Impedance control is an effective method in controlling the rehabilitation robots. The therapeutic exercises are performed well with satisfactory performances. The previous impedance control approaches were developed based on the torque control strategy whereas the proposed impedance control is based on the voltage control strategy. The proposed approach is free of manipulator dynamics, thus is simpler, less computational, and more effective compared with the torque based control approaches. Additionally, since it is difficult to be sure about the ideal value of the impedance parameters, **interval** **type**-**2** **fuzzy** **logic** **systems** are used to regulate impedance parameters. The proposed technique for applying the adaptive impedance parameters is shown to be more efficient than using the constant impedance parameters. The control approach has been verified by stability analysis. The simulation results show the superiority of the proposed control approach over a constant impedance control scheme.

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of **type**-1 **fuzzy** **logic** inappropriate in many cases especially with problems related to inefficiency of performance in **fuzzy** **logic** control [21]. Problems related to model- ing uncertainty using membership functions of **type**-1 **fuzzy** sets have been recognized early and [50] introduced higher types of **fuzzy** sets called **type**-n **fuzzy** sets including **type**-**2** **fuzzy** sets [37]. **Type**-**2** **fuzzy** **logic** **systems** have many advantages compared with **type**-1 **fuzzy** **logic** **systems**, including the ability to handle different types of uncer- tainties and the ability to model problems with fewer rules [21]. Two factors should be considered regarding the the widespread perception that a general **type**-**2** **fuzzy** **logic** system should outperform the **interval** form which also should outperform a **type**-1 **fuzzy** **logic** system [46]. These two factors are the dependence of performance on the choice of the model parameters as well as on the variability of uncertainty within the application [46]. Therefore, a good choice of the model’s parameters using automated methods is desirable to get clearer conclusions regarding this comparison. Despite these promising indicators of the general **type**-**2** **fuzzy** **logic** **systems**, almost all devel- opments of **type**-**2** **fuzzy** **logic** **systems** have been based on **interval** **type**-**2** **fuzzy** **logic** **systems**. However, new representations allow us to consider general **type**-**2** **fuzzy** **logic** **systems**. These representations include geometric T2FLS [15], alpha-planes [41], al- pha cuts [22] and Z-slices [45, 10][47]. There have been a number of developments in reducing the computations for general **type**-**2** **fuzzy** **logic** **systems**. For **type**-reduction, the geometric defuzzifier [15], the sampling defuzzifier [19] followed by importance sampling defuzzifier [31] and a centroid defuzzifier based on the alpha representation [32] have been proposed. One attempt to design general **type**-**2** sets based on zSlices representation was proposed in [10] where survey data and device characteristics were used to build zSlices automatically

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Abstract This paper presents the application of **Interval** **Type**-**2** **fuzzy** **logic** **systems** (**Interval** **Type**-**2** FLS) in short term load forecasting (STLF) on special days, study case in Bali Indonesia. **Type**-**2** FLS is characterized by a concept called footprint of uncertainty (FOU) that provides the extra mathematical dimension that equips **Type**-**2** FLS with the potential to outperform their **Type**-1 counterparts. While a **Type**-**2** FLS has the capability to model more complex relationships, the out- put of a **Type**-**2** **fuzzy** inference engine needs to be **type**-reduced. **Type** reduction is used by applying the Karnik-Mendel (KM) iterative algorithm. This **type** reduction maps the output of **Type**-**2** FSs into **Type**-1 FSs then the defuzzification with centroid method converts that **Type**-1 reduced FSs into a number. The proposed method was tested with the actual load data of special days using 4 days peak load before special days and at the time of special day for the year 2002-2006. There are 20 items of special days in Bali that are used to be forecasted in the year 2005 and 2006 respectively. The test results showed an accurate forecasting with the mean average percentage error of 1.0335% and 1.5683% in the year 2005 and 2006 res- pectively.

