Abstract—Fuzzylogic systems have been extensively applied for solving many real world application problems because they are found to be universal approximators and many methods, particularly, gradient descent (GD) methods have been widely adopted for the optimization of fuzzy membership functions. Despite its popularity, GD still suffers some drawbacks in terms of its slow learning and convergence. In this study, the use of decoupled extendedKalmanfilter (DEKF) to optimize the parameters of an intervaltype-2intuitionisticfuzzylogicsystem of Tagagi-Sugeno-Kang (IT2IFLS-TSK) fuzzy inference is proposed and results compared with IT2IFLS gradient descent learning. The resulting systems are evaluated on a real world dataset from Australia’s electricity market. The IT2IFLS-DEKF is also compared with its type-1 variant and intervaltype-2fuzzylogicsystem (IT2FLS). Analysis of results reveal performance superiority of IT2IFLS trained with DEKF (IT2IFLS-DEKF) over IT2IFLS trained with gradient descent (IT2IFLS-GD). The proposed IT2IFLS-DEKF also outperforms its type-1 variant and IT2FLS on the same learning platform.
fuzzylogic is a growing research topic with much evidence of successful applications. However, almost all developments of type-2fuzzylogic systems have been based on intervaltype-2fuzzylogic . The heavy computational load associated with the generalized form of type-2 sets is the main driver for the lack of applications of general type-2fuzzy sets compared with the interval model. This prior work has reinforced the common concept that intervaltype-2fuzzylogic systems can add more modeling capabilities than type-1 fuzzylogic systems but with extra computational cost. Learn- ing and optimization of general type-2fuzzylogic systems are open areas for more research, as well as the ongoing research on how to reduce the complexity of general type-2fuzzylogic systems, especially in the type-reduction phase of the system. The large number of methods used to design type-1 and intervaltype-2fuzzylogic systems can be seen as potential candidates for general type-2fuzzylogic systems and some of them might uncover further possibilities for modeling uncertainty. However, recent ad- vances in general type-2fuzzylogic systems research, including new representations, optimized operations and faster type-reduction methods, indicate an expected growth in applications. Despite the larger number of computations associated with general type- 2fuzzy sets, there may well be benefits compared to intervaltype-2fuzzy sets. This ability can be unveiled using automated designing methods rather than being chosen by the designer manually. Automated methods can fine-tune initial fuzzylogicsystem designs due to the lack of a rational basis for choosing secondary membership func- tions for general type-2fuzzy sets [36, p.302]. This issue enforces the need for using automated methods in such problem. The other factor affecting the usage of general type-2fuzzylogic systems is the lack of practical parameterization methods to handle the third dimension in general type-2fuzzy sets. In general, a general type-2fuzzylogicsystem has the potential to model more uncertainties despite the large amount of computations associated with it especially when applied to non real-time applications. In consequence, the question of how much general type-2fuzzylogic systems can add to modeling performance over intervaltype-2fuzzylogic systems is another issue that warrants investigation.
The IT2 FSs have been extensively used in the literature to model uncertainty (see , –). Despite literature being replete with several works revolving round IT2 FSs, they only make use of the MFs alone in uncertainty modeling with an implicit assertion that NMF is complementary to the MF (lower or upper). In a real life context, it is not necessarily the case that NMF is complementary to MF as there may exist some degree of hesitation or indeterminacy, otherwise known as intuitionisticfuzzy index (IF-index) or neutral degree. The conventional IT2 FLS cannot singularly model these IF-indices in a fuzzy set. Barrenechea et al.  pointed out that valuable information of an element can be obtained using the IF-index of IFS. The authors in  also noted that the IF-index plays a very important role in algorithm’s performance. Our study is an attempt in this direction to enhance the capabilities of IT2 FLS by incorporating IFL into IT2 FLS. As earlier discussed, with the capability of the IT2 FSs to adequately model uncertainty in their FOUs and the ability of the IFS to separately cater for MF and NMF of an element with some level of hesitation, we are motivated to integrate these two concepts (IT2 FS and IFS) to design a new TSK-typeinterval T2 intuitionisticfuzzylogicsystem (IT2 IFLS-TSK) . The new framework apart from incorporating fuzzy NMF into the conventional IT2 FS is able to deal with indeterminate (hesi- tant) states which are not well managed by alternative fuzzy approaches such as IT2 FLSs. The introduction of additional NMF and IF-indices into IT2 FS increases the fuzziness of the model. According to Hisdal , “increased fuzziness in a description means increased ability to handle inexact information in a logically correct manner.” We believe that the fusion of these two kinds of fuzzy sets is able to provide a synergistic capability in managing the effects of uncertainties in data. The proposed framework of IT2 IFLS is enhanced with a neural network learning capability similar to adaptive neuro-fuzzy inference system (ANFIS) and T2-ANFIS  for modeling uncertainty in data. The combination of these two approaches, fuzzylogic and artificial neural network (ANN), have been very popular with increasing interest in recent years. With the integration of ANN into FLS, the FLS is enhanced with the learning and generalisation capabilities of ANN.
Successful implementations of many commercial and military applications require reliable, timely, and precise information to support decisions for remote security op- erations. Developing effective security monitoring mecha- nisms to provide situation awareness has become an in- creasingly important focus. Thus, relying on raw senor data is extremely challenging primarily because security events change continuously and security space informa- tion is usually incomplete and noisy. Some dynamic se- curity monitoring systems combine a number of different techniques to data collected from distributed sensors like intrusion detection based on fusing decisions and infor- mation correlation to compute event indicators .
The GCS data is a complex dataset consisting of different operational conditions of a gas plant. The GCS data consist of 825 data points and modeled as a time series using input generating format: [y(t − 3), y(t − 2), y(t − 1)] with y(t) as the output. The inputs are normalised to lie between small range of [0,1], so that larger input values do not overshadow the smaller values, thereby leading to poor prediction and learning using the embedded neural network architecture. For each run of the experiments, the data are randomly sampled and split into 70% training and 30% testing set with each data point having equal chance of being chosen for training and testing. For a clear and objective discussion and evaluation of the three models of IT2IFLS, IT2FLS and IFLS, the Kalmanfilter parameters R, Q and P for both MFs and NMFs are initially set as 40, 0.01I 32
where I is the total number of start position, K is the number of step simulation for each start position, ω(k), and v(k) are the rotational speed and the faulty speed at k, respectively, and c is constant for health check of IM, 0 if there is no fault and 1 if there is fault. This function is minimized in order to achieve the condition than the motor run by avoiding fault, higher speed, and mostly reliable speed. After that, three operators of GA are carried out, namely recombination, crossover and mutation, with fixed crossover probability rate (Pc) and probability mutation rate (Pm), that are 0.7, and 0.7/parameter numbers, respectively. The number of new generation is adjusted by Generation Gap constant (GGAP), which is 0.9. The procedure is repeated until the termination condition is reached. It has been presented Interval Type2Fuzzy Logic Controller (IT2FLC) where the fuzzy knowledge based, i.e. membership functions and rule bases, are tuned by Genetic Algorithm (GAs), known as Genetic FuzzySystem (GIT2FS), to generate individual command action. The model is designed in order to detect faults in IM. The best fitness knowledge base is obtained by learning the RB in advance and then tuning the MF after. Besides that, the motor has improved its performance, for instance it can generate motor control for individual fault.
Atanassov  extended the concept of Zadeh’s fuzzy sets to intuitionisticfuzzy sets (IFSs), which deal with uncertainty by considering both the degrees of membership and non- membership of an element x to a fuzzy set A with some degree of hesitancy. According to Olej and Hajek , the representation of attributes by means of membership and non- membership functions provides a better way to express uncer- tainty. Castillo et al  lend credence to this when they opined that the presence of non-membership or hesitation index gives more possibility to represent imperfect knowledge and to adequately describe many real world problems. Atanassov and Gargov  extended the concept of IFS to interval valued intuitionisticfuzzy sets (IVIFS) which are characterised by membership and non-membership functions and defined in the interval [0,1]. The resulting T2 fuzzylogic systems (FLSs)
Beginning in around 1985, the goal of rotating machinery (here steam turbine) fault diagnostics was primarily to store the vibration spectra and to provide graphical tools so that the analyst could quickly access the data and determine what might be wrong with the machine. But as the data collection devices (originally spectrum analyzers) became smaller, faster, and more portable, the amount of data to be analyzed rapidly grew. The data acquisition system could soon store hundreds of spectra. As the data acquisition systems and measurement techniques improved, the analyst was faced with mountains of data. The overwhelming amount of data resulted in the new technique of data mining, which seeks to extract knowledge from huge volumes of data through numerical analysis of the data. Data mining is not only database analysis method, but also an important machine learning tool. This paper describes Fuzzy decision tree classifier using intervaltype-2fuzzylogic rule based data mining for steam turbine fault analysis of a power system rotatory machine component. Many methods have been used for data mining, with the decision tree (DT) often shown to be the most valuable form of data mining. The most important feature of Decision Tree Classifier (DTC) is their capability to break down a complex decision-making process into a collection of simpler decisions, thus providing a solution which is often easier to interpret.
The tree ring time series obtained from  contains annual measures of tree rings width measured in Argentina for the pe- riod 441-1974. The dataset is randomly split into 75% training and 25% testing. In , the evolving fuzzy optimally pruned extreme learning machine (eF-OP-ELM), was reported for analysing this time series. The dynamic evolving neuro-fuzzy inference system (DENFIS), evolving Takagi-Sugeno (eTS) model and online sequential method for fuzzy systems based on online sequential ELM (OS-fuzzy-ELM) were also reported in  for tree ring time series analysis. All computational protocols in this study are arranged as close as possible to those reported in  to ease comparison. Table II shows the average cross validation NDEI and standard deviation (Std) of the tree ring dataset for 25 trials. From Table II, IT2IFLS outperforms other fuzzy models with reduced NDEI.
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-2fuzzy sets. A type-2fuzzy 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-2fuzzy set is three dimensional and includes a footprint of uncertainty. It is the third dimension of the type-2fuzzy 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 basedfuzzy inference system (ANFIS) was used as intervaltype-2fuzzylogic controller (IT-2FL) in control strategies of the Heat Exchanger. Interval type2 fuzzylogic 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-2fuzzylogic controller combines two different control techniques which are adaptive network basedfuzzylogic inference system control and intervaltype-2fuzzylogic control, and uses their control performances together. Adaptive network basedfuzzy inference system (ANFIS) uses a hybrid learning algorithm to identify parameters of Sugeno-typefuzzy 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 basedfuzzylogic inference system controllers.
network with fuzzy adaptive resonance theory (GRNNFA) for the analysis of this first set of data. Similar to , 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  we adopt self-constructing neural fuzzy inference network (SONFIN) and support vector basedfuzzy 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 intervaltype-2fuzzy neural network (SEIT2FNN) and intervaltype-2fuzzy 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 Kalmanfilter together with GDA for parameter learning. SEIT2FNN has IT2FS in the antecedents trained with GDA with TSK intervaltype-1 sets in the consequent. Two flavors of IT2FNN-SVR are proposed in  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 . 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.
Abstract— In this paper, a new fuzzy regression model that is supported by support vector regression is presented. Type- 2fuzzy systems are able to tackle applications that have significant uncertainty. However general type-2fuzzy systems are more complex than type-1 fuzzy systems. Support vector machines are similar to fuzzy systems in that they can also model systems that are non-linear in nature. In the proposed model the consequent parameters of type-2fuzzy rules are learnt using support vector regression and the computational cost is reduced with the use of a closed-form type reduction. Support vector regression improved the generalisation perfor- mance of the fuzzy rule-basedsystem in which the fuzzy rules were a set of interpretable IF-THEN rules. The performance of the proposed model was demonstrated by conducting case studies for the non-linear system approximation and prediction of chaotic time series. The model yielded promising results and the simulation results are compared to the results published in the area.
the case of low resolution image and video content. Jun-ying zeng et. al.  propsed a model for partially occluded face recognition based on Biometric Pattern Recognition. An experiment based on biomimetic pattern recognition adopting a PCA and LDA feature extraction method was performed and results were quite satisfactory. Brian Cheung  trained a convolutional neural network to distinguish between images of human faces from computer generated avatars as part of the ICMLA 2012 Face Recognition Challenge. It can be inferred that the regions of our interest in a face can be located correctly even if the face image is of low quality. In an attempt to further improve the performance of the face recognition method we have presented an improved algorithm by designing a feature vector comprising of wavelet horizontal, vertical and diagonal coefficients, determined from the wavelet energy function capturing global features of the face and, the facial parameter capturing local features of the face. The result of this algorithm when compared with that of the PCA method is found more satisfactory.
The basis for this approach is constituted by the fundamental works on fuzzy set theory of Zadeh (1978), Dubois and Prade (1980), Zimmerman (1986) and other. The theory of fuzzy reliability was proposed and development by several authors, Cai, Wen and Zhang (1991, 1993); Cai (1996); Chen, Mon (1993); Hammer (2001); El-Hawary (2000), Onisawa, Kacprzyk (1995); Utkin, Gurov (1995). The recent collection of papers by Onisawa and Kacprzyk (1995), gave 654 I.M. ALIEV, Z. KARA many different approach for fuzzy reliability. According to Cai, Wen and Zhang (1991, 1993); Cai (1996) various form of fuzzy reliability theories, including profust reliability theory Dobois, Prade (1980); Cai, Wen and Zhang (1993); Cai (1996); Chen, Mon (1993); Hammer (2001); El-Hawary (2000); Utkin, Gurov(1995), posbist reliability theory, Cai, Wen and Zhang (1991, 1993) and posfust reliability theory, can be considered by taking new assumptions, such as the possibility assumption, or the fuzzy state assumption, in place of the probability assumption or the binary state assumption. Chen  analyzed the fuzzysystem reliability using vague set theory. The values of the membership and non-membership of an element, in a vague set, are represented by a real number in [0, 1]. Cai, Wen and Zhang (1993) presented a fuzzy set based approach to failure rate and reliability analysis, where profust failure rate is defined in the context of statistics. El-Nawary (2000) presented models for fuzzy power system reliability analysis, where the failure rate of a system is represented by a triangular fuzzy number.
Abstract. In recent years, the segmentation of images now is confronted with presence of uncertainty and noise. Because the fuzzy clustering algorithm is not very effective in noise processing and the accuracy of image segmentation is not high enough. So one hybrid clustering algorithm combined with intuitionisticfuzzy factor and local spatial information is proposed. Experimental results show that the proposed algorithm is superior to other methods in image segmentation accuracy and improves the robustness of the algorithm. In noise image segmentation, noise interference is better suppressed.
Based on the evaluation of this research, there are three input sensor that we used. Each sensor should achieve the task of moving to the destination and avoid obstacles. Thus, the robot has three tasks: avoiding obstacles, moving to the destination, as well as keeping by avoiding collisions among robots. The environment used is an environment without obstacles with different arena shapes and sizes. In an environment without obstacles, there was no disturbance effects occured. If the robot was closed that obstacles, the robot had to stay away to avoid a collision. This research used three swarm robots with its each tasks. If the robot was far from that group, then the robot would move towards one another to defend the swarm. If each robot was closed, the robot had to stay away one another to avoid a collision.
Navigation of autonomous mobile robots in dynamic and unknown environments needs to take into account different kinds of uncertainties. Type-1 fuzzylogic 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 fuzzysystem. Recently many researchers have applied type-2fuzzylogic to improve performance. As control using type-2fuzzy sets represents a new generation of fuzzy controllers in mobile robotic issue, it is interesting to present the performances that can offer type-2fuzzy sets by regards to type-1 fuzzy sets. The paper presented deep and new comparisons between the two sides of fuzzylogic and demonstrated the great interest in controlling mobile robot using type-2fuzzylogic. We deal with the design of new controllers for mobile robots using type-2fuzzylogic 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.
Quality of web service (QoWS) monitoring is an important component in web service as it evaluates web service delivery performance and detects problems. Our previous work proposed a fuzzy model for QoWS monitoring due to uncertain nature of web service environment. However, fuzzy models are computationally costly. In this work, we propose a parallelization implementation of the models. The objective of this paper is to compare the performance between Mamdani- and Sugeno-basedfuzzy inference systems (FIS) when they are applied to the QoWS monitoring models. The results suggested that Sugeno models produced less processing time than that of Mamdani models. However, Mamdani models benefited from parallelization more than that of Sugeno models by recoding higher percentage of improvement in terms of average processing time. This work will be expanded to investigate the implementation of the models in cluster computers and using a higher type of fuzzylogic, namely intervaltype-2fuzzy.
In this section we investigate the α-cuts of IVFSs. We already introduced a method for defining α-cuts of IVFSs in ,  based on earlier work done by Kaufmann and Gupta  on fuzzy arithmetic. It is also related to the aggre- gation method defined by Wu and Mendel , . Zeng et al. ,  defined a variety of α-cut RTs for IVFSs and defined the α-EP that makes possible to extend operations from crisp sets to IVFSs directly. Recently, Yager  also defined α-cuts and the α-EP for discrete IVFSs. Figueroa Garcia ,  independently introduced alpha-cuts for type- 2intervalfuzzy sets, providing an alternative approach to the Karnik-Mendel iterative method for defuzzicafion and for the purposes of formulating and solving linear programming problems. In this section we investigate these methods. We define α-cuts for IVFSs by taking the α-cut of its LMF and UMF which are themselves FSs, i.e.,
Logic Theory. Martinez et al. ,  made the same work as Astudillo but with adding GA for optimization. Leottau and Melgarejo  presented an approach for designing an IT2 FLS for a mobile robot application and described how it could be developed involving the use of T1 and T2 fuzzy sets. Junratanasiri et al.  proposed a navigation system in an uncertain environment focusing on dynamic obstacles for a mobile robot. IT2 FLS was utilized to compute the linear and angular velocities of a mobile robot.