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1. Unit -5 Applications of Hybrid Systems Hybrid Systems -Neural Networks, Fuzzy Logic - LR-Type Fuzzy Numbers - Fuzzy Neuron – Fuzzy BP Architecture - Learning in Fuzzy BP- Inference by Fuzzy BP - Fuzzy Art Map: A Brief Introduction- Soft Computing Tools - Fuzzy Logic Controller.

2. Hybrid Systems Hybrid systems employ more than one technology to solve a problem. Hybridization of technologies can have pitfalls and therefore need to be done with care. If one technology can solve a problem then a hybrid technology ought to be used only if its application results in a better solution. Hybrid systems have been classified as Sequential , Auxiliary and Embedded. In Sequential hybrid system, the technologies are used in pipelining fashion. In Auxiliary hybrid system, one technology calls the other technology as subroutine. In Embedded hybrid system, the technologies participating appear to be fused totally. Neural Networks and Fuzzy logic represents two distinct methodologies to deal with uncertainty. Each of these has its own merits and demerits

3. Typical Hybrid Systems The Systems considered are listed below. 1. Genetic algorithm based back propagation network (Neuro Genetic Hybrid) 2. Fuzzy back propagation network (Neuro – Fuzzy Hybrid with Multilayer Feed forward Network as the host architecture) 3. Simplified Fuzzy ARTMAP (Neuro – Fuzzy Hybrid with Recurrent Network as the host architecture) 4. Fuzzy Associative Memory ( Neuro – Fuzzy Hybrid with single layer Feed forward architecture) 5. Fuzzy logic controlled Genetic algorithm (Fuzzy – Genetic Hybrid)

4. Characteristics of Hybrid Systems The ability to combine multiple technologies or methodologies to provide a solution that cannot be achieved by any single technology or methodology alone. The ability to adapt to changing circumstances or environments, making them more flexible and efficient. The ability to optimize performance and minimize costs by using the best technology or methodology for each task. The ability to improve reliability and reduce risk by providing redundancy and fault tolerance.

5. Neural Networks Neural networks are artificial systems that were inspired by biological neural networks. These systems learn to perform tasks by being exposed to various datasets and examples without any task-specific rules. The idea is that the system generates identifying characteristics from the data they have been passed without being programmed with a pre-programmed understanding of these datasets. Components of a typical neural network involve neurons, connections which are known as synapses, weights, biases, propagation function, and a learning rule. Propagation computes the input and outputs the output and sums the predecessor neurons function with the weight.The learning of neural network basically refers to the adjustment in the free parameters i.e. weights and bias.

6. Types of Neural Networks There are seven types of neural networks that can be used. The first is a multilayer perceptron which has three or more layers and uses a nonlinear activation function. The second is the convolutional neural network that uses a variation of the multilayer perceptrons . The third is the recursive neural network that uses weights to make structured predictions. The fourth is a recurrent neural network that makes connections between the neurons in a directed cycle. The long short-term memory neural network uses the recurrent neural network architecture and does not use an activation function. The final two are sequence-to-sequence modules which use two recurrent networks and shallow neural networks which produce a vector space from an amount of text.

7. Fuzzy Logic Fuzzy Logic is a mathematical framework for dealing with uncertainty and imprecision. It allows for reasoning with vague or uncertain information and can be used to model complex systems. Fuzzy Logic is based on the concept of fuzzy sets, which are sets that allow for partial membership. Fuzzy Logic is often used in control systems, where it can provide more robust and flexible control than traditional methods. In the Boolean system, only two possibilities (0 and 1) exist, where 1 denotes the absolute truth value and 0 denotes the absolute false value. But in the fuzzy system, there are multiple possibilities present between the 0 and 1, which are partially false and partially true.

8. LR-Type Fuzzy Numbers LR-type fuzzy numbers are a type of fuzzy numbers that are used to represent uncertain or imprecise information in a mathematical way. They are characterized by three parameters, namely the left slope (L), the right slope (R), and the peak (P) of the membership function. The membership function of an LR-type fuzzy number has a trapezoidal shape, with a left-hand slope (L) and a right-hand slope (R) that represent the degree of membership of the number in the lower and upper intervals, respectively. The peak (P) of the membership function represents the degree of membership in the central interval, and is typically set to 1.

9. LR-Type Fuzzy Numbers

10. Example LR-type fuzzy numbers can be represented mathematically as follows: { (x - a) / (b - a), a <= x < p μ(x) = { 1, p <= x <= q { (c - x) / (c - b), q < x <= c where a, b, c are the left end, the center, and the right end of the LR-type fuzzy number, respectively. LR-type fuzzy numbers are useful in many applications, such as decision-making, pattern recognition, and control systems, where imprecise or uncertain information needs to be modeled and analyzed.

11. LR-Type Fuzzy Numbers Fuzzy model of artificial neuron can be constructed by using fuzzy operations at single neuron level . Instead of weighted sum of inputs, more general aggregation function is used • Fuzzy union, fuzzy intersection and, more generally, s-norms and t-norms can be used as an aggregation function for the weighted input to an artificial neuron.

12. OR Fuzzy Neuron Transfer function g is linear

13. AND Fuzzy Neuron In the generalized forms based on t-norms, operators other than min and max can be used such as algebraic and bounded products and sums

14. Fuzzy BP Architecture Fuzzy BP (backpropagation) architecture is a type of neural network architecture that combines fuzzy logic and backpropagation algorithms. Fuzzy logic is a mathematical approach for dealing with uncertain or vague information, while backpropagation is a popular machine learning algorithm used for training neural networks. In the fuzzy BP architecture, the input values are first fuzzified using fuzzy logic, which assigns a degree of membership to each input value based on its similarity to different linguistic terms. These fuzzified values are then passed through the neural network, which consists of multiple layers of interconnected nodes.

15. Fuzzy BP Architecture Fuzzy Back Propagation Network (BP) is a 3-layered feed forward architecture. The 3 layers are: input layer, hidden layer and output layer. Considering a configuration of ℓ-input neurons, m-hidden neurons and n-output neurons, the architecture of Fuzzy BP is shown below.

16. Learning in Fuzzy BP

17. Learning in Fuzzy BP

18. Inference by Fuzzy BP Inference by Fuzzy BP (backpropagation) is a process in which the fuzzy BP architecture is used to make predictions or decisions based on input data that is uncertain or imprecise. The process of inference by Fuzzy BP involves the following steps: Fuzzification : The input data is fuzzified using fuzzy logic to convert it into linguistic terms that can be easily processed by the neural network. Each input value is assigned a degree of membership to different linguistic terms based on its similarity to those terms. Forward propagation : The fuzzified input values are then passed through the neural network, which consists of multiple layers of interconnected nodes. Each node performs a weighted sum of its inputs, applies an activation function, and passes the result to the next layer.

19. Inference by Fuzzy BP Backpropagation: The output of the neural network is compared with the desired output, and the error is calculated. The backpropagation algorithm is then used to adjust the weights and biases of the nodes in the network based on the error, with the goal of minimizing the error between the actual and desired outputs. Defuzzification: The final output of the neural network is obtained by defuzzifying the output of the last layer, which represents the degree of membership of the output value to different linguistic terms. The process of inference by Fuzzy BP is particularly useful in situations where the input data is uncertain or imprecise, as it can handle this type of data more effectively than traditional neural networks. It has been used in various applications, such as decision-making, control systems, and pattern recognition.

20. Fuzzy Art Map ART is a neural network topology whose dynamics are based on Adaptive Resonance Theory (ART). ART networks follow both supervised and unsupervised algorithms. The Unsupervised ARTs are similar to many iterative clustering algorithms where "nearest" and "closer" are modified slightly by introducing the concept of "resonance" . Resonance is just a matter of being within a certain threshold of a second similarity measure. The Supervised ART algorithms that are named with the suffix "MAP" , as ARTMAP. Here the algorithms cluster both the inputs and targets and associate two sets of clusters. The basic ART system is an unsupervised learning model.

21. Fuzzy Art Map The ART systems have many variations : ART1, ART2, Fuzzy ART, ARTMAP. ART1: The simplest variety of ART networks, accepting only binary inputs. ART2 : It extends network capabilities to support continuous inputs. ARTMAP : Also known as Predictive ART. It combines two slightly modified ART-1 or ART-2 units into a supervised learning structure. Here, the first unit takes the input data and the second unit takes the correct output data, then used to make the minimum possible adjustment of the vigilance parameter in the first unit in order to make the correct classification. The Fuzzy ARTMAP model is fuzzy logic based computations incorporated in the ARTMAP model. Fuzzy ARTMAP is neural network architecture for conducting supervised learning in a multidimensional setting. When Fuzzy ARTMAP is used on a learning problem, it is trained process.

22. Fuzzy Art Map

23. Soft Computing Tools Soft Computing tools are mathematical and computational models and algorithms that are used to implement Soft Computing systems. Some of the commonly used Soft Computing tools are: Fuzzy Logic : Fuzzy Logic is a mathematical framework that deals with uncertainty and vagueness in data. It is used to model the uncertain relationships between input and output variables, and to make decisions based on imprecise or incomplete information. Neural Networks: Neural Networks are computational models inspired by the structure and function of the human brain. They are used for pattern recognition, classification, and prediction tasks.

24. Soft Computing Tools Evolutionary Algorithms : Evolutionary Algorithms are a family of optimization algorithms that are based on the principles of natural selection and evolution. They are used to optimize complex systems and to find optimal solutions to problems. Swarm Intelligence: Swarm Intelligence is a computational paradigm inspired by the collective behavior of social insects, such as ants, bees, and termites. It is used to solve optimization and decision-making problems that require distributed and decentralized systems. Rough Sets: Rough Sets is a mathematical framework that deals with uncertainty and vagueness in data by dividing it into sets with crisp boundaries. It is used for feature selection and data reduction.

25. Fuzzy Logic Controller Fuzzy logic control (FLC) is the most active research area in the application of fuzzy set theory, fuzzy reasoning, and fuzzy logic. The application of FLC extends from industrial process control to biomedical instrumentation and securities. Following are some reasons of using Fuzzy Logic in Control Systems − While applying traditional control, one needs to know about the model and the objective function formulated in precise terms. This makes it very difficult to apply in many cases. By applying fuzzy logic for control we can utilize the human expertise and experience for designing a controller. The fuzzy control rules, basically the IF-THEN rules, can be best utilized in designing a controller.

26. Architecture of Fuzzy Logic Controller

27. Fuzzy Logic Controller Followings are the major components of the FLC as shown in the above figure − Fuzzifier − The role of fuzzifier is to convert the crisp input values into fuzzy values. Fuzzy Knowledge Base − It stores the knowledge about all the input-output fuzzy relationships. It also has the membership function which defines the input variables to the fuzzy rule base and the output variables to the plant under control. Fuzzy Rule Base − It stores the knowledge about the operation of the process of domain. Inference Engine − It acts as a kernel of any FLC. Basically it simulates human decisions by performing approximate reasoning. Defuzzifier − The role of defuzzifier is to convert the fuzzy values into crisp values getting from fuzzy inference engine.

28. Fuzzy Logic Controller Following are the steps involved in designing FLC − Identification of variables − Here, the input, output and state variables must be identified of the plant which is under consideration. Fuzzy subset configuration − The universe of information is divided into number of fuzzy subsets and each subset is assigned a linguistic label. Obtaining membership function − Now obtain the membership function for each fuzzy subset that we get in the above step. Fuzzy rule base configuration − Now formulate the fuzzy rule base by assigning relationship between fuzzy input and output. Fuzzification − The fuzzification process is initiated in this step. Combining fuzzy outputs − By applying fuzzy approximate reasoning, locate the fuzzy output and merge them. Defuzzification − Finally, initiate defuzzification process to form a crisp output.