Lecture 1 computational intelligence
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This document discusses computational intelligence and fuzzy set theory. It defines soft computing constituents like neural networks, fuzzy set theory, genetic algorithms, and conventional AI. It then discusses fuzzy set theory, including fuzzy sets, membership functions, α-cuts, and set theoretic operations like union, intersection, and complement. It also defines two-dimensