analyses are much more difficult. This paper presents the use of **neuro**-**fuzzy** networks as means of implementing algorithms suitable for **nonlinear** black-box **prediction** and **control**. In engineering applications, two attractive tools have emerged recently. These two attractive tools are: the artificial neural networks and the **fuzzy** logic system. One area of particular importance is the design of networks capable of modeling and predicting the behavior of systems that involve complex, multi-variable processes. To illustrate the applicability of the **neuro**-**fuzzy** networks, a case study involving air-fuel ratio is presented here. Air-fuel ratio represents complex, **nonlinear** and stochastic behavior. To monitor the engine conditions, an **adaptive** **neuro**-**fuzzy** inference system (ANFIS) is used to capture the **nonlinear** connections between the air-fuel ratio and **control** parameters such manifold air pressure, throttle position, manifold air temperature, engine temperature, engine speed, and injection opening time. This paper describes a **fuzzy** **clustering** method to initialize the ANFIS.

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Introduction: Inverted Pendulum is a good **model** for, an automatic aircraft landing system, the attitude **control** of a space booster rocket and a satellite stabilization of a cabin in a ship, aircraft stabilization in the turbulent air-flow etc. To solve such problem with non-linearity and time variant system, there are alternatives such as a real time computer simulation of these equations or linearization. The inverted pendulum is a highly **nonlinear** and open-loop unstable system [5, 6, 8]. This means that standard linear techniques cannot be modeled as the **nonlinear** dynamics of the system. In the **Neuro**-**Fuzzy** systems the neural networks (NN) are incorporated in **fuzzy** systems, which can use **fuzzy** knowledge automatically by learning algorithms of NNs. They can be visualized as a mixture of local experts. **Adaptive** **Neuro**-**Fuzzy** inference system (ANFIS) is one of the of **Neuro** **Fuzzy** systems in which a **fuzzy** system is incorporated in the framework of **adaptive** networks. ANFIS constructs an input-output mapping based both on human knowledge i.e. rules and on generated input-output data pairs. The **Neuro**- **Fuzzy** systems can be visualized as a mixture of local experts and their par least squares optimization methods. The most frequently used NNs in **Neuro**-**Fuzzy** systems are radial basis function networks (RBFN). ANFIS forms an input output mapping based both on human knowledge

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University of Jammu Campus, India Abstract- Data **clustering** is a well known technique for **fuzzy** **model** identification or **fuzzy** modelling for apprehending the system behavior in the form of **fuzzy** if-then rules based on experimental data. **Fuzzy** c- Means (FCM) **clustering** and subtractive **clustering** (SC) are efficient techniques for **fuzzy** rule extraction in **fuzzy** modeling of **Adaptive** **Neuro**-**fuzzy** Inference System (ANFIS). In this paper we have employed a novel technique to build the rule base of ANFIS based on the kernel based variants of these two **clustering** techniques which have shown better **clustering** accuracy. In kernel based **clustering** approach, the kernel functions are used to calculate the distance measure between the data points during **clustering** which enables to map the data to a higher dimensional space. This generalization makes data set more distinctly separable which results in more accurate cluster centers and therefore a more precise rule base for the ANFIS can be constructed which increases the **prediction** performance of the system. The performance analysis of ANFIS models built using kernel based FCM and kernel based SC has been done on three business **prediction** problems viz. sales forecasting, stock price **prediction** and qualitative bankruptcy **prediction**. A performance comparison with the ANFIS models based on conventional SC and FCM **clustering** for each of these forecasting problems has been provided and discussed.

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ANFIS is a kind of hybrid of neural network and **fuzzy** logic and is based on Takagi–Sugeno **fuzzy** inference system. In ANFIS, we combine both the learning capabilities of a neural network and reasoning capabilities of **fuzzy** logic in order to give enhanced **prediction** capabilities [2]. Since it integrates both neural networks and **fuzzy** logic principles, it has potential to capture the benefits of both in a single framework. Its inference system corresponds to a set of **fuzzy** [3] IF–THEN rules that have learning capability to approximate **nonlinear** functions. Hence, ANFIS is considered to be universal approximator. The ANFIS **model** is very suitable and can generate excellent classiﬁcation results provided that the right type and number of Membership Functions (MFs) are used in the classiﬁcation task [4].In the classification [5] two different classification techniques are employed: an artificial neural network-based classifier and a hybrid ANFIS classifier. A neural classifier can learn from data, but the output does not lead itself naturally to interpretation. An ANFIS classifier is based on a three-layer feed-forward neural network and combines the merits of both neural and **fuzzy** classifiers while overcoming their drawbacks and limitations. The developed **Adaptive** **Neuro** **Fuzzy** Inference System (ANFIS) classifier exhibits high levels of accuracy, consistency and reliability, with acceptably low computational time and is a promising new development in the field of diagnosis of cancer.

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The **nonlinear** forward **model** of the TRMS has been successfully obtained and reported in [7], [8], [9]. Therefore, the same system identification technique based on experimental input-output data pairs is employed to obtain the inverse **model** of the system. The advantage of an inverse **model** is that it can be used to build a controller. The desired behavior is treated as an input variable in the **model**, and the action is treated as an output variable. Since the input–output dynamics of the **model** and the controller are the same, they share the same stability properties, thus it is sufficient to show stability of the **model** only, when determining stability of the **model** and of the controller [10]. An **adaptive** **neuro**- **fuzzy** inference system (ANFIS) is augmented to the **control** system to improve the **control** response. Thus, the **control** techniques embraced in this work are augmented ANFIS 2009 Third UKSim European Symposium on Computer Modeling and Simulation

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An interval **prediction** is usually comprised of the upper and lower limits between which a future unknown value is expected to lie with a prescribed probability. The **prediction** interval deals with the accuracy of the estimates with respect to the observed target values [7]. The use of **prediction** interval in machine learning is appropriate when dealing with multivariate functions where available data are very imprecise and limited and when explanatory variables are interacting in uncertain, vague manners [1]. In other words a **fuzzy** phenomenon is best modeled by a **fuzzy** functional relationship. The use of **prediction** interval in machine learning is referred to as **fuzzy** linear regression technique.

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Shafigh, A. S. Abdollahi , K. Kassler Andeas J [1] proposed **Fuzzy** logic **control** method to improve the performance and reliability of the multicast routing protocols in MANET. Strong and small forwarding group is established to decrease the resource consumption and higher stability of the delivery structure. A forwarding group is made out of set of strong /weak nodes. **Fuzzy** logic is proposed to distinguish the strong and weak nodes in the network. Join query packet is periodically broadcasted to update the routes in the network. An intermediate node receives a non-duplicate join query; it stores the upstream node ID into the routing table and rebroadcasts the packet. A node receives a join query message; it needs to fuzzyfys the parameters such as bandwidth, node speed and power level of previous node. The value of previous node's parameter is used to classify them as low, medium or high. After fuzzification, inference process is used to derive the probability of caching and forwarding the join query to other nodes. Using **fuzzy** based approach only links and nodes which are more robust or have more available power will participate in the forwarding mesh.

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research have strong linear relation with horizontal solar radiation and are readily available at the meteorological station in Nigeria. The developed WT-ANFIS **model** proves to be good **model** for horizontal solar radiation **prediction**. The statistical values of the MAPE, RMSE and R² obtained are 0.23712, 0.82161 and 0.9887 respectively. Based on the values of R² used for comparison between the developed **model** and the validated models, the WT-ANFIS show better accuracy and performance. Also, by adding more meteorological data more **prediction** accuracy is attained. With the obtained results, it indicates that the addition of WT for data decomposition and reconstruction improves the ANFIS **model** accuracy for horizontal solar radiation **prediction**. More meteorological data will be considered in future study and new models will be developed using new soft computing techniques.

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where m ij and ij represent a Gaussian membership function with mean and deviation, respectively, of the ith dimension and the jth rule node. The consequents Bj of the jth rule are aggregated into one **fuzzy** set for the output variable y’. Crisp action is obtained through defuzzification, which calculates the centroid of the output **fuzzy** set. The more common **fuzzy** inference method proposed by Mamdani, Takagi, Sugeno, and Kang introduced a modified inference scheme [5]. The first two parts of the **fuzzy** inference process, fuzzifying the inputs and applying the **fuzzy** operator, are exactly the same. A Takagi-Sugeno-Kang (TSK)-type **fuzzy** **model** employs different implications and aggregation methods than the standard Mamdani controller. Instead of **fuzzy** sets being used, the conclusion part of a rule is a linear combination of the crisp inputs.

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For our proposed solution, we intend to **model** a **Fuzzy** Infe rence System that predicts when a patient needs to undergo Decompressive He mic raniecto my. The inputs to this system are the pred icted output fro m the baseline solution and the predicted output of a **model** trained to predict whether a patient needs to undergo the surgery. Simila r to [4], which our work is an extension of, we want to prove that we can use FIS to accurately predict for an argumentatively unique and significantly complicated proble m than those already addressed in the literature by others. Complication occurs due to the fact that unlike in most other medical conditions already addressed in the literature that usually have a larger sized offline dataset available to mode l their proposed solution on, the dataset available for stroke is on the other hand very limited. A lso unlike in other medica l prob le ms as those discussed above that deal with d iagnosis or detection of a med ical condition that can be done over a period of time , **prediction** of infa rction volume and thus the decision to operate on a patient, on the other hand, is very time critica l. These decisions need to be taken as accurately and as fast as possible to avoid further health co mp licat ions such as disabilit ies or death . By build ing an e ffective **prediction** **model**, we offer to not only significantly reduce the decision time required by doctors but also help reduce the number of CT scans required by patients to only one.

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Abstract Although many algorithms and techniques have been developed for estimating the reliability of component-based software systems (CBSSs), much more research is needed. Accurate estimation of the reliability of a CBSS is dif- ﬁcult because it depends on two factors: component reliability and glue code reli- ability. Moreover, reliability is a real-world phenomenon with many associated real-time problems. Soft computing techniques can help to solve problems whose solutions are uncertain or unpredictable. A number of soft computing approaches for estimating CBSS reliability have been proposed. These tech- niques learn from the past and capture existing patterns in data. The two basic elements of soft computing are neural networks and **fuzzy** logic. In this paper, we propose a **model** for estimating CBSS reliability, known as an **adaptive** **neuro** **fuzzy** inference system (ANFIS), that is based on these two basic elements of soft computing, and we compare its performance with that of a plain FIS (**fuzzy** inference system) for different data sets.

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In the ﬁrst simulation, the outside weather conditions are T out = 35 C and w out = 4 g/kg (RH = 10%), while Si = 300 W/m 2 . The humidity ratio set point was raised from 18 to 24 g/kg (which corresponds to a relative humidity change from 60% to 80%) at t = 100 min, with the temperature set point 30 C; then the temperature set point was decreased from 30 to 28 C at t = 200 min (humidity ratio set point 24 g/kg), the responses for set point step changes in humidity ratio and temperature are in Fig. 4 . As we see the response under pro- posed G-ANFIS controller is very smooth and nearly close to set point than that given by ANFIS without tuning .The ventilation rate and water capacity of fog system as a **control** signals are shown in Fig. 5 . The simulation results clearly demonstrate the interacting **control** was attained and the closed-loop system response is very acceptable. Moreover, the response of the G-ANFIS controller is much faster than AFISN.

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Bell-shaped membership functions are used to **model** the inputs and outputs. By choosing these membership functions, each input signal is assigned to all linguistic groups which can reduce the ambiguity in the border areas. Figures2 and 3 show the bell-shaped membership functions chosen for FIS inputs, and Figure 4 shows the bell-shaped membership functions chosen for the output. In these figures NL, NM, NS, Z, PS, PM and PL denote negative large, negative medium, negative small, zero, positive small, positive medium and positive large, respectively. Inputs and output cured face of **fuzzy** inference is illustrated in Figure 5.The following **control** rule is applied in **fuzzy** controller:

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For describing relationships between different combinations of inputs and outputs such as those that must be determined for accurately predicting soil hydraulic conductivity, ANN is currently the most widely used technique (Erzin et al., 2009; Moosavi and Sepaskhah, 2012). Since Zadeh (1965) proposed the **fuzzy** logic approach to describe complicated systems, it has become popular and been successfully used to solve **prediction** purposes in various agricultural and engineering problems (Sarmadian and Mehrjardi, 2010). A recent literature review shows that the use of **adaptive**-network-based **fuzzy** inference system (ANFIS) (Jang, 1993; Ho et al., 2011) for such purposes is relatively rare and applied in predicting soil properties in the conditions where there isn’t enough information about how parameters relate to each other (El Awady et al., 2002; Minasny et al., 2004; Akbarzadeh et al., 2009; Sezer et al., 2009; Anari et al., 2011; Yilmaz and Kaynar, 2011; Kalkhajeh et al., 2012; Moosavi and Sepaskhah, 2012; Xue and Yang, 2013).

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been found to be particularly useful to **model** unknown functions in **nonlinear** systems rather that only unknown parameters. There have been signicant research efforts on **adaptive** **fuzzy** **control** for **nonlinear** systems [2–4]. The major advantage in all these **adaptive** **fuzzy** **control** schemes are that the developed controllers can be handled the complex **nonlinear** functions instead of linearly parameters.

Due to the fact that material cost is one of the major factors in the construction of a structure, it is preferable to reduce it by minimizing the weight of the structural system. All of the methods used for minimizing the weight intend to achieve an optimum design having a set of design variables under certain design criteria. A great development of structural optimization took place in the early 60's when programming techniques were used in the minimization of structure weight. From then on, various general approaches have been developed and adopted for structural optimization [1- 6]. Moreover, one of the main diculties of structural optimization methods is that they need a great number of structural analyses to achieve an optimal solution. This deciency may increase when **nonlinear** analysis must be implemented. This inherent nature of op- timization methods can impose much computational eort on the process. Over the last years, some

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METHODOLOGY 3.1 Overview 3.2 Design of a Modified Adaptive Fuzzy Inference Engine MAFIE 3.2.1 Fuzzy Inference System FIS 3.2.2 Hybrid Fuzzy clustering algorithm for Automatic Generation [r]

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