# Neuro Fuzzy And Soft Computing Approach Notes Pdf

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*To overcome this problem, several artificial intelligence techniques such as Artificial Neural Networks ANN and Fuzzy Logic FL have recently been employed with various architectures and properties. However, due to the constraints of both methods, they yield the desired results only under the specific circumstances. As an example, one major problem in FL is the difficulty of constructing the membership functions MFs.*

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## Intelligent Control (Taught in English, 2019)

To overcome this problem, several artificial intelligence techniques such as Artificial Neural Networks ANN and Fuzzy Logic FL have recently been employed with various architectures and properties. However, due to the constraints of both methods, they yield the desired results only under the specific circumstances. As an example, one major problem in FL is the difficulty of constructing the membership functions MFs. Other problems such as architecture and local minima could also be located in ANN designing.

Therefore, a new methodology is presented in this paper for grade estimation. The combination of these two artificial intelligence approaches is achieved via the verbal and numerical power of intelligent systems. To improve the performance of this system, a Genetic Algorithm GA — as a well-known technique to solve the complex optimization problems — is also employed to optimize the network parameters including learning rate, momentum of the network and the number of MFs for each input.

The results show that CANFIS—GA could be a faster and more accurate alternative to the existing time-consuming methodologies for ore grade estimation and that is, therefore, suggested to be applied for grade estimation in similar problems.

One of the most important parameters which can have a major effect on mining feasibility and its future management is grade estimation accuracy. Subsequently, there is a special sensitivity on the methods which are used for reserve evaluation, since these methods can have a significant role in the mining future planning. The estimation is utilized during the mining primary stages and it may be reused up to the end of the mine activities.

Therefore, the accuracy of the estimation methods has a continuous effect on the mining project. Several methods and techniques have already been utilized in order to increase the accuracy of the grade or tonnage estimation such as geostatistics Journel and Huijbregts, ; Hornik et al.

Obviously, geostatistics is one of the most prevalent techniques for grade estimation. Most of the common geostatistical methods such as Kriging Journel and Huijbregts, ; Hornik et al. However, to overcome these problems, some geostatistical simulations have been proposed, but each of them has its own problems Strebelle, In addition, two-point based geostatistical methods have a low accuracy which cause to make some constrains and limitations Kapageridis et al.

Therefore, it is tried to use the nonlinear estimators like ANN to overcome the complex spatial relationship. It is clear that assignment of the weights in ANN structure is one of the most important problems which has a direct effect on its performance. Basically, the weights are controlled by both network architecture and the parameters of learning algorithm. For example, using several layers and nodes in hidden layers causes the network to be much more complex.

Other parameters of the network such as inputs, the number of hidden layers and their nodes, number of memory taps and the learning rates could also affect the ANN performance Tahmasebi and Hezarkhani, Therefore, researchers try to solve these problems by combining the ANN with other optimization methods such as genetic algorithm GA and simulated annealing. For example, Mahmoudabadi et al. Samanta et al. Also, Chatterjee et al.

But in both above mentioned studies, it was ignored to optimize the ANN's parameters and topology. The concept of uncertainty resulting from fuzziness has been recognized and applied in various aspects of geology and mining tasks such as fuzzy kriging Bardossy et al. For example, Cheng and Agterberg proposed fuzzy weights which allow a complementary utilization of both empirical and conceptual information.

In a hybrid fuzzy weights-of-evidence model, knowledge-based fuzzy membership values are combined with data-based conditional probabilities to derive fuzzy posterior probabilities.

Moreover, Tahmasebi and Hezarkhani a applied FL to predict the grade in case of lack of data which showed that this method can provide better results. Like the other methods, FL has some problems while its application. One of the most important issues of FL is making decision s on its appropriate parameters.

Therefore, all of these problems and lack of the knowledge, lead us to combine ANN with FL to minimize the error and make a better decision on FL's parameters. The CANFIS model is the result of the combination of adaptable fuzzy inputs with a neural network in order to have a rapid and more accurate predictor.

Actually, by this combination, it is possible to use both advantages of fuzzy inference systems with the explanatory nature of rules membership functions and ANN as a dynamic estimator. Also, another reason for applying this technique for grade estimation is several problems which have been mentioned in geostatistical methods and also making some uncertainties in grade estimation by ANN.

Therefore, to skip this step and select the right parameters to reach the best performance, we applied the GA which shows a good potential in ANN optimization Gupta and Sexton, ; McInerney and Dhawan, ; Ishigami, ; Sexton et al. Therefore, hereafter the methodology will be demonstrated. Basically, FL and ANN are the model-free and nonlinear estimators that their aim is mostly achieving a stable and reliable model which can justify the noise and uncertainties in the complex data Yager and Zadeh, According to earlier discussions, it is obvious that some problems such as determining the shape and the location of membership functions MFs for each fuzzy variable are involved with FL.

