Figure 1–1: Soft computing as a composition of fuzzy logic, neural networks and probabilistic reasoning. Intersections include. • neuro-fuzzy. Why expert systems, fuzzy systems, neural networks, and hybrid systems for knowledge engineering and problem solving? Generic and specific AI. 3 1 Fuzzy Systems 8 An introduction to fuzzy logic. Tuning fuzzy control parameters by neural nets Fuzzy rule.

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Neural Networks and Fuzzy Systems: Theory and Applications discusses theories DRM-free; Included format: PDF; ebooks can be used on all reading devices. Integration of fuzzy logic and neural networks . In theory, neural networks, and fuzzy systems are equivalent in that they. The choice of describing engineering applications coincides with the Fuzzy Logic and Neural Network research interests of the readers. Modeling and control of.

Free Preview. This extension of the problem is defined as follows: Koczy and K. We will describe two learning methods for these types of networks: Magrez and P. The term fuzzy logic was used for the first time in

Pedrycz, Why triangular membership functions? Fuzzy Sets and Systems, Vol. The inference engine of a fuzzy expert system operates on a series of production rules and makes fuzzy inferences. There exist two approaches to evaluating relevant production rules. The first is data-driven and is exemplified by the generalized modus ponens.

In this case, available data are supplied to the expert system, which then uses them to evaluate relevant production rules and draw all possible conclusions. An alternative method of evaluation is goal-driven; it is exemplified by the generalized modus tollens form of logical inference. Here, the expert system searches for data specified in the IF clauses of production rules that will lead to the objective; these data are found either in the knowledge base, in the THEN clauses of other production rules, or by querying the user.

Since the data-driven method proceeds from IF clauses to THEN clauses in the chain through the production rules, it is commonly called forward chaining. Similarly, since the goal-driven method proceeds backward from THEN clauses to the IF clauses, in its search for the required data, it is commonly called backward chaining. Backward chaining has the advantage of speed, since only the rules leading to the objective need to be evaluated.

Example 7.

What are the different approaches to evaluating relevant production rules? Explain Mamdani inference mechanism. Explain Tsukamoto inference mechanism.

Explain Sugeno inference mechanism. Explain Larsen inference mechanism. Explain simplified reasoning scheme. Zadeh, Fuzzy logic and approximate reasoning, Synthese, Vol. Zadeh, The concept of a linguistic variable and its application to approximate reasoning I, Information Sciences, Vol.

Zadeh, The concept of a linguistic variable and its application to approximate reasoning II, Information Sciences, Vol. Zadeh, The concept of a linguistic variable and its application to approximate reasoning III, Information sciences, Vol. Mamdani and B. Pedrycz, Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data, Fuzzy Sets and Systems, Vol.

Sanchez and L. K, Turksen, Four methods of approximate reasoning with interval-valued fuzzy sets, International Journal of Approximate Reasoning, Vol. Basu and A. Schwecke, Fuzzy reasoning in a multidimensional space of hypotheses, International Journal of Approximate Reasoning, Vol. Prade, Fuzzy sets in approximate reasoning, Part I: Inference with possibility distributions, Fuzzy Sets and Systems, Vol. Dutta, Approximate spatial reasoning: Pawlak, Rough sets: Theoretical aspects of reasoning about data, Kluwer, Bostan, Chen, A new improved algorithm for inexact reasoning based on extended fuzzy production rules, Cybernetics and Systems, Vol.

Nakanishi, I. Turksen and M. The purpose of the feedback controller is to guarantee a desired response of the output y. The output of the controller which is the input of the system is the control action u. Zadeh was introduced the idea of formulating the control algorithm by logical rules.

In a fuzzy logic controller FLC , the dynamic behaviour of a fuzzy system is characterized by a set of linguistic description rules based on expert knowledge. The expert knowledge is usually of the form IF a set of conditions are satisfied THEN a set of consequences can be inferred.

Since the antecedents and the consequents of these IF-THEN rules are associated with fuzzy concepts linguistic terms , they are often called fuzzy conditional statements. In our terminology, a fuzzy control rule is a fuzzy conditional statement in which the antecedent is a condition in its application domain and the consequent is a control action for the system under control. Basically, fuzzy control rules provide a convenient way for expressing control policy and domain knowledge.

Furthermore, several linguistic variables might be involved in the antecedents and the conclusions of these rules. When this is the case, the system will be referred to as a multi-input-multi- output MIMO fuzzy system.

However, it does not mean that the FLC is a kind of transfer function or difference equation.

A prototypical rule-base of a simple FLC realizing the control law above is listed in the following R1: So, our task is the find a crisp control action z0 from the fuzzy rule-base and from the actual crisp inputs x0 and y0: Furthermore, the output of a fuzzy system is always a fuzzy set, and therefore to get crisp value we have to defuzzify it.

A fuzzification operator has the effect of transforming crisp data into fuzzy sets. In most of the cases we use fuzzy singletons as fuzzifiers fuzzifier x0: A fuzzy control rule Ri: Fuzzy control rules are combined by using the sentence connective also.

Since each fuzzy control rule is represented by a fuzzy relation, the overall behavior of a fuzzy system is characterized by these fuzzy relations. In other words, a fuzzy system can be characterized by a single fuzzy relation which is the combination in question involves the sentence connective also.

Symbolically, if we have the collection of rules R1: To infer the output z from the given process states x, y and fuzzy relations Ri, we apply the compositional rule of inference: In the on-line control, a nonfuzzy crisp control action is usually required. Consequently, one must defuzzify the fuzzy control action output inferred from the fuzzy control algorithm, namely: The most often used defuzzification operators are: Z0 Fig.

Example 8. Consider a fuzzy controller steering a car in a way to avoid obstacles. A suitable defuzzification method would have to choose between different control actions choose one of two triangles in the Figure and then transform the fuzzy set into a crisp value.

Namely, he proved the following theorem Theorem 8. What is fuzzy logic controller? Explain two-input-single-output fuzzy system. Explain Mamdani type of fuzzy logic controller.

What are the various parts of fuzzy logic control system? What are the various defuzification methods? What is the effectivity of fuzzy logic control systems? Zadeh, a rationale for fuzzy control, Journal of dynamical systems, Measurement and Control, Vol. Mamdani and S. King and E. Mamdani, The application of fuzzy control systems to industrial process, Automatica, Vol. Kickert and E. Mamdani, Analysis of a fuzzy logic controller, Fuzzy sets and systems, Vol.

Brase and D. Ray and D. Sugeno, An introductory survey of fuzzy control, Infromation Sciences, Vol. Takagi and M.

Gupta, J. Kiszks and G. Graham and R. Bladwin and N. Guild, Modeling controllers using fuzzy relations, Kybernets, Vol. Buckley, Theory of the fuzzy controller: Tanaka and M.

Abdelnour, C. Chang, F. Huang and J. Boullama and A. Kandel , L. Li and Z. Yager, A general approach to rule aggregation in fuzzy logic control, Applied Intelligence, Vol. Wong, C. Chou and D.

Ragot and M. Chung and J. Chen and L. Kiupel and P. Yagar, Three models of fuzzy logic controllers, Cybernetics and Systems, Vol.

Pedrycz, Fuzzy controllers: Han and V.

Altrock, H. Arend, B. Krause, C. Steffess and E. Yager, and D. Bugarin, S. Barro and R. Here is a list of general observations about fuzzy logic: Fuzzy logic is conceptually easy to understand.

The mathematical concepts behind fuzzy reasoning are very simple. Fuzzy logic is flexible. Fuzzy logic is tolerant of imprecise data. Everything is imprecise if you look closely enough, but more than that, most things are imprecise even on careful inspection. Fuzzy reasoning builds this understanding into the process rather than tacking it onto the end. Fuzzy logic can model nonlinear functions of arbitrary complexity.

You can create a fuzzy system to match any set of input-output data. Fuzzy logic can be built on top of the experience of experts. In direct contrast to neural networks, which take training data and generate opaque, impenetrable models, fuzzy logic lets you rely on the experience of people who already understand your system. Fuzzy logic can be blended with conventional control techniques. In many cases fuzzy systems augment themand simplify their implementation. Fuzzy logic is based on natural language.

The basis for fuzzy logic is the basis for human communication. This observation underpins many of the other statements about fuzzy logic.

Natural language, that which is used by ordinary people on a daily basis, has been shaped by thousands of years of human history to be convenient and efficient. Sentences written in ordinary language represent a triumph of efficient communication. We are generally unaware of this because ordinary language is, of course, something we use every day. Since fuzzy logic is built. Why should this be useful? The answer is commercial and practical. Commercially, fuzzy logic has been used with great success to control machines and consumer products.

In the right application fuzzy logic systems are simple to design, and can be understood and implemented by non- specialists in control theory. In most cases someone with a intermediate technical background can design a fuzzy logic controller.

The control system will not be optimal but it can be acceptable. Control engineers also use it in applications where the on-board computing is very limited and adequate control is enough. Fuzzy logic is not the answer to all technical problems, but for control problems where simplicity and speed of implementation is important then fuzzy logic is a strong candidate. A cross section of applications that have successfully used fuzzy control includes: Fuzzy logic is not a cure-all. When should you not use fuzzy logic?

If you find it is not convenient, try something else. If a simpler solution already exists, use it. Fuzzy logic is the codification of common sense-use common sense when you implement it and you will probably make the right decision. Many controllers, for example, do a fine job without using fuzzy logic. However, if you take the time to become familiar with fuzzy logic, you will see it can be a very powerful tool for dealing quickly and efficiently with imprecision and non- linearity.

However, many people died or injured because of traffic accidents all over the world. When statistics are investigated India is the most dangerous country in terms of number of traffic accidents among Asian countries.

Many reasons can contribute these results, which are mainly driver fault, lack of infrastructure, environment, literacy, weather conditions etc.

However, agree that this rate is higher in India since many traffic accidents are not recorded, for example single vehicle accidents or some accidents without injury or fatality. In this study, using fuzzy logic method, which has increasing usage area in Intelligent Transportation Systems ITS , a model was developed which would obtain to prevent the vehicle pursuit distance automatically. Using velocity of vehicle and pursuit distance that can be measured with a sensor on vehicle a model has been established to brake pedal slowing down by fuzzy logic.

This goal forms the background for the present traffic safety program. The program is partly based on the assumption that high speed contributes to accidents.

Many researchers support the idea of a positive correlation between speed and traffic accidents. One way to reduce the number of accidents is to reduce average speeds.

Speed reduction can be accomplished by police surveillance, but also through physical obstacles on the roads. Obstacles such as flower pots, road humps, small circulation points and elevated pedestrian crossings are frequently found in many residential areas around India. However, physical measures are not always appreciated by drivers. These obstacles can cause damages to cars, they can cause difficulties for emergency vehicles, and in winter these obstacles can reduce access for snow clearing vehicles.

The major objectives with ITS are to achieve traffic efficiency, by for instance redirecting traffic, and to increase safety for drivers, pedestrians, cyclists and other traffic groups. Input data are most often crisp values. The task of the fuzzifier is to map crisp numbers into fuzzy sets cases are also encountered where inputs are fuzzy variables described by fuzzy membership functions.

A set of a large number of rules of the type: If premise Then conclusion is called a fuzzy rule base. In fuzzy rule-based systems, the rule base is formed with the assistance of human experts; recently, numerical data has been used as well as through a combination of numerical data-human experts. An interesting case appears when a combination of numerical information obtained from measurements and linguistic information obtained from human experts is used to form the fuzzy rule base.

In this case, rules are extracted from numerical data in the first step. In the next step this fuzzy rule base can but need not be supplemented with the rules collected from human experts.

The inference engine of the fuzzy logic maps fuzzy sets onto fuzzy sets. A large number of different inferential procedures are found in the literature. In most papers and practical engineering applications, minimum inference or product inference is used. During defuzzification, one value is chosen for the output variable.

The literature also contains a large number of different defuzzification procedures. The final value chosen is most often either the value corresponding to the highest grade of membership or the coordinate of the center of gravity.

The general structure of the model is shown in Fig. Membership functions are given in Figures 9. Because of the fact that current distance sensors perceive approximately m distance, distance membership function is used m scale. Brake rate membership function is used scale for expressing percent type. Low Medium High 1 0. Fuzzy Allocation Map rules of the model was constituted for membership functions whose figures are given on Table It is important that the rules were not completely written for all probability.

Figure 6 shows that the relationship between inputs, speed and distance, and brake rate. Table 9. For this model, various alternatives are able to cross- examine using the developed model. Many reasons can contribute these results for example mainly driver fault, lack of infrastructure, environment, weather conditions etc. In this study, a model was established for estimation of brake rate using fuzzy logic approach.

Car brake rate is estimated using the developed model from speed and distance data. So, it can be said that this fuzzy logic approach can be effectively used for reduce to traffic accident rate.

This model can be adapted to vehicles. These decisions could be the determination of a flow rate for a chemical process or a drug dosage in medical practice. The form of the control model also determines the appropriate level of precision in the result obtained. Numerical models provide high precision, but the complexity or non-linearity of a process may make a numerical model unfeasible.

In these cases, linguistic models provide an alternative. Here the process is described in common language. The linguistic model is built from a set of if-then rules, which describe the control model. Although Zadeh was attempting to model human activities, Mamdani showed that fuzzy logic could be used to develop operational automatic control systems.

Much of the fuzzy literature uses set theory notation, which obscures the ease of the formulation of a fuzzy controller. Although the controllers are simple to construct, the proof of stability and other validations remain important topics. The outline of fuzzy operations will be shown here through the design of a familiar room thermostat. A fuzzy variable is one of the parameters of a fuzzy model, which can take one or more fuzzy values, each represented by a fuzzy set and a word descriptor.

The room temperature is the variable shown in Fig. Three fuzzy sets: The power of a fuzzy model is the overlap between the fuzzy values. A single temperature value at an instant in time can be a member of both of the overlapping sets. In conventional set theory, an object in this case a temperature value is either a member of a set or it is not a member. In fuzzy logic, the boundaries between sets are blurred.

In the overlap region, an object can be a partial member of each of the overlapping sets. The blurred set boundaries give fuzzy logic its name. By admitting multiple possibilities in the model, the linguistic imprecision is taken into account. The membership functions defining the three fuzzy sets shown in Fig. There are no constraints on the specification of the form of the membership distribution. The Gaussian form from statistics has been used, but the triangular form is commonly chosen, as its computation is simple.

The number of values and the range of actual values covered by each one are also arbitrary. Finer resolution is possible with additional sets, but the computation cost increases. As the complexity of a system increases, our ability to make precise and yet significant statements about its behaviour diminishes until a threshold is reached beyond which precision and significance or relevance become almost mutually exclusive characteristics.

The operation of a fuzzy controller proceeds in three steps. The first is fuzzification, where measurements are converted into memberships in the fuzzy sets.

The second step is the application of the linguistic model, usually in the form of if-then rules. Finally the resulting fuzzy output is converted back into physical values through a defuzzfication process. The membership functions are used to calculate the memberships in all of the fuzzy sets.

The fuzzy inference is extended to include the uncertainty due to measurement error as well as the vagueness in the linguistic descriptions. In Fig. The minimum operation yields the overlap region of the two sets and the maximum operation gives the highest membership in the overlap.

It is interesting to note that there is no requirement that the sum of all memberships be 1. These use the measured state of the process, the rule antecedents, to estimate the extent of control action, the rule consequents. Although each rule is simple, there must be a rule to cover every possible combination of fuzzy input values.

Thus, the simplicity of the rules trades off against the number of rules. For complex systems the number of rules required may be very large. The rules needed to describe a process are often obtained through consultation with workers who have expert knowledge of the process operation. The rules can include both the normal operation of the process as well as the experience obtained through upsets and other abnormal conditions.

Exception handling is a particular strength of fuzzy control systems. For very complex systems, the experts may not be able to identify their thought processes in sufficient detail for rule creation. Rules may also be generated from operating data by searching for clusters in the input data space.

A simple temperature control model can be constructed from the example of Fig. Rule 1 transfers the 0. Similar values from rules 2 and 3 are 0.

When several rules give membership values for the same output set, Mamdani used the maximum of the membership values. The result for the three rules is then 0. The rules presented in the above example are simple yet effective. To extend these to more complex control models, compound rules may be formulated. For example, if humidity was to be included in the room temperature control example, rules of the form: These can be used directly where the membership values are viewed as the strength of the recommendations provided by the rules.

It is possible that several outputs are recommended and some may be contradictory e. In automatic control, one physical value of a controller output must be chosen from multiple recommendations. In decision support systems, there must be a consistent method to resolve conflict and define an appropriate compromise.

Defuzzification is the process for converting fuzzy output values to a single value or final decision. Two methods are commonly used. The first is the maximum membership method. All of the output membership functions are combined using the OR operator and the position of the highest membership value in the range of the output variable is used as the controller output. This method fails when there are two or more equal maximum membership values for different recommendations. Here the method becomes indecisive and does not produce a satisfactory result.

These integrals are taken over the entire range of the output. By taking the center of gravity, conflicting rules essentially cancel and a fair weighting is obtained. The output values used in the thermostat example are singletons.

Singletons are fuzzy values with a membership of 1. With singletons, the center of gravity equation integrals become a simple weighted average. The sum of the membership functions was normalized by the denominator of the center of gravity calculation. The rules are generated a priori from expert knowledge or from data through system identification methods. Input membership functions are based on estimates of the vagueness of the descriptors used. Output membership functions can be initially set, but can be revised for controller tuning.

Once these are defined, the operating procedures for the calculations are well set out. Measurement data are converted to memberships through fuzzification procedures. The rules are applied using formalized operations to yield memberships in output sets. Finally, these are combined through defuzzification to give a final control output. Efforts to develop automated fruit classification systems have been increasing recently due to the drawbacks of manual grading such as subjectivity, tediousness, labor requirements, availability, cost and inconsistency.

However, applying automation in agriculture is not as simple as automating the industrial operations. There are two main differences. First, the agricultural environment is highly variable, in terms of weather, soil, etc. Second, biological materials, such as plants and commodities, display high variation due to their inherent morphological diversity. Techniques used in industrial applications, such as template matching and fixed object modeling are unlikely to produce satisfactory results in the classification or control of input from agricultural products.

Therefore, self-learning techniques such as neural networks NN and fuzzy logic FL seem to represent a good approach. It provides a means of translating qualitative and imprecise information into quantitative linguistic terms. Fuzzy logic is a non- parametric classification procedure, which can infer with nonlinear relations between input and output categories, maintaining flexibility in making decisions even on complex biological systems.

Fuzzy logic was successfully used to determine field trafficability, to decide the transfer of dairy cows between feeding groups, to predict the yield for precision farming, to control the start-up and shut- down of food extrusion processes, to steer a sprayer automatically, to predict corn breakage, to manage crop production, to reduce grain losses from a combine, to manage a food supply and to predict peanut maturity.

The main purpose of this study was to investigate the applicability of fuzzy logic to constructing and tuning fuzzy membership functions and to compare the accuracies of predictions of apple quality by a human expert and the proposed fuzzy logic model.

Grading of apples was performed in terms of characteristics such as color, external defects, shape, weight and size. Readings of these properties were obtained from different measurement apparatuses, assuming that the same measurements can be done using a sensor fusion system in which measurements of features are collected and controlled automatically.

The following objectives were included in this study: To design a FL technique to classify apples according to their external features developing effective fuzzy membership functions and fuzzy rules for input and output variables based on quality standards and expert expectations. To compare the classification results from the FL approach and from sensory evaluation by a human expert.

To establish a multi-sensor measuring system for quality features in the long term. Only defects occurring naturally or forcedly on apple surfaces during the growing season and handling operations were accounted for in terms of number and size, ignoring their age.

Scars, bitter pit, leaf roller, russeting, punctures and bruises were among the defects encountered on the surfaces of Golden Delicious apples. In addition to these defects, a size defect lopsidedness was also measured by taking the ratio of maximum height of the apple to the minimum height. Color was measured using a CR Minolta colorimeter in the domain of L, a and b, where L is the lightness factor and a and b are the chromaticity coordinates.

Sizes of surface defects natural and bruises on apples were determined using a special figure template, which consisted of a number of holes of different diameters. Size defects were determined measuring the maximum and minimum heights of apples using a Mitutoya electronic caliper.

Maximum circumference measurement was performed using a Cranton circumference measuring device. Weight was measured using an electronic scale. Programming for fuzzy membership functions, fuzzification and defuzzification was done in Matlab. A total of golden delicious apples were graded first by a human expert and then by the proposed fuzzy logic approach. The USDA standards for apple quality explicitly define the quality criteria so that it is quite straightforward for an expert to follow up and apply them.

Extremely large or small apples were already excluded by the handling personnel. In addition, 21 of the apples were harvested before the others and kept for 15 days at room temperature for the same purpose of creating a variation in the appearance of the apples to be tested. Although it was measured at the beginning, firmness was excluded from the evaluation, as it was difficult for the human expert to quantify it nondestructively.

After the combinations of features given in the above equations, input variables were reduced to 3 defect, size and color.

Fuzzy logic techniques were applied to classify apples after measuring the quality features. The grading performance of fuzzy logic proposed was determined by comparing the classification results from FL and the expert.

A trial and error approach was used to develop membership functions. Although triangular and trapezoidal functions were used in establishing membership functions for defects and color Fig. Yellow Greenish-yellow Green 1 90 95 Small Medium Big 1 6. The rules used in the evaluations of apple quality are given in Table 9. Two of the rules used to evaluate the quality of Golden Delicious apples are given below: If the color is greenish, there is no defect, and it is a well formed large apple, then quality is very good rule Q1,1 in Table 9.

Finally, D1 represents a low amount of defects desired , while D2 and D3 represent moderate medium and high bad amounts of defects, respectively. The second subscript of Q shows the number of rules for the particular quality group, which ranges from 1 to 17 for the bad quality group. If the color is pure yellow overripe , there are a lot of defects, and it is a badly formed small apple, then quality is very bad rule Q3,17 in Table 9. A fuzzy set is defined by the expression below: Degree of membership for any set ranges from 0 to1.

A value of 1. If there are three subgroups of size, then three memberships are required to express the size values in a fuzzy rule. The minimum method chooses the most certain output among all the membership degrees.

An example of the fuzzy AND the minimum method used in if-then rules to form the Q11 quality group in Table 9. These functions can be defined either by linguistic terms or numerical ranges, or both. The membership function used in this study for defect quality in general is given in equation 9. The membership function for high amounts of defects, for instance, was formed as given below: It was also seen that color, defects and size are three important criteria in apple classification.

However, variables such as firmness, internal defects and some other sensory evaluations, in addition to the features mentioned earlier, could increase the efficiency of decisions made regarding apple quality.

First the problem is solved using the conventional non-fuzzy method, writing MATLAB commands that spell out linear and piecewise-linear relations. Then, the same system is solved using fuzzy logic. Consider the tipping problem: Given a number between 0 and 10 that represents the quality of service at a restaurant where 10 is excellent , what should the tip be?

This problem is based on tipping as it is typically practiced in the United States. An average tip for a meal in the U. Now our relation looks like this: The formula does what we want it to do, and it is pretty straight forward. However, we may want the tip to reflect the quality of the food as well.

This extension of the problem is defined as follows: Given two sets of numbers between 0 and 10 where 10 is excellent that respectively represent the quality of the service and the quality of the food at a restaurant, what should the tip be? Suppose we try: Suppose you want the service to be a more important factor than the food quality.

Suppose you want more of a flat response in the middle, i. This, in turn, means that those nice linear mappings no longer apply. We can still salvage things by using a piecewise linear construction Fig. You can string together a simple conditional statement using breakpoints like this: If we extend this to two dimensions Fig.

It was a little tricky to code this correctly, and it is definitely not easy to modify this code in the future. Moreover, it is even less apparent how the algorithm works to someone who did not witness the original design process. If we make a list of what really matters in this problem, we might end up with the following rule descriptions: If service is poor, then tip is cheap 2. If service is good, then tip is average 3. If service is excellent, then tip is generous The order in which the rules are presented here is arbitrary.

It does not matter which rules come first. If food is rancid, then tip is cheap 5. If food is delicious, then tip is generous In fact, we can combine the two different lists of rules into one tight list of three rules like so: If service is poor or the food is rancid, then tip is cheap 2. If service is excellent or food is delicious, then tip is generous These three rules are the core of our solution.

And coincidentally, we have just defined the rules for a fuzzy logic system. The details of the method do not really change much from problem to problem - the mechanics of fuzzy logic are not terribly complex. What matters is what we have shown in this preliminary exposition: The picture above was generated by the three rules above.

We found a piecewise linear relation that solved the problem. It worked, but it was something of a nuisance to derive, and once we wrote it down as code, it was not very easy to interpret. Also, we were able to add two more rules to the bottom of the list that influenced the shape of the overall output without needing to undo what had already been done.

In other words, the subsequent modification was pretty easy. Moreover, by using fuzzy logic rules, the maintenance of the structure of the algorithm decouples along fairly clean lines. The notion of an average tip might change from day to day, city to city, country to country, but the underlying logic the same: You can recalibrate the method quickly by simply shifting the fuzzy set that defines average without rewriting the fuzzy rules.

You can do this sort of thing with lists of piecewise linear functions, but there is a greater likelihood that recalibration will not be so quick and simple. For example, here is the piecewise linear tipping problem slightly rewritten to make it more generic.

It performs the same function as before, only now the constants can be easily changed. What we are doing here is not that complicated. True, we can fight this tendency to be obscure by adding still more comments, or perhaps by trying to rewrite it in slightly more self-evident ways, but the medium is not on our side. The truly fascinating thing to notice is that if we remove everything except for three comments, what remain are exactly the fuzzy rules we wrote down before: Why use fuzzy logic?

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The architecture of each network is based on very similar building blocks, which perform the processing.

In this chapter we first discuss these processing units and discuss different network topologies. Learning strategies as a basis for an adaptive system will be presented in the last section. The human brain consists of nearly neurons nerve cells of different types. In a typical neuron, one can find nucleus with which the connections with other neurons are made through a network of fibres called dendrites.

Extending out from the nucleus is the axon, which transmits, by means of complex chemical process, electric potentials to the neurons, with which the axon is connected to Fig.

In this way, the message is transferred from one neuron to the other. In the neural network, the neurons or the processing units may have several input paths corresponding to the dendrites. The units combine usually by a simple summation, that is, the weighted values of these paths Fig.

The weighted value is passed to the neuron, where it is modified by threshold function such as sigmoid function. The modified value is directly presented to the next neuron. A set of major aspects of a parallel distributed model can be distinguished as: Figure Apart from this processing, a second task is the adjustment of the weights. The system is inherently parallel in the sense that many units can carry out their computations at the same time.

Within neural systems it is useful to distinguish three types of units: During operation, units can be updated either synchronously or asynchronously. With synchronous updating, all units update their activation simultaneously; with asynchronous updating, each unit has a usually fixed probability of updating its activation at a time t, and usually only one unit will be able to do this at a time. In some cases the latter model has some advantages. The total input to unit k is simply the weighted sum of the separate outputs from each of the connected units plus a bias or offset term qk: In some cases more complex rules for combining inputs are used, in which a distinction is made between excitatory and inhibitory inputs.

We call units with a propagation rule Although these units are not frequently used, they have their value for gating of input, as well as implementation of lookup tables. We need a function Fk which takes the total input sk t and the current activation yk t and produces a new value of the activation of the unit k: Generally, some sort of threshold function is used: For this smoothly limiting function often a sigmoid S-shaped function like i i i Sgn Semi-linear Sigmoid Fig.

In some cases, the output of a unit can be a stochastic function of the total input of the unit. In that case the activation is not deterministically determined by the neuron input, but the neuron input determines the probability p that a neuron get a high activation value: In all networks we consider that the output of a neuron is to be identical to its activation level. This section focuses on the pattern of connections between the units and the propagation of data.

As for this pattern of connections, the main distinction we can make is between: The data processing can extend over multiple layers of units, but no feedback connections are present, that is, connections extending from outputs of units to inputs of units in the same layer or previous layers.

Contrary to feed-forward networks, the dynamical properties of the network are important. In some cases, the activation values of the units undergo a relaxation process such that the network will evolve to a stable state in which these activations do not change anymore. In other applications, the change of the activation values of the output neurons are significant, such that the dynamical behavior constitutes the output of the network.

Classical examples of feed-forward networks are the Perceptron and Adaline, which will be discussed in the next chapter. Examples of recurrent networks have been presented by Anderson, Kohonen, and Hopfield and will be discussed in subsequent chapters. Various methods to set the strengths of the connections exist. One way is to set the weights explicitly, using a priori knowledge.

These are: These input-output pairs can be provided by an external teacher, or by the system, which contains the network self-supervised. Unlike the supervised learning paradigm, there is no a priori set of categories into which the patterns are to be classified rather the system must develop its own representation of the input stimuli.

Virtually all learning rules for models of this type can be considered as a variant of the Hebbian learning rule. The basic idea is that if two units j and k are active simultaneously, their interconnection must be strengthened. Another common rule uses not the actual activation of unit k but the difference between the actual and desired activation for adjusting the weights: This is often called the Widrow-Hoff rule or the delta rule, and will be discussed in the next chapter.

Many variants often very exotic ones have been published the last few years.

In the next chapters some of these update rules will be discussed. Note that not all symbols are meaningful for all networks, and that in some cases subscripts or superscripts may be left out e. Vectors are indicated with a bold non-slanted font: Since there is no need to do otherwise, we consider the output and the activation value of a unit to be one and the same thing.

That is, the output of each neuron equals its activation value. Bias, offset, threshold: These terms all refer to a constant i.

They may be used interchangeably, although the latter two terms are often envisaged as a property of the activation function. Furthermore, this external input is usually implemented and can be written as a weight from a unit with activation value 1. Number of layers: In a feed-forward network, the inputs perform no computation and their layer is therefore not counted.

Thus a network with one input layer, one hidden layer, and one output layer is referred to as a network with two layers. This convention is widely though not yet universally used. Representation vs. When using a neural network one has to distinguish two issues which influence the performance of the system.

The first one is the representational power of the network, the second one is the learning algorithm. The representational power of a neural network refers to the ability of a neural network to represent a desired function.

Because a neural network is built from a set of standard functions, in most cases the network will only approximate the desired function, and even for an optimal set of weights the approximation error is not zero. The second issue is the learning algorithm. Given that there exist a set of optimal weights in the network, is there a procedure to iteratively find this set of weights? What are the major aspects of parallel distributed model?

Explain the biological neural network. What are the basic components of artificial neural network? What are the network topologies? What are the various activation function? Explain them schematically. What are the paradigms of neural network learning? Wiley, Jovitz, G. Jacobi, G. Goldstein, Washington, D.

Spartan Books, PP. Anderson, Neural models with cognitive implications. LaBerge and S. Samuels Eds. Hillsdale, NJ: Erlbaum, Kohonen, Associative Memory: Feldman, and D. Ballard, Connectionist models and their properties, Cognitive Science, Vol. Neural networks and physical systems with emergent collective computational abilities, Proceedings of the National Academy of Sciences, Vol. Rumelhart and J. Neural Networks and Fuzzy Systems: Theory and Applications discusses theories that have proven useful in applying neural networks and fuzzy systems to real world problems.

The book includes performance comparison of neural networks and fuzzy systems using data gathered from real systems. Topics covered include the Hopfield network for combinatorial optimization problems, multilayered neural networks for pattern classification and function approximation, fuzzy systems that have the same functions as multilayered networks, and composite systems that have been successfully applied to real world problems.

The author also includes representative neural network models such as the Kohonen network and radial basis function network. New fuzzy systems with learning capabilities are also covered. The advantages and disadvantages of neural networks and fuzzy systems are examined. The performance of these two systems in license plate recognition, a water purification plant, blood cell classification, and other real world problems is compared. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser.

Computer Science Artificial Intelligence. Free Preview.