reveal that they are (nonlinear) variable gain/structure controllers, i.e., the gains are a function of input variables and the structure of the controller changes in the input space. The variations of gain and the properties of the controllers are investigated. The bounded-input bounded-output (BIBO) stability of the closed loop system with one of the proposed models in the loop is studied. The applicability of the controllers is demonstrated with the help of two examples.

A Modified Grey Wolf Optimizer for Optimum Parameters of Multilayer Type-2 Asymmetric Fuzzy Controller

This study presents a modified algorithm of the grey wolf optimizer to solve the problem of learning rate selection in the multilayer type-2 asymmetric fuzzy controller (MT2AFC). The improvements of our modified optimizer are: the best position of the swarm is memorized, thus making the alpha wolves only update when a better position appears in the next iteration; search performance is enhanced by giving more freedom to update the grey wolf position. The proposed optimizer algorithm is then applied to optimize the suitable learning rates for the proposed controller. The multilayer type-2 asymmetric membership function is used in the fuzzy control network to enhance the learning ability and flexibility of the designed network architecture. The gradient descent method is used to adjust the parameters of the proposed MT2AFC controller online. The stability of the system is guaranteed using the Lyapunov approach. Besides, the self-evolving algorithm is used to construct the network structure autonomously. Ultimately, the numerical simulations of the chaotic synchronization systems are carried out to verify the effectiveness of our proposed method.

Sensitivity analysis applied to fuzzy inference on the value of information in the oil and gas industry

Value of information is a widely accepted methodology for evaluating the need to acquire new data in the oil and gas industry. In the conventional approach to estimating the value of information, the outcomes of a project assessment relate to the decision reached by following Boolean logic. However, human thinking is based on a more complex logic that includes the ability to process uncertainty. In value of information assessment, it is often desirable to make decisions based on multiple economic criteria which, if independently evaluated, may suggest opposite decisions. Artificial intelligence has been used successfully in several areas of knowledge, increasing and enhancing analytical capabilities. This paper aims at enriching the value of information methodology by integrating fuzzy logic into the decision-making process; this integration makes it possible to develop a human thinking assessment and coherently combine several economic criteria. To the authors’ knowledge, this is the first use of a fuzzy inference system in the specified knowledge domain. The methodology is successfully applied to a case study of an oil and gas subsurface assessment where the results of the standard and fuzzy methodologies are compared, leading to a more robust and complete evaluation. Sensitivity analysis is undertaken for several membership functions used in the case study to assess the impact that shifting, narrowing and stretching the membership relationship has on the value of information. The results of the sensitivity study show that, depending on the shifting, the membership functions lead to different decisions; additional sensitivities to the type of membership functions are investigated, including the functions’ parameters.

Games with fuzzy payment matrix

We consider a method for solving an antagonistic game with a fuzzy payment matrix based on converting fuzzy estimates of the consequences of possible strategies into an integral estimate in the form of an equivalent fuzzy set with a triangular membership function. The method does not impose restrictions on the type of membership functions for fuzzy elements of the payment.

Sensitivity analysis applied to fuzzy inference on the value of information in the oil and gas industry

This paper aims at enriching the value of information methodology by integrating fuzzy logic into the decision-making process; this integration makes it possible to develop a human thinking assessment and coherently combine several economic criteria. To the authors' knowledge, this is the first use of a fuzzy inference system in the specified domain. The methodology is successfully applied to a case study of an oil subsurface assessment where the results of the standard and fuzzy methodologies are compared, leading to a more robust and complete evaluation. Sensitivity analysis is undertaken for several membership functions used in the case study to assess the impact that shifting, narrowing and stretching the membership relationship has on the value of information. The results of the sensitivity study show that, depending on the shifting, the membership functions lead to different decisions; additional sensitivities to the type of membership functions are investigated, including the functions' parameters.

An approach for non-singleton generalized Type-2 fuzzy classifiers

In recent years, successful applications of singleton fuzzy inference systems have been made in a plethora of different kinds of problems, for example in the areas of control, digital image processing, time series prediction, fault detection and classification. However, there exists another relatively less explored approach, which is the use of non-singleton fuzzy inference systems. This approach offers an interesting way for handling uncertainty in complex problems by considering inputs with uncertainty, while the conventional Fuzzy Systems have their inputs with crisp values (singleton systems). Non-singleton systems have as inputs Type-1 membership functions, and this difference increases the complexity of the fuzzification, but provides the systems with additional non-linearities and robustness. The main limitations of using a non-singleton fuzzy inference system is that it requires an additional computational overhead and are usually more difficult to apply in some problems. Based on these limitations, we propose in this work an approach for efficiently processing non-singleton fuzzy systems. To verify the advantages of the proposed approach we consider the case of general type-2 fuzzy systems with non-singleton inputs and their application in the classification area. The main contribution of the paper is the implementation of non-singleton General Type-2 Fuzzy Inference Systems for the classification task, aiming at analyzing its potential advantage in classification problems. In the present paper we propose that the use of non-singleton inputs in Type-2 Fuzzy Classifiers can improve the classification rate and based on the realized experiments we can observe that General Type-2 Fuzzy Classifiers, but with non-singleton fuzzification, obtain better results in comparison with respect to their singleton counterparts.

On multi-level quadratic fractional programming problem with modified fuzzy goal programming approach

The present paper addresses an extended algorithm for the solution of multi-level quadratic fractional programming problem(ML-QFPP) based on fuzzy goal programming (FGP) approach. In this algorithm, suitable linear and nonlinear membership functions for the fuzzily described numerator and denominator of the quadratic objective functions of all levels as well as the control vectors of higher levels are respectively defined using individual optimal solutions. Then usual fuzzy goal programming approach is applied for the achievement of highest degree of each of the membership goal by minimising the negative deviational variables. The proposed algorithm is an extension of modified FGP approach for ML-QFPPs and a simple algorithm to obtain compromise optimal solution of ML-QFPPs with all major types of nonlinear membership functions. Comparative analysis over the variation in the types of membership functions is also carried out with numerical example to show suitability of different membership functions in the proposed algorithm.

A new approach to fuzzy control using the distending function

Here, we develop a fuzzy controller using fuzzy arithmetics and a new type of membership function. The proposed new fuzzy control technique is simple, fast and computationally efficient, compared to the classical techniques (Mamdani, Takagi Sugeno) and it can also adapt to the process dynamics. The unique features are: 1) A new class of parametric membership function called the Distending Function (DF) is introduced; 2) A general parametric operator system is used. It utilizes most of the fuzzy operator systems for evaluating the knowledge base; 3) Inference is based on fuzzy arithmetic operations; 4) This leads to a computationally efficient single-step defuzzification. With these concepts, the paradigm of fuzzy control design changes radically. Using this technique with an optimization method, an adaptive fuzzy controller is designed. This adaptive controller adjusts to the changing dynamics of the non-linear processes by tuning our new type of membership function. The effectiveness of the proposed methodology is demonstrated on two industrial processes (a water tank system and continuously stirred tank reactor system).