The FL efficiency basically depends on the estimation of premise and the consequent parts. Besides, the problems like number of hidden layers, number of neurons in each hidden layer, learning rate and momentum coefficient are also involved with ANN modeling. However, one of the most important capabilities of FL is to model the qualitative aspects of human by using the simple rules. In contrast, the ANN also have some advantages such as its capability of learning and high computational power.

However, Asadi and Tahmasebi presented a comprehensive study in which a global methodology for ANN is demonstrated. Furthermore, a sensitivity analysis on different ANN parameters can be found in their study. Fuzzy inference system FIS which is composed of five functional block: a rule base containing a number of fuzzy if-then rules , a database defines the MFs of the fuzzy sets used in the fuzzy rules , a decision-making unit performs the inference operations on the rules , a fuzzification interface to calculate fuzzy input and a defuzzification interface to calculate the actual output Jang Actually, this technique is an appropriate solution for function approximation in which a hybrid learning algorithm applied for the shape and the location of MFs Buragohain and Mahanta, ; Ying and Pan, Moreover, a practical example of this method is introduced in Tahmasebi and Hezarkhani To be more clear, by combination these two techniques, ANN will help to define the FL's rules, because most of the mining and geology conditions and specifically grade estimation are mixed with uncontrolled ambiguities which cause the rules to be difficult to define.

In other words, by using this new hybrid system, one can use both capabilities of FL's qualification and ANN's quantification aspects. More detailed information of ANFIS such as their different structures and learning algorithms is also discussed in the literature Jang et al. In this section, the utilized structure for the current considered case study is described. The purelin transfer function has been used as the output function.

Suppose that the rules contain three fuzzy if-then rules of Takagi and Sugeno's type Jang, :. As the values of these parameters change, the bell function varies accordingly and shows the various forms of MF for fuzzy set, subsequently. In the current study, this form of membership function is also used. Layer 2 Every node in this layer is a fixed node that its output is the product of all incoming signals. Layer 3 Includes the fixed node labeled N function of normalization:.

Therefore, the aim of this paper is to utilize CANFIS to construct a fuzzy inference system FIS which its MF's parameters are adjusted using a BP algorithm that allows the fuzzy system to capture the spatial relationships among the data and finally estimates the grade efficiently.

Considering Fig. The reason of this problem is due to using ANN. Although the ANN has an excellent learning algorithm and can help the FL to find the appropriate parameters, there are some parameters remaining in both ANN and FL which could have effect on performance indirectly. To encounter this problem, we use GA as a powerful optimization tool to find the best number of MFs for each input and the best values for learning rate and momentum coefficient.

The performance of this method will be demonstrated via a case study. Once we obtain the results, we will evaluate the reliability of the new model by comparing the predictions with the real grade.

The flowchart for grade estimation and the applied methods with their designing details. The GA was first introduced by Holland It is a universal method for solving the variety of constrained and unconstrained optimization problems Holland, GA can also be used to solve a diversity of optimization problems that are not well-suited for standard optimization algorithms, including problems in which the objective function is discontinuous, non-differentiable, stochastic, or highly nonlinear Goldberg, Some researchers also suggested that global search techniques including the GA might prevent ANN from falling into a local minimum McInerney and Dhawan, ; Sexton et al.

The initial population will be modified to reach a better answer. At each step, the GA selects individuals chromosomes from the current population parents randomly and uses them to produce the children for the next generation. After several generations, according to essence of the GA, it tries to move to the best solution. At each step, the GA uses three main types of rules to create the next generation from the current population. These types of rules are discussed as follows Deb, :.

Selection rules select the individuals called parents which contribute to the population at the next generation. Crossover rules combine the chromosomes in order to produce the next generation. Mutation rules lead the chromosome to change and alter their values. Initially, the variables should be represented by a binary string which encodes the parameters of the CANFIS and each chromosome individuals consists of several genes which represent the network's parameters.

Then, a population of strings with initial random parameters is created as candidates of the best solution i. In this study, the roulette wheel method is used to determine the next chromosomes with randomly selected length. Moreover, it is possible to give a chance to the pervious chromosome to cooperate in the future generation to become a stronger chromosome. It should also be noted that in this study, we used the rulette-wheel, two-point method and boundary method for the genetic operators of selection, crossover and mutation, respectively.

Afterwards, the values of fitness function which is mainly related to the difference between the output CANFIS—GA and the real grade are sorted and then the best and the worst chromosomes are identified note that only the best chromosomes can crossover or mutate by rating.

According to the available features and alteration indicators, Etminan supposed that this deposit is very similar to presented porphyry deposit characters by Lowell and Guilbert and he concluded that this deposit is one of the porphyry deposits Hezarkhani et al. Simplified geologic map of the Sungun area Hezarkhani Numbers on surface indicate drill holes Hezarkhani At the beginning of the modeling, the data is normalized which helps to reduce the noises and finally leads to a better prediction.

For this aim, different normalization methods should be tested to improve the network training Demuth and Beale, ; Chaturvedi et al. Each of the variables are normalized by applying the following three methods to find the most effective and precise one. Moreover, X norm is the normalized data that is transformed. The obtained results indicate that application of final equation to normalization leads to better responses. The applied data includes exploratory boreholes.

For grade estimation, the coordinates are used as input variables, and grade attribute is used as output variable for the respective dataset.

While applying the GA, there is no need to come back and correct the model, because the training phase will be controlled by the GA and the best parameters are stored at each iteration. Also, we pick the sets at equally spaced points throughout the original data. Table 1 represents the summary statistics of the datasets in which the copper dataset reveals less variance.

## Soft Computing

In the field of artificial intelligence , neuro-fuzzy refers to combinations of artificial neural networks and fuzzy logic. Neuro-fuzzy hybridization results in a hybrid intelligent system that these two techniques by combining the human-like reasoning style of fuzzy systems with the learning and connectionist structure of neural networks. Neuro-fuzzy system the more popular term is used henceforth incorporates the human-like reasoning style of fuzzy systems through the use of fuzzy sets and a linguistic model consisting of a set of IF-THEN fuzzy rules. The main strength of neuro-fuzzy systems is that they are universal approximators with the ability to solicit interpretable IF-THEN rules. The strength of neuro-fuzzy systems involves two contradictory requirements in fuzzy modeling: interpretability versus accuracy. In practice, one of the two properties prevails. The neuro-fuzzy in fuzzy modeling research field is divided into two areas: linguistic fuzzy modeling that is focused on interpretability, mainly the Mamdani model ; and precise fuzzy modeling that is focused on accuracy, mainly the Takagi-Sugeno-Kang TSK model.

Granular Computing pp Cite as. The basic premise of granular computing is that, by reducing precision in our model of a system, we can suppress minor details and focus on the most significant relationships in the system. In this chapter, we will test this premise by defining a granular neural network and testing it on the Iris data set. Our hypothesis is that the granular neural network will be able to learn the Iris data set, but not as accurately as a standard neural network. Our network is a novel neuro-fuzzy systems architecture called the linguistic neural network. The defining characteristic of this network is that all connection weights are linguistic variables, whose values are updated by adding linguistic hedges.

LECTURE NOTES ON SOFT COMPUTING Introduction to Neuro, Fuzzy and Soft Computing, Fuzzy Sets: Basic Definition Why soft computing approach?

## Journal of Autonomous Intelligence

Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required. This well-organized and clearly-presented book offers a detailed understanding of the constituent methodologies underlying neuro-fuzzy and soft computing-an evolving branch of computational intelligence which is aimed at solving real-world decision making, modeling, and control problems. It is intended for use as a text for computer science and computer engineering students. The methodologies covered include "fuzzy set theory, neural networks, data clustering techniques, and several gradient-free stochastic optimization methods-with equal emphasis on their theoretical aspects as well as empirical observations and verifications of various applications in practice.

This course will cover fundamental concepts used in Soft computing. Applications of Soft Computing techniques to solve a number of real life problems will be covered to have hands on practices. In summary, this course will provide exposure to theory as well as practical systems and software used in soft computing. An outline of the course is as follows. You can also download the syllabus for your reference.

*In recent years, several studies using smart methods and soft computing in the field of HVAC systems have been provided. In this paper, we propose a framework which will strengthen the benefits of the Fuzzy Logic FL and Neural Fuzzy NF systems to estimate outdoor temperature.*

По крайней мере Мидж не станет болтать. У нее есть и свои слабости. Она ведь и сама кое-что себе позволяла: время от времени они массировали друг другу спину. Мысли его вернулись к Кармен. Перед глазами возникло ее гибкое тело, темные загорелые бедра, приемник, который она включала на всю громкость, слушая томную карибскую музыку.

*Беккер опустился на колени на холодный каменный пол и низко наклонил голову.*

Коммандер, - сказала. - Это еще не конец. Мы еще не проиграли.

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