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An Improved Type 1 Fuzzy Logic Method for Edge Detection

An Improved Type 1 Fuzzy Logic Method for Edge Detection

Abstract — In this paper, we describe a method for edge detection in gray scale images based on the Sobel operator and fuzzy logic. The goal is to improve a standard method for edge detection in order to obtain better results. The tests were made with an efficient type-1fuzzy inference system (T1FIS) and the results shows that the edges obtained with the fuzzy logic are better and more precise than the basic edge detection method. For defuzzification process, centroid method is used. The proposed type-1 fuzzy logic edge detection method was tested with the benchmark images and synthetic images. We used the merit of pratt measure to illustrate the performance of using type-1 fuzzy logic.
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Contrasting singleton type 1 and interval type 2 non singleton type 1 fuzzy logic systems

Contrasting singleton type 1 and interval type 2 non singleton type 1 fuzzy logic systems

Abstract—Most applications of both type-1 and type-2 fuzzy logic systems are employing singleton fuzzification due to its simplicity and reduction in its computational speed. However, using singleton fuzzification assumes that the input data (i.e., measurements) are precise with no uncertainty associated with them. This paper explores the potential of combining the uncer- tainty modelling capacity of interval type-2 fuzzy sets with the simplicity of type-1 fuzzy logic systems (FLSs) by using interval type-2 fuzzy sets solely as part of the non-singleton input fuzzifier. This paper builds on previous work and uses the methodological design of the footprint of uncertainty (FOU) of interval type-2 fuzzy sets for given levels of uncertainty. We provide a detailed investigation into the ability of both types of fuzzy sets (type- 1 and interval type-2) to capture and model different levels of uncertainty/noise through varying the size of the FOU of the underlying input fuzzy sets from type-1 fuzzy sets to very “wide” interval type-2 fuzzy sets as part of type-1 non-singleton FLSs using interval type-2 input fuzzy sets. By applying the study in the context of chaotic time-series prediction, we show how, as uncertainty/noise increases, interval type-2 input fuzzy sets with FOUs of increasing size become more and more viable.
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Interval Type 2 Fuzzy Logic Control of Mobile Robots

Interval Type 2 Fuzzy Logic Control of Mobile Robots

Navigation of autonomous mobile robots in dynamic and unknown environments needs to take into account different kinds of uncertainties. Type-1 fuzzy logic research has been largely used in the control of mobile robots. However, type-1 fuzzy control presents limitations in handling those uncertainties as it uses precise fuzzy sets. Indeed type-1 fuzzy sets cannot deal with linguistic and numerical uncertainties associated with either the mechanical aspect of robots, or with dynamic changing environment or with knowledge used in the phase of conception of a fuzzy system. Recently many researchers have applied type-2 fuzzy logic to improve performance. As control using type-2 fuzzy sets represents a new generation of fuzzy controllers in mobile robotic issue, it is interesting to present the performances that can offer type-2 fuzzy sets by regards to type-1 fuzzy sets. The paper presented deep and new comparisons between the two sides of fuzzy logic and demonstrated the great interest in controlling mobile robot using type-2 fuzzy logic. We deal with the design of new controllers for mobile robots using type-2 fuzzy logic in the navigation process in unknown and dy- namic environments. The dynamicity of the environment is depicted by the presence of other dynamic robots. The per- formances of the proposed controllers are represented by both simulations and experimental results, and discussed over graphical paths and numerical analysis.
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Type 2 fuzzy elliptic membership functions for modeling uncertainty

Type 2 fuzzy elliptic membership functions for modeling uncertainty

Fuzzy logic has had a significant impact on identification and control prob- lems since it was firstly proposed by Zadeh in 1965 [1]. Fuzzy logic owes its exceptional scientific reputation to its unique ability to simultaneously deal with uncertainties in the system and use the expert knowledge as an input to the fuzzy system design. As an extension of type-1 fuzzy logic systems (T1FLSs), their type-2 counterparts – type-2 fuzzy logic systems (T2FLSs) – have also made an impact on dealing with uncertainties over the last two decades. The concept of type-2 fuzzy sets first appeared in 1975 [2]. Unfortunately, researchers had to wait for a while the theory to be developed more by Mendel and Karnik [3]. The progress of T2FLSs was primarily impeded by algorithmic and hardware limi- tations. Whereas the former refers to the procedure of starting from the type-2 fuzzy set and ending up with a crisp number which is called a sequence of two operations: type reduction and defuzzification, the latter refers to the relatively low computational power of processors. In particular, type reduction is challenging, because no closed form formulation exists for type-reduction as the only option is to use iterative algorithms such as Karnik-Mendel algorithm. These limitations delayed the real-time implementations of T2FLSs until the 1990s. Luckily, these limitations have diminished over the time due to several simplified algorithms which make the type reduction operation easier and relatively simpler, especially those who do not need iterative algorithms.
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Edge Detection Through Integrated Morphological Gradient and Type 2 Fuzzy Systems