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Liang and Mendel [5] introduced the theory and design procedures of **Interval** **Type**-**2** **Fuzzy** **Logic** **Systems** (IT2 FLS). The IT2 FLS has always been considered to be a special case of a general T2 FLS; consequently, things that were developed for the latter were then specialized to the former. Research works about developing IT2 FLS were presented since Mendel et al. [6] have proposed a simple way to implement an IT2 FLS from T1 FLS mathematics. The use of IT2 FLS began to increase since then. Some papers [7] – [9] investigated the importance of IT2 FLS theoretically and practically, especially in intelligent control **systems**.

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Atanassov [3] introduced the concept of intuitionistic FS (IFS) with MF and NMF separately defined such that none is complementary to the other. In the literature, IFSs have been found to be one of the useful tools for dealing with imprecise information [4]. The reader is referred to [5] for more details on IFS. Similar to classical **type**-1 FSs, the MFs and NMFs of IFSs may not handle the plethora of uncertainty that fraught many applications. The T2FS introduced by Zadeh is a three dimensional structure which provides the extra degrees of freedom needed to handle higher forms of uncertainty. For the generalised T2FS, the third dimension is weighted differently which makes it complex and difficult to use [6, 7]. The simpler and manageable version - **interval** **type**-**2** FS (IT2FS) - have values in the third dimension equal to 1 and this makes it easier for IT2FS to be represented on a two dimensional plane. The IFSs and IT2FSs have been widely and extensively adopted by researchers in uncertainty modeling in many applications. For example, in Nguyen et al. [8], IT2 **fuzzy** C-mean (FCM) cluster- ing using IFS is proposed. The authors show that the use of IFS with IT2FCM led to improved clustering quality particularly in the presence of noise. In Naim and Hagras [9, 10] and Naim et al. [11], IFS and IT2FS are combined to develop a multi-criteria group decision making (MCGDM) system for the assessment of post-graduate study, selection of appropriate lighting level in intelligent environ- ment and evaluation of different techniques for the choice of illumination in a shared environments respectively. The authors pointed out that the use of IFS and IT2FS in a MCGDM system provided decisions that are closer to the group decisions compared to some existing methods. However, in [9, 10, 11], only the IT2FS MFs are utilised and the intuitionistic **fuzzy** (IF) indices are evaluated on the primary MFs of the IT2FSs and no learning whatsoever is carried out on these sets.

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Abstract—**Fuzzy** **logic** **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 extended Kalman filter (DEKF) to optimize the parameters of an **interval** **type**-**2** intuitionistic **fuzzy** **logic** system 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 **interval** **type**-**2** **fuzzy** **logic** system (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.

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Abstract—This paper presents an approach to prediction based on a new **interval** **type**-**2** intuitionistic **fuzzy** **logic** system (IT2IFLS) of Takagi-Sugeno-Kang (TSK) **fuzzy** inference. The gradient descent algorithm (GDA) is used to adapt the parame- ters of the IT2IFLS. The empirical comparison is made on the designed system using two synthetic datasets. Analysis of our results reveal that the presence of additional degrees of freedom in terms of non-membership functions and hesitation indexes in IT2IFLS tend to reduce the root mean square error (RMSE) of the system compared to a **type**-1 **fuzzy** **logic** approach and some **interval** **type**-**2** **fuzzy** **systems**.

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In a GPU each SGC trip implies in at least two hours of shutdown until the SGC system can be restarted, which represents a cost of thousands of dollars for the company. This work shows the potentiality, simplicity and viability of a **fuzzy** inference system using only **interval** **type**-**2** **fuzzy** sets to instrument fault detection and diagnosis. The IFDD system developed can be applicable and useful for a variety of real-world **systems**.

Sahraoui (2009) presented work on **Fuzzy** **Logic** Approach for the Diagnosis of Rotor Faults in Squirrel Cage Induction Motors. Motor Current Signature Analysis (MCSA) was used. The strategy rests on the follow-up (in amplitude and frequency) of the harmonics representing the defects of the broken bars, preparing and thus generating the adequate inputs for the treatment where the decision is made by **fuzzy** **logic**. Z. Ye, A. Sadeghian, B. Wu (2006) presented Mechanical fault diagnostics for induction motor with variable speed drives using adaptative neuro-**fuzzy** inference system. Takagi & Sugeno (1985) studied on the **fuzzy** identification of **systems** and its application to modeling and control of engineering **systems**. Jamshidi (1997) contributed on his work for **fuzzy** control of complex **systems** in soft computing methods. Mamdani E.H. (1974, 76) contributed his work on application of **fuzzy** algorithm for simple dynamic plant and advances in linguistic synthesis of **fuzzy** controllers. Tong R.M. (1978) reported on synthesis of **fuzzy** models for industrial process. R. Alcal´a, J. Alcal´a-Fdez, and F. Herrera (2007) introduced a proposal for the genetic lateral tuning of linguistic **fuzzy** **systems** and its interaction with rule selection. An innovative study on fault diagnosis of Induction Motor using hybrid FFT and soft computing techniques is proposed in this research work. In the proposed methodology a genetically tuned **type**-**2** FFT **fuzzy** system and also ANFIS is to be developed. Before using the raw data available from the industrial and commercial sources, it will be normalized for mapping in 0,1 range. This section presented the literature review on different **fuzzy** techniques, various fault diagnosis of induction motor, fast Fourier transform implementation and **fuzzy** **logic**. Review covered variety of topic, methods, techniques and approaches

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Abstract— Organizations rely on security experts to improve the security of their **systems**. These professionals use background knowledge and experience to align known threats and vulnerabilities before selecting mitigation options. The substantial depth of expertise in any one area (e.g., databases, networks, operating **systems**) precludes the possibility that an expert would have complete knowledge about all threats and vulnerabilities. To begin addressing this problem of fragmented knowledge, we investigate the challenge of developing a security requirements rule base that mimics multi-human expert reasoning to enable new decision-support **systems**. In this paper, we show how to collect relevant information from cyber security experts to enable the generation of: (1) **interval** **type**-**2** **fuzzy** sets that capture intra- and inter-expert uncertainty around vulnerability levels; and (**2**) **fuzzy** **logic** rules driving the decision-making process within the requirements analysis. The proposed method relies on comparative ratings of security requirements in the context of concrete vignettes, providing a novel, interdisciplinary approach to knowledge generation for **fuzzy** **logic** **systems**. The paper presents an initial evaluation of the proposed approach through 52 scenarios with 13 experts to compare their assessments to those of the **fuzzy** **logic** decision support system. The results show that the system provides reliable assessments to the security analysts, in particular, generating more conservative assessments in 19% of the test scenarios compared to the experts’ ratings.

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Abstract—Robotics control system with leader-follower approach has a weakness in the case of formation failure if the leader robot fails. To overcome such problem, this paper proposes the formation control using **Interval** **Type**-**2**- **Fuzzy** **Logic** controller (IT2FLC). To validate the performance of the controller, simulations were performed with various environmental **systems** such as open spaces, complexes, circles and ovals with several parameters. The performance of IT2FLC will be compared with **Type**-1 **Fuzzy** **Logic** (T1FL) and Proportional Integral and Derivative (PID) controller. As the results found using IT2FLC has advantages in environmental uncertainty, sensor imprecision and inaccurate ac- tuator. Moreover, IT2FLC produce good performance compared to T1FLC and PID controller in the above environments, in terms of small data generated in the **fuzzy** process, the rapid response of the leader robot to avoid collisions and stable movements of the follower robot to follow the leader's posture to reach the target without a crash. Especially in some situations when a leader robot crashes or stops due to hardware failure, the follower robot still continue move to the target without a collision.

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Summary. In this chapter, we will present the novel applications of the **Interval** **Type**-**2** (IT2) **Fuzzy** **Logic** Controllers (FLCs) into the research area of computer games. In this context, we will handle two popular computer games called Flappy Bird and Lunar Lander. From a control engineering point of view, the game Flappy Bird can be seen as a classical obstacle avoidance while Lunar Lander as a position control problem. Both games inherent high level of uncertainties and randomness which are the main challenges of the game for a player. Thus, these two games can be seen as challenging testbeds for benchmarking IT2-FLCs as they provide dynamic and competitive elements that are similar to real- world control engineering problems. As the game player can be considered as the main controller in a feedback loop, we will construct an intelligent control **systems** composed of three main subsystems: reference generator, the main controller, and game dynamics. In this chapter, we will design and then employ an IT2-FLC as the main controller in a feedback loop such that to have a satisfactory game performance while be able to handle the various uncertainties of the games. In this context, we will briefly present the general structure and the design methods of two IT2-FLCs which are the Single Input and the Double Input IT2-FLCs. We will show that an IT2 **fuzzy** control structure is capable to handle the uncertainties caused by the nature of the games by presenting both simulations and real-time game results in comparison with its **Type**-1 and conventional counterparts. We believe that the presented design methodology and results will provide a bridge for a wider deployment of **Type**-**2** **fuzzy** **logic** in the area of the computer games.

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This work, introduced a new class of **fuzzy** **logic** sys- tems—**interval** **type**-**2** **fuzzy** **logic** system (IT2 FLS), where the antecedent or/and consequent membership functions (MFs) are **interval** **type**-**2** **fuzzy** sets (IT2 FSs), [Mendel et al. 2009, 2006 and 2004], which is an extension of the concept of a **type**-1 **fuzzy** set (T1 FS). In an IT2 FLS, the knowledge used to construct rules is uncertain, and this uncertainty drives to rules having uncertain antecedents and/or consequents, [Wu and Mendel 2012, 2007 and 2002]. Now as MFs of a general T2 FSs are **fuzzy**, therefore T2 FSs are able to model as uncertainties, and their MFs are three-dimensional, [Zeng et al. 2008]. T2 FSs third dimension provides additional degrees that make it possible to directly models uncertainties, [Liang and Mendel 2000]. T2 FSs are difficult to use and under- stand because: i) T2 FSs three-dimensional makes them very difficult to depict; ii) there is no simple terms set that let us effective communication about T2 FSs, and to then be mathematically accurate, and iii) using T2 FSs is computationally more complex than using T1 FSs, [Mendel et al. 2009, 2007 and 2002]. Most people only use an IT2 FSs in a T2 FLS,

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The first demand of electrical system reliability is to keep the synchronous generators working in parallel and with adequate capacity to satisfy the load demand. If at any time, a generator looses synchronism with the rest of the system, significant voltage and current fluctuation can occur and transmission lines can be automatically removed from the system by their relays deeply affecting the system configuration. The second demand is maintaining power system integrity. The high voltage transmission system connects the generation sources to the load centers. Interruption of these nets can obstruct the power flow to the load. This usually requires the power system topology study, once almost all electrical **systems** are connected to each other. When a power system under normal load condition suffers a disturbance there is synchronous machine voltage angles rearrangement. If at each disturbance occurrence an unbalance is created between the system generation and load, a new operation point will be established and consequently there will be voltage angles adjustments. The system adjustment to its new operation condition is called "transient period" and the system behavior during this period is called “dynamic performance”.

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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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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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In the new era of power **systems**, power quality (PQ) is- sues have attained considerable attention in the last few decades due to increased demand of power electronics and/or microprocessor based non-linear controlled loads. While these devices create power quality prob- lems, at the same time, devices may also malfunction due to the severe power quality problems [1]. Electricity is now treated as commercial product that is evaluated not only by its reliability but also by its quality. The customer will choose the supplier providing electrical energy having better power quality, at lower cost and ac- ceptable reliability that meet his load needs. The utilities or other electric power providers have to ensure a high quality of power delivery to remain competitive and to retain/attract the customers in new electricity market scenario [**2**].

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