defuzzifications. Moreover, the **fuzzy** rule base and **interval** **type**-**2** **fuzzy** sets are complicated when determining the exact membership function and complete **fuzzy** rule base. So, the optimization of **interval** **type**-**2** **fuzzy** set and **fuzzy** rule base must be used to estimate the value by an expert system. Many researchers have proposed and introduced optimization of **interval** **type**-**2** **fuzzy** set and **fuzzy** rule base such as Zhao [3] proposed adaptive **interval** **type**-**2** **fuzzy** set **using** gradient descent algorithms to optimize inference engine **fuzzy** rule base, Hidalgo [4] proposed optimization **interval** **type**-**2** **fuzzy** set applied to modular neural network **using** a genetic **algorithm**. Moreover, many researchers apply the **interval** **type**-**2** **fuzzy** **logic** system for uncertain datasets. Also, the creation of an optimized **interval** **type**-**2** **fuzzy** **logic** system will gain the maximum accurate outputs. There are also many optimization techniques which have been proposed for building **interval** **type**-**2** **fuzzy** **systems**. Some traditional optimization techniques are based on mathematics and some are based on **heuristic** algorithms. Some optimization techniques are often difficult and time consuming such as **heuristic** optimization. Sometimes, the improvement of the **heuristic** algorithms provides good performance such as the **hybrid** **heuristic** algorithms [5]. Moreover, **hybrid**

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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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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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The simulated annealing **algorithm** is a simple and general optimization **algorithm** for finding global minima [30]. It has been used widely to search for optimal or nearly optimal solutions in a wide range of optimization problems. In this work, it acts as a learning **algorithm** to automatically design **fuzzy** **logic** **systems** by search- ing for the best configurations of these **systems**. One of the motivations for **using** simulated annealing with **fuzzy** **systems** is that it does not require the existence of mathematical properties such as differentiability in the problem, which allows the pos- sibility of **using** all **fuzzy** structure components including non-differentiable t-norms and non-differentiable membership functions. Although the combination might have more complexity and longer search time than local search algorithms, it is more likely to find the global or near global optima of the configuration of **fuzzy** **logic** **systems** than local search approaches. This is due to the ability of simulated annealing to avoid local optima by accepting higher-cost states with some probability in order to explore the problem space. In addition, simulated annealing can suit high dimensionality prob- lems as it scales well with the increase of variable numbers, which makes it a good candidate for the optimization of **fuzzy** **logic** **systems** [16]. Also, it is able to handle cost functions with different degrees of non-linearities, discontinuities, and stochastic- ity [23]. The problem of **optimizing** membership functions of the **fuzzy** **logic** system in order to minimize the objective function is a complex problem due to the large number of parameters used as well as the the non-differentiable and non-continuous objective functions [20]. The simulated annealing convergence normally requires an exponential time which causes the **algorithm** to be impractical in some cases [1, p.14]. One of the criticisms of simulated annealing is the difficulty in fine-tuning its parameters, so it can be time-consuming for developers to find an optimal fit [23]. The formalizations and configurations for simulated annealing to design **fuzzy** **logic** **systems** can be chosen from a large number of choices proposed in the literature.

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Integration of the ABC **algorithm** with **fuzzy**-based **systems** and mobile robotics is still in the early stages. Few research presents integrating ABC for **optimizing** the rule base in **fuzzy** controllers. One of these researches was O. Abedinia et al. [30]. Bhattacharjee et al. [31] used ABC for **optimizing** multi- robot path planning. The proposed method tries to determine a trajectory of motion to known targets where ABC is used to minimize the path through obstacle and collision avoidance.

Although, **type**-**2** **fuzzy** **logic** is a growing research topic with much evidence of successful applications (John and Coupland, 2007), up to now, almost all developments **type**- **2** **fuzzy** **logic** **systems** were based on **interval** **type**-**2** **fuzzy** **logic** **systems** with some exceptions related to some works **using** different representations of **type**-**2** sets and **systems** such as geometric **type**-**2** **fuzzy** **logic** **systems** (Coupland and John, 2007), alpha- planes (Mendel et al., 2009), alpha cuts (Hamrawi et al., 2010) and Z-slices (Wagner and Hagras, 2010a; Christian Wagner, 2009). The ease of computation associated with the **interval** form of **type**-**2** sets is the main driver for the wide usage of **interval** **type**-**2** set and **systems** compared to the generalised form. One attempt to design general **type**-**2** sets based on zSlices representation was proposed in (Christian Wagner, 2009) where survey data and device characteristics were used to build zSlices sets automatically. Another attempt to learn general **type**-**2** **fuzzy** **logic** **systems** **using** alpha-plane representation has been introduced in (Mendel et al., 2009). Some other works **using** some neural networks concepts or **classification** algorithms such as: **type** **2** Adaptive Network Based **Fuzzy** Inference System (ANFIS) (John and Czarnecki, 1998), general **type**-**2** **fuzzy** neural network (GT2FNN) (Jeng et al., 2009) and **fuzzy** C-means **algorithm** with a model known as “efficient triangular **type**-**2** **fuzzy** **logic** system” (Starczewski, 2009b). To the best of the author’s knowledge, no attempt to employ a learning method on general **type**-**2** **fuzzy** **logic** **systems** **using** the vertical-slice representation has been made. The next section will introduce the simulated annealing **algorithm**.

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This paper proposes a sliding mode control-based learning of **interval** **type**-**2** intuitionistic **fuzzy** **logic** system for time series and identification problems. Until now, derivative-based algorithms such as gradient descent back propagation, extended Kalman filter, decoupled extended Kalman filter and **hybrid** method of decoupled extended Kalman filter and gradient descent methods have been utilized for the optimization of the parameters of **interval** **type**-**2** intuitionistic **fuzzy** **logic** **systems**. The proposed model is based on a Takagi-Sugeno-Kang inference system. The evaluations of the model are conducted **using** both real world and artificially generated datasets. Analysis of results reveals that the proposed **interval** **type**-**2** intuitionistic **fuzzy** **logic** system trained with sliding mode control learning **algorithm** (derivative-free) do outperforms some existing models in terms of the test root mean squared error while competing favourable with other models in the literature. Moreover, the proposed model may stand as a good choice for real time applications where running time is paramount compared to the derivative-based models.

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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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Different studies of researchers on the behavior of structures against earthquakes and the more familiarity with the nature of earthquakes has led to the fact that in the last two decades, the discussion of the control of structures is of great interest to researchers. Reducing structural responses to enhance safety and providing conditions for serviceability and maintenance is one of the goals of the researchers. Control tools are very effective in achieving these goals. Structural control methods are classified into several categories including passive, active, semi-active, and **hybrid** **systems**. In this research, reducing the damages to the structures against earthquakes by semi-active control method **using** MR damper and **using** the results of Incremental incremental Analysis analysis of structures has been studied. Spencer, Dyke et al. studied the MR damper and presented a model for its dynamic behavior. They compared their proposed dynamic model with existing idealized models as well as laboratory samples and showed that proposed models are suitable for analyzing and designing structures equipped with MR damper [1-3]. Carlson, Spencer, Yang et al. studied the dampers in real dimensions of the structures. They examined dampers in real dimensions and they **evaluated** dynamic models of MR dampers [4-6].

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Defuzzification involves a considerable number of predicate **logic** statements. These are **evaluated** **using** generalized modus pones and sometimes more directly. This likely involves a good deal more skill in **logic** than most physicians would poses. Licata’s work points out that the **fuzzy** **logic** approach is in lieu of the probabilistic approach generally employed. Licata suggests that the **fuzzy** set theory solution is more exacting and probably superior to the usual process where individual decisions in the chain leading to a conclusion are made on the basis of probabilistic estimates. This paper is of course not able to present accuracy figures since there is only one case considered. It is recounted here as an indication of the pervasive influence of **fuzzy** **logic** on the medical discipline.

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Association rule learning is a rule-based machine learning method for discovering interesting relations between variables in large databases. It is intended to identify strong rules discovered in databases **using** some measures of interestingness. Initially Market basket analysis [1] is the major application of ARM. Based on the concept of strong rules, association rules can be formulated for discovering regularities between products in transactional data recorded by **systems** in supermarkets. For example, the rule {onion, potato}->{burger bun} found in the sales data of a supermarket would indicate that if a customer buys onions and potatoes together, they are likely to also buy burger buns. Such information can be used as the basis for decisions making about marketing activities such as, e.g., promotional pricing or product placements. Now a day, ARM can be used in many application areas including Web usage mining, intrusion detection, continuous production, bioinformatics and many more.

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Many researches dealt with the problem of induction motors fault detection and diagnosis. The major difficulty is the lack of an accurate model that describes a fault motor. An **interval** **type**-**2** **fuzzy** **logic** approach may help to diagnose induction motor faults. The motor condition is described **using** linguistic variables. An **interval** **type**-**2** **fuzzy** **logic** system (IT2FLS), which can handle rule uncertainties. The implementation of this **interval** **type**-**2** **fuzzy** **logic** (IT2FLS) involves the operations of fuzzification, inference, and output processing. We focus on “output processing,” which consists of **type** reduction and defuzzification. **Type**-reduction methods are extended versions of **type**-1 defuzzification methods. **Type** reduction captures more information about rule uncertainties than does the defuzzified value (a crisp number). **Interval** **type**-**2** **fuzzy** subsets and the corresponding membership functions describe stator current amplitudes. A knowledge base, comprising rule and data bases, is built to support the **interval** **type**-**2** **fuzzy** inference. The induction motor condition is diagnosed **using** a compositional rule of **interval** **type**-**2** **fuzzy** inference. This paper presents a use of **interval** **type**-**2** **fuzzy** **logic** technique to diagnose stator fault by sensing stator currents and voltage.

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(e.g. reduce number of tap operations, satisfy the desired consumers demand or maximise utility of DGs), and a given context (e.g. decision according to severity or economical targets). This context established whether to satisfy or not the local goals. The way the context works not differs much from a selection priority index [119] which maps the requirements with the control budget and decides which action to deploy (i.e. Table 4.2). For example, the budget is the sum of local sensitivities that is used as an approximation as actions can cancel each other or flows within the network may change affecting voltage levels. Thus, all these inputs are mapped into crisp actions as in [59] and applied and validated **using** a Matpower network model [45]. This process is continuously re-run until the violation is solved according to the network model, there no changes in the solution or until a maximum number of iterations is reached. Oscillations in voltage magnitude, but also interactions between devices may appear during the solution calculation due to the fact that removing one violation could cause another one to occur. Sequential validation can help avoid trailing

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where a, b and n are constant real numbers, t is the current time and τ is a non-negative time delay constant. The system tends to display a deterministic/periodic behaviour at τ ≤ 17 which turns chaotic when τ > 17. For comparison with other works in the literature such as [14], [20]–[23], where the target output is chosen as x(t + 6), from input vector (x(t − 18), x(t − 12), x(t − 6), x(t)) and τ = 17. For each input in this study, two intuitionistic Gaussian membership functions with uncertain standard deviation are used. Similar to [22], the 1000 learning data are generated from time series (t = 19-1018) with the first 500 data points used for training and the remaining 500 for testing. The results of applying different approaches to the prediction of Mackey-Glass are listed in Table I. As shown in Table I, IT2IFLS outperforms the modified differential evolution radial basis function neural network (MDE-RBF NN) and the **fuzzy** approaches.

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In order to show the improvement of the proposed AIT2-FLC, the IT2-FLC proposed previously [24] is also implemented for comparison purposes. Anaesthestic drugs normally have stable and slow acting response, consequently, step response is the most common identiﬁcation procedure used by clinicians [3] . During surgical operations in theatre the anaesthetist who is normally specify the set-point of muscle relaxation and blood pressure [3,5] . In these simulation tasks, the initial conditions were 0% paralysis and sampling period was 1 min. The set-point command signal for muscle relaxation and change in blood pres- sure were 0.8 (80% paralysis 20% EMG) and 30 mmHg respectively. These values of set-point for the muscle relaxation and the mean arterial blood pressure were used practically pre- viously [3] . The control signal 1 was limited between 0 and 1 for the atracurium drug input and between 0% and 5% for the iso- ﬂurane input (control signal **2**). For anaesthesia system, the con- trol objective is to attain and maintain an adequate of anaesthetic level without any overshoot. This is the maintaining of a steady level of muscle relaxation and blood pressure with minimum deviation from set-point [3,5] . The simulation results were divided into the following three tasks.

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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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In polymer processing, melt temperature is one of the most important process variables and even small variations can cause poor product quality (Dormeier and Panreck, 1990). Under poor thermal conditions, several processing problems can occur, e.g. thermal degradation, output surging, poor mechanical properties, dimensional in stability, poor surface finish and poor optical clarity (Rauwendaal, 2001; Maddock, 1964; Fenner, 1979). Diemelt temperature homogeneity depends on the selection of processing conditions, machine geometry, and material properties (Brown et al., 2004b; Kelly et al., 2006;A beykoon et al., 2010b,a). Moreover, it has been found that melt temperature non-homogeneity increases with screw speed. Therefore, it is a challenging task to run extruders at higher screw speeds although the process energy efficiency then increases (Abeykoon et al., 2010c).An ideal controller would minimize poor thermal conditions such as melt flow non-homogeneity and achieve the highest possible thermal and energy efficiencies enabling the extruder to run at high speeds. Varying degrees of success have been achieved in the area of extrusion melt thermal control by manipulation of barrel temperature and screw speed settings **using** empirical modeling techniques. The majority of schemes have been concentrated on transfer function models mostly in combination with proportional- integral-derivative (PID) approaches (Fingerle, 1978; Muhrer et al., 1983; Previdiet al., 2006). Some other work has used linear time-series regression techniques in process disturbances rejection and melt temperature control (Parna by et al., 1975; Kochhrand Parnaby, 1977; Hassn and Parnaby, 1981; Pattersonand Kerf, 1978; Costin et al., 1982; Germuska et al., 1984;Lin and Lee, 1997). Mercure and Trainor (1989) proposed time dependent partial differential equations to formulate a first principle mathematical model for the extruder barrel temperature control.

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Abstrak Makalah ini menyajikan sebuah aplikasi **Interval** **Type**-**2** **Fuzzy** **Logic** System (**Interval** **Type**-**2** FLS) untuk peramalan beban jangka pendek (STLF) pada hari-hari libur dalam sebuah studi kasus di Bali, Indonesia. Sistem logika **fuzzy** **Type**-**2** ditandai dengan konsep yang disebut footprint of uncertainty (FOU). Penggunaan dimensi matematika tambahan pada sistem **Type**-**2** FLS ini memberikan hasil yang lebih baik dibandingkan dengan **Type**-1 FLS. **Type**-**2** FLS juga memiliki kemam- puan untuk memodelkan hubungan yang lebih kompleks dengan output dari **Type**-**2** **fuzzy** inference engine yaitu memerlukan apa yang disebut dengan **type** reduction. **Type** reduction yang digunakan ini menerapkan algoritma iteratif Karnik-Mendel (KM **Algorithm**) yaitu pemetaan output **Type**-**2** **fuzzy** set (**Type**-**2** FSs) menjadi **Type**-1 **fuzzy** set (**Type**-1 FSs) dengan proses defuzzi- fikasi menggunakan centroid untuk selanjutnya mengkonversi **Type**-1 FSs ke suatu bilangan. Metode yang diusulkan ini diuji dengan data beban puncak hari libur sebenarnya pada sistem kelistrikan Bali, yaitu hari libur menggunakan beban puncak 4 hari sebelum hari libur dan pada saat hari libur untuk periode tahun 2002 hingga tahun 2006. Ada 20 item hari libur di Bali yang digunakan untuk peramalan pada tahun 2005 dan 2006. Hasil tes menunjukkan tingkat keakuratan peramalan dengan persentase kesalahan rata-rata (MAPE) sebesar 1,0335% di tahun 2005 dan 1,5683% di tahun 2006.

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During the last two decades, the Internet has changed people’s habits and improved their daily life activities and services. In particular, the emergence of e-commerce provided manufac- tures and vendors with more business opportunities. This allowed customers to beneﬁt from a global, quicker and cheaper shopping environment. However, e-commerce is evolving from a centralised approach, where consumers directly purchase products and services from busi- nesses, to a Peer-to-Peer (P2P) perspective, in which customers buy and sell goods amongst themselves. In P2P scenarios, it is crucial to protect both buyers and sellers (the peers) from being victimised by possible fraud arising from the uncertainties, vagueness and ambiguities that characterise the interactions amongst unknown business entities. For this reason, the so-called reputation models are becoming a key architectural component of any e-commerce portal. These **systems** are intended to evaluate the basic features of each entity (buyer, seller, goods, etc.) involved in a given trading transaction in order to assess the trust level of the given transaction and minimise fraud. However, in spite of their wide deployment, the rep- utation models need to be enhanced to handle the various sources of uncertainties in order to produce more accurate outputs which will allow to increase the trust and decrease the fraud levels within e-commerce **systems**. In this paper, we present an **interval** **type**-**2** **fuzzy** **logic** based framework for reputation management in (P2P) e-commerce which is capable of better handling the faced uncertainties. We have carried out various experiments based on eBay ® -like transaction datasets which have shown that the proposed **type**-**2** **fuzzy** **logic** based

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Climate changes during the day influence the power produced by the PV panel. Therefore, the operating point does not intersect with the MPP, which causes a loss of power. It is then essential to extract the novel MPP **using** MPPT algorithms. They are used to vary the equivalent resistance of the load to extract the maximum power by automatically varying the duty cycle of the DC/DC converter [10]. Nowadays, several methods of MPPT exist and can be classified by their tracking techniques to:

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