Edge Detection Through Integrated Morphological Gradient and Type 2 Fuzzy Systems

The simulation results of the edge detectors implemented in MATLABR2010a software [20] are shown. This simulation is done on the test image lena and two synthetic images, square and polar shown in figure 11[21] ,created in MATLABR2010a. The results of Morphological gradient, Integrated Type 1 fuzzy logic system and Integrated interval T2FS and integrated generalized T2FS are shown in fig 7, 8, 9, 10 respectively..

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Application of Type-1 and Type-2 Fuzzy Logic Controller for The Real  Swarm Robot

Application of Type-1 and Type-2 Fuzzy Logic Controller for The Real Swarm Robot

This paper aimed to compare type-1 and type-2 fuzzy logic performance in controlling swarm robot as tools for complex problem modeling, especially for path navigation. Each has its advantages and disadvantages with some type of fuzzy logic system. In general, the Type 2 Fuzzy Logic System (T2FLS) has better performance rather than the Type-1 Fuzzy Logic System (T1FLS). T1FLS is much faster than others, particularly when considering Real Time apps and easier to design when compared to T2FLS, but has no resistance to interference, and does not support some degree of uncertainty. At T2FLS though it is more complex computation than T1FLS but effective in handling uncertainty. In resolving the problem of uncertainty, Type-2 Fuzzy Logic System (T2FLS) has been used in modeling uncertainties in solving complex problems as well as improving accuracy.
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Online Full Text

Online Full Text

T2FLSs are more complex than type-1 ones. The major difference being the present of type-2 is their antecedent and consequent sets. T2FLSs result in better performance than type-1 fuzzy logic systems (T1FLSs) on the applications of function approximation, modeling, and control. Besides, neural networks have found numerous practical applications, especially in the areas of prediction, classification, and control [18, 23]. The main aspect of neural networks lies in the connection weights which are obtained by training process. Based on the advantages of T2FLSs and neural networks, the type-2 fuzzy neural network (T2FNN) systems
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Type 2 Fuzzy Logic Controllers Based Genetic Algorithm for the Position Control of DC Motor

Type 2 Fuzzy Logic Controllers Based Genetic Algorithm for the Position Control of DC Motor

Genetic operators such as crossover and mutation are ap- plied to the parents in order to produce a new generation of candidate solutions. As a result of this evolutionary cycle of selection, crossover and mutation, more and more suitable solutions to the optimization problem emerge with- in the population. Increasingly, GA is used to facilitate FLSs design [9]. However, most of the works discuss type-1 FLC design. This paper focuses on genetic algo- rithm of type-2 FLCs. There are two very different ap- proaches for selecting the parameters of a type-2 FLS [4]. Type-2 FLCs designed via the partially dependent ap- proach are able to outperform the corresponding type-1 FLCs [9], The type-2 FLC has a larger number of de- grees of freedom because the fuzzy set is more complex. The additional mathematical dimension provided by the type-2 fuzzy set enables a type-2 FLS to produce more complex input-output map without the need to increase the resolution. To address this issue, a comparative study involving type-2 and type-1 FLCs with similar number of degrees of freedom is performed. The totally independent approach is adopted so that the type-2 FLC evolved using GA has maximum design flexibility.
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Hybrid learning for interval type 2 intuitionistic fuzzy logic systems as applied to identification and prediction problems

Hybrid learning for interval type 2 intuitionistic fuzzy logic systems as applied to identification and prediction problems

The EKF has been used to learn the parameters of some traditional fuzzy logic systems [44], [45] and intuitionistic fuzzy systems of type-1 [46], [47]. However, because of the high dimensionality of the fuzzy system parameters, using the standard EKF can be more complicated [44], [48] especially for larger problem domains. In order to alleviate this computa- tional burden, the EKF is used in a decoupled form - DEKF - because it is faster and easier to implement [48] with the most useful properties of the EKF still preserved [49]. The DEKF algorithm has been used previously in [44] to train a T2 FLS where the parameters of both the antecedent and consequent parts of the T2 FLS were gathered into two separate vectors (antecedent and consequent parameter vectors). Similar to [38], we adopt a hybrid learning methodology (KF-based and GD) to adjust the antecedent and consequent parameters of the proposed model. While GD is also adopted for the update of the antecedent parameters, our model utilises the DEKF approach, different from [38], to adjust the consequent parameters of the new and extended framework of IT2 FLS, otherwise known as IT2 IFLS [34] for the first time in this study with the aim of achieving improved system performance in terms of error minimisation and faster convergence. To the best knowledge of the authors, there is previously no work in the literature where DEKF and GD is used for the optimisation of IT2 IFLS-TSK parameters.
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Interval type 2 A intuitionistic fuzzy logic for regression problems

Interval type 2 A intuitionistic fuzzy logic for regression problems

network with fuzzy adaptive resonance theory (GRNNFA) for the analysis of this first set of data. Similar to [65], we also study the performance of IT2AIFLS when the output of the nonlinear Friedman equation is noise free. In this second case, 1000 test samples are generated with ˆ n = 0 (this we refer to test dataset 2). Similar to [65] we adopt self-constructing neural fuzzy inference network (SONFIN) and support vector based fuzzy model (SVR-FM) for type-1 comparison with our model. The parameters of SONFIN are learned using training-error minimisation through the com- bination of Kalman filtering and GDA. For type-2 systems, we adopt type-2 models such as type-2 FLS, self-evolving interval type-2 fuzzy neural network (SEIT2FNN) and interval type-2 fuzzy neural network with support vector regression (IT2FNN-SVR). T2FLS employs GDA for parameter learning referred to as T2FLS-G. SEIT2FNN is designed with structure learning and utilises rule-ordered Kalman filter together with GDA for parameter learning. SEIT2FNN has IT2FS in the antecedents trained with GDA with TSK interval type-1 sets in the consequent. Two flavors of IT2FNN-SVR are proposed in [65] namely IT2FNN-SVR(N) and IT2FNN-SVR(F). The difference between the two is in the representation of the input nodes. The former consists of input nodes with numerical values with interval output nodes while the latter consists of input nodes with fuzzy numbers and interval output nodes. SONFIN and SEIT2FNN are previous studies involving the first author in [65]. We compare our results with these models already reported in the literature as shown in Table III. The results in Table III indicate the RMSE and standard deviation for AIFLS, IT2AIFLS and similar works in the literature. It is shown that IT2AIFLS exhibits lower RMSE compared to its type-1 counterpart, the non-fuzzy, the two T1FLSs and the T2FLSs. For 30 Monte-Carlo realisations, the average RMSE and standard deviation for IT2AIFLS on Friedman#2 with additive noise are 1.5057 and 0.1022 respectively.
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A Study on Performance of Fuzzy Logic Type 2 PSS

A Study on Performance of Fuzzy Logic Type 2 PSS

Step (4): The interface mechanism of the FLC is represented by a 7  7 decision table. The set of decision rules relating all possible combinations of input to outputs is based on previous experience in the field. This set is made up of 49 rules expressed using the same linguistic variables as those of the inputs and is stored in the form of a decision table shown in Table 1.

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Type-2 fuzzy logic control in computer games

Type-2 fuzzy logic control in computer games

part of Table 4. The system responses for Scenario 5 and 7 are illustrated in Fig.10c and Fig.10d, respectively. It can clearly observe that the T2 fuzzy moon landing system was able to pilot the spaceship to the dock without a crash for all testing scenarios while T1 and conventional PD controller structures crashed the spaceship in three of them. The PD structure was not able to handle the uncertainty and thus, in the first three testing scenarios, the crash occurred for several reasons. Scenario 5 was failed because the 4 condition of the successful landing (presented in Section 4.1) was violated. PD structure has also violated 1 condition at Scenario 6 and 7. The T1 fuzzy structure crashed the spaceship in Scenario Numbers 6 and 7 since it hit/touched the terrain (1 condition). The last crash (Scenario 8) of the T1-FLC structure occurred due to the fact the required angle condition (5 condition) for a successful landing could not be satisfied as it resulted with oscillating system response. The handled scenarios clearly show that the proposed T2 fuzzy moon landing system can handle uncertainties and various operating points when compared to its T1 and conventional PD controller counterparts.
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Time series forecasting with interval type 2 intuitionistic fuzzy logic systems

Time series forecasting with interval type 2 intuitionistic fuzzy logic systems

T IME series forecasting is an important application area that has been extensively researched. It involves the sequential collection of observations over time with the purpose of developing a model that captures the underlying dependencies among attributes of the data. A wide range of approaches have been employed in the analysis of time series data. More recently, the use of soft computing methodologies such as fuzzy logic (type-1 and type-2), neural networks, simulated annealing and genetic algorithms have been reported in the literature for time series forecasting [1]–[4]. These latter approaches have shown significant improvements over the traditional statistical methods because they are non-linear and are able to approximate any complex dynamical systems better than linear statistical models [5].
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A Study on Performance of Fuzzy Logic Type 2 PSS and Fuzzy type 2 Model Reference Learning PSS

A Study on Performance of Fuzzy Logic Type 2 PSS and Fuzzy type 2 Model Reference Learning PSS

ABSTRACT: A low power programmable frequency divider is proposed in this paper which is appropriate for WLAN applications. Multi- modulus architecture in dynamic logic with the minimum number of transistors is designed in 0.18µm CMOS technology. By using mixer, bandpass filter and switches, the divide ratios improved to 18. A technique is implemented in the dynamic 2-3 programmable divider cell for decreasing the glitches which leads to low power consumption. Based on simulation results it works up to 5GHz, with the average power about 37nW. Under a supply voltage of 1.8V, the total chip area of the multi- modulus programmable divider is 3100µm 2 .
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Power System Transient Stability Analysis Based On Interval Type-2 Fuzzy Logic Controller And Genetic Algorithms

Power System Transient Stability Analysis Based On Interval Type-2 Fuzzy Logic Controller And Genetic Algorithms

Recent work had proposed the use of neural based systems to learn the type-2 FLC parameters. However, these approaches require existing data to optimize the type-2 FLC. Thus, they are not suitable for applications where there is no or not sufficient data available to represent the various situations faced by the IT2FLC controller. Genetic Algorithms (GAs) do not require a priori knowledge such as a model or data but perform a search through the solution space based on natural selection, using a specified fitness function. We did not evolve the interval type-2 FLC rule base as it will remain the same as the interval type-1 FLC rule base. However, the FLC antecedents and consequents will be represented by interval type-2 MFs rather than type-1 MFs.
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Development Of Control System For Solar Plant Using Genetic Fuzzy PID Techniques

Development Of Control System For Solar Plant Using Genetic Fuzzy PID Techniques

Conventional PID controllers have been well developed and applied for about half a century [1], and are extensively used for industrial automation and process control today. The main reason is due to their simplicity of operation, ease of design, in expensive maintenance, low cost, and effectiveness for most linear systems. Recently, motivated by the rapidly dev eloped advanced micro-electronics and digital processors, conventional PID controllers have gone through a technological evolution, from pneumatic controllers via analog electronics to micro-processors via digital circuits [1, 5]. However, it has been known that conventional PID controllers generally do not work well for nonlinear systems, higher-order and time-delayed linear systems, and particularly complex and vague systems that have no precise mathematical models. To overcome these difficulties, various types of modified conventional PID controllers sue h as auto-tuning and adaptive controllers were developed lately [5]. Also, a class of non-conventional type of PID controllers employing fuzzy logic have been designed and simulated for this purpose [4, 5, and 12]. Stability of these fuzzy PID controllers are analyzed and guaranteed [4, 5, and 12]. Many simulation examples have been given to show the superior performance of this class of fuzzy PID controllers. Yet, despite the significant improvement of the fuzzy PID controllers over their classical counterparts, the constant control gains of these controllers are tuned manually; so generally do not achieve their best performance due to the lack of optimization.
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Efficient Hybrid Control of Shell and Tube Heat Exchanger Using Interval Type-2 and Adaptive Neuro Fuzzy Based Fuzzy Inference System

Efficient Hybrid Control of Shell and Tube Heat Exchanger Using Interval Type-2 and Adaptive Neuro Fuzzy Based Fuzzy Inference System

The use of a large number of rules in a fuzzy logic controller makes the control system more accurate and precise, providing a high performance, but increases the computational load of the processor. The reduction of the rule number of adaptive interval type-2 fuzzy controllers is possible through the ANFIS optimization technique that uses as inputs a type-1 fuzzy controller with a large number of rules and the error and the integral of the error. In the proposed optimization method, the inputs and the outputs of a type-1 fuzzy controller with a 49 rule base constitute the training data for the adaptive network-based fuzzy inference system (ANFIS). The training paradigm uses a gradient descent and a least squares algorithm to optimize the antecedent and the consequent parameters respectively. This allows obtaining a new fuzzy system with a rule base made up of only three rules Fig. 4(a) but with the same high control performance of the original fuzzy controller. The optimized type-1 fuzzy system, with first order Sugeno inference, represents the new type-1 fuzzy controller and takes the place of the previous type-1 fuzzy controller with 49 rules.
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Extended Kalman filter based learning of interval type 2 intuitionistic fuzzy logic system

Extended Kalman filter based learning of interval type 2 intuitionistic fuzzy logic system

The proposed EKF-based learning IT2IFLS model is evalu- ated using a real world datasets from the Australia’s National Electricity Market (NEM) namely New South Wales (NSW) electricity market. Similar to [29], the NSW electricity market for the year 2008 is used for the analysis. The dataset was downloaded from [30] and consists of 17568 instances with attributes of regional reference price (RRP) as the input. The price data are treated as time series data and are partitioned into four separate datasets according to [29] as representatives of the four seasons in Australia. The input data for analysis is generated from four previous values [x(t − 4), x(t − 3), x(t − 2), x(t − 1)] with x(t + 1) as the output. There are a total of 336 data samples for each season which reduces to 331 after input generation. The first 231 data points are used for training while the remaining 100 data samples are used for testing in each season. There are 16 rules generated with a total of 6(4) + 2*16(4+1) = 184 parameters.
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Interval Type-2 Fuzzy Logic And Ga Techniques: A Review

Interval Type-2 Fuzzy Logic And Ga Techniques: A Review

As previously stated, GIT2FS is basically a fuzzy system augmented by a learning process based on a genetic algorithm (GA). In GIT2FS, GAs operates to search an appropriate Knowledge Base (KB) of a fuzzy system for a particular problem and to make sure those parameter values that are optimal with respect to the design criteria. The KB parameters constitute the optimization space, which is transformed into suitable genetic representation on which the search process operates. The KB is composed by interval type-2 membership functions (IT2MF), shortly (MF), and fuzzy rule base (RB), as mentioned before. So, there are some options to design Genetic IT2 Fuzzy System, e.g. tuning or learning membership functions, or fuzzy rule base or both of them, sequentially or concurrently. When tuning membership functions, an individual population represents parameters of the membership function shapes at which fuzzy rule base is predefined in advance. In contrast, if be desired to tune fuzzy rules base, the population represents all of fuzzy rules possibility that membership functions is assumed before. Fig.1 shows these conceptions.
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Intelligent Optimal Control of a Heat Exchanger Using ANFIS and Interval Type-2 Based Fuzzy Inference System

Intelligent Optimal Control of a Heat Exchanger Using ANFIS and Interval Type-2 Based Fuzzy Inference System

otherwise; the type-1 FLC performance might deteriorate (Mendel, 2001). As a consequence, research has started to focus on the possibilities of higher order FLCs, such as type-2 FLCs that use type-2 fuzzy sets. A type-2 fuzzy set is characterized by a fuzzy MF, that is, the membership value (or membership grade) for each element of this set is a fuzzy set in [0, 1], unlike a type-1 fuzzy set where the membership grade is a crisp number in [0,1] (Hagras, 2004). The MF of a type-2 fuzzy set is three dimensional and includes a footprint of uncertainty. It is the third dimension of the type-2 fuzzy sets and the footprint of uncertainty that provide additional degrees of freedom making it possible to better model and handle uncertainties as compared to type-1 fuzzy sets. In this paper, adaptive network based fuzzy inference system (ANFIS) was used as interval type-2 fuzzy logic controller (IT-2FL) in control strategies of the Heat Exchanger. Interval type2 fuzzy logic control was not taken into consideration by this approach in most of the cited investigations, despite some of its advantages indicated in this study. Proposed type-2 fuzzy logic controller combines two different control techniques which are adaptive network based fuzzy logic inference system control and interval type-2 fuzzy logic control, and uses their control performances together. Adaptive network based fuzzy inference system (ANFIS) uses a hybrid learning algorithm to identify parameters of Sugeno-type fuzzy inference systems. A combination of the least squares method and the back propagation gradient descent method is used in training interval type2 fuzzy inference system (IT2FIS) membership function parameters to emulate a given training data set. Moreover MATLAB/Sim-Mechanics toolbox and computer aided design program (Solid Works) was used together for visual simulations.. Also MATLAB/ANFIS toolbox was used to create adaptive network based fuzzy logic inference system controllers.
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