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    Soft Computing: Fundamentals and Applications
    Soft Computing: Fundamentals and Applications
    Soft Computing: Fundamentals and Applications
    Ebook146 pages1 hour

    Soft Computing: Fundamentals and Applications

    By Fouad Sabry

    ()

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    About this ebook

    What Is Soft Computing


    The term "soft computing" refers to a collection of computer programming techniques, such as neural networks, fuzzy logic, and evolutionary algorithms.These algorithms can handle imprecision, uncertainty, partial truth, and approximation without causing any problems.It is in contrast to hard computing, which refers to the use of algorithms to find solutions to problems that are both right and optimal.


    How You Will Benefit


    (I) Insights, and validations about the following topics:


    Chapter 1: Soft computing


    Chapter 2: Fuzzy logic


    Chapter 3: Evolutionary algorithm


    Chapter 4: Machine learning


    Chapter 5: Computational intelligence


    Chapter 6: Fuzzy concept


    Chapter 7: Quantum neural network


    Chapter 8: Fuzzy mathematics


    Chapter 9: Evolving intelligent system


    Chapter 10: Adaptive neuro fuzzy inference system


    (II) Answering the public top questions about soft computing.


    (III) Real world examples for the usage of soft computing in many fields.


    (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of soft computing' technologies.


    Who This Book Is For


    Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of soft computing.

    LanguageEnglish
    PublisherOne Billion Knowledgeable
    Release dateJul 3, 2023
    Soft Computing: Fundamentals and Applications

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      Book preview

      Soft Computing - Fouad Sabry

      Chapter 1: Soft computing

      Soft computing is a group of algorithms, including neural networks, fuzzy logic, and evolutionary algorithms. These algorithms are tolerant to imprecision, uncertainty, partial truth and approximation. It is contrasted with hard computing: algorithms which discover provably accurate and optimum solutions to issues.

      In the 1980s, the theory and methods associated with soft computing were presented for the very first time.

      {End Chapter 1}

      Chapter 2: Fuzzy logic

      One kind of many-valued logic is known as fuzzy logic. In this type of logic, the truth value of variables may be any real integer that falls between 0 and 1. It is used to manage the idea of partial truth, in which the truth value may vary between being totally true and being completely false. This concept is used to handle. In contrast, the truth values of variables in Boolean logic can only ever be the integer values 0 or 1, and not any other value.

      In 1965, Iranian-Azerbaijani mathematician Lotfi Zadeh proposed the fuzzy set theory, which is often credited as being the birthplace of the term fuzzy logic.

      There have been several successful applications of fuzzy logic, ranging from control theory to artificial intelligence.

      In traditional reasoning, one can only reach conclusions that are either correct or incorrect. However, there are other propositions that might have a variety of responses, such as the responses you could get from a group of individuals when you ask them to name a color. In situations like these, the truth is revealed as the consequence of reasoning based on inaccurate or incomplete information, in which the responses that were tested are mapped out on a spectrum.

      An example of a fundamental application would be one that describes the numerous sub-ranges of a continuous variable. For instance, a temperature measurement for anti-lock brakes might have many distinct membership functions, each establishing a certain temperature range that is necessary for effective operation of the brakes. Every function converts the given temperature measurement to a truth value that falls somewhere in the range of 0 to 1. Once these truth values have been determined, they may be utilized to figure out how the brakes should be adjusted. The fuzzy set theory offers a method for accurately describing ambiguity.

      In applications of fuzzy logic, non-numerical values are often used as a means of facilitating the presentation of rules and facts.

      The rule-based Mamdani system is the one that is most well recognized. It operates according to the regulations listed below:

      All input values will be fuzzy-checked using fuzzy membership functions.

      To calculate the fuzzy output functions, carry out all of the rules in the rulebase that are appropriate.

      In order to get crisp output values, the fuzzy output functions must first be defuzzed.

      The act of allocating the numerical input of a system to fuzzy sets that include a certain degree of membership is referred to as fuzzification. This level of membership may take on any value within the range of 0 to 1, inclusive. If it is zero, then the value does not fit into the fuzzy set that has been provided, but if it is one, then the value fits in perfectly with the fuzzy set that has been provided. The degree of uncertainty that a given value belongs in the set may be represented by any number between 0 and 1, inclusive. Because these fuzzy sets are often characterized by words, assigning the system input to fuzzy sets enables us to reason with it in a way that is linguistically natural.

      For instance, the meanings of the terms cold, warm, and hot are represented by functions mapping a temperature scale in the figure that can be seen further down on this page. One truth value corresponds to each of the three functions, therefore each point on that scale has a total of three truth values. The three arrows, which indicate the truth values, are used to measure a certain temperature, which is shown by the vertical line in the picture. The fact that the red arrow is pointing to zero indicates that this temperature should be read as not hot. Another way to say this is that this temperature does not belong to the fuzzy set hot. The orange arrow, which points to 0.2, may say that the temperature is somewhat warm, while the blue arrow, which points to 0.8, would say that the temperature is quite chilly. As a result, this temperature has a membership of 0.2 in the fuzzy set referred to as warm, and a membership of 0.8 in the fuzzy set referred to as cold. Fuzzification is the process that determines the degree of membership that is given to each fuzzy collection.

      Each value in a fuzzy set will have a slope when the value is growing, a peak where the value is equal to 1 (which might have a length of 0 or longer), and a slope while the value is falling. This is because fuzzy sets are sometimes specified as being in the form of a triangle or a trapezoid. One example of this is the typical logistic function, which can be expressed as

      {\displaystyle S(x)={\frac {1}{1+e^{-x}}}} , characterized by the symmetry properties listed below

      {\displaystyle S(x)+S(-x)=1.}

      Because of this, it stands to reason that

      {\displaystyle (S(x)+S(-x))\cdot (S(y)+S(-y))\cdot (S(z)+S(-z))=1}

      The relationship between membership values and fuzzy logic may be compared to that of Boolean logic. In order to do this, suitable alternatives for the fundamental operators AND, OR, and NOT need to be accessible. There are a few different approaches to take here. The Zadeh operators are an example of a frequent kind of replacement:

      The results that the fuzzy expressions provide for TRUE/1 and FALSE/0 are the same as the results that the Boolean expressions produce.

      There are also additional operators, which are of a more linguistic character and are referred to as hedges, which may be employed. In most cases, these are adjectives like extremely or somewhat that are used to change the meaning of a set by the application of a mathematical formula. A criterion has been developed to determine whether or not a particular choice table defines a fuzzy logic function. Additionally, a straightforward algorithm for the synthesis of fuzzy logic functions has been proposed, and it is based on the previously introduced concepts of minimum and maximum constituents. A fuzzy logic function is the representation of a disjunction between components of minimum, where a constituent of minimum is the conjunction of variables of the current area that are larger than or equal to the function value in this area (to the right of the function value in the inequality, including the function value).

      The concept of multiplication gives rise to a second group of AND/OR operators, which

      x AND y = x*y

      NOT x = 1 - x

      Hence, x OR y = NOT( AND( NOT(x), NOT(y) ) )

      x OR y = NOT( AND(1-x, 1-y) )

      x OR y = NOT( (1-x)*(1-y) )

      x OR y = 1-(1-x)*(1-y)

      x OR y = x+y-xy

      It is feasible to deduce the third element using any two of AND, OR, or NOT as inputs. One example of a t-norm is the generalization of the operator AND.

      The IF-THEN rules map truth values that are either input or calculated to the required truth values for the output. Example:

      IF temperature IS very cold THEN fan_speed is stopped

      IF temperature IS cold THEN fan_speed is slow

      IF temperature IS warm THEN fan_speed is moderate

      IF temperature IS hot THEN fan_speed is high

      When a certain temperature is input, the fuzzy variable hot will have a particular truth value, and this value will be transferred to the high variable.

      In the event when more than one THEN part has an output variable, the OR operator is used to combine the results of each corresponding IF part with the output variable's value.

      The objective here is to generate a continuous variable using fuzzy truth values.

      If the output truth values were precisely those that were acquired from the fuzzification of a particular integer, then this would be a simple task. However, given that every output truth value is calculated on its own, the vast majority of the time, these values do not reflect such a collection of integers. The next step is to choose a number that most closely corresponds to the intention that is stored in the value of the truth. Given instance, for multiple different truth values of fan speed, it is necessary to identify a real speed that most closely corresponds to the calculated truth values of the variables slow, moderate, and so on.

      There is not a single algorithm that can fulfill this requirement.

      A typical algorithm is as follows:

      At each individual truth value, the membership function should be terminated at this value.

      The OR operator is used to combine the curves that were generated.

      Find the point in the middle of the region beneath the curve that has the most weight.

      The final result is the x location of this center, so pay attention to it.

      The TSK system is comparable to the Mamdani system, with the exception that the defuzzification procedure is integrated into the fuzzy rule execution. These are also modified such that the consequent of the rule is represented by a polynomial function rather than the original representation (usually constant or linear). One example of a rule that always produces the same result would be:

      IF temperature IS very cold = 2

      This being the case, the output will be equivalent to the constant of the consequent (for example, if the consequent is x).

      2).

      In the vast majority of cases, we would have a comprehensive rule basis, with at least two different regulations.

      In the event that this is the case, the output of the entire rule base will be the average of the consequent of each rule i (Yi), weighted according to the membership value of its antecedent (hi):

      {\displaystyle {\frac {\sum _{i}(h_{i}\cdot Y_{i})}{\sum _{i}h_{i}}}}

      Instead is a good illustration of a rule that may provide linear results:

      IF temperature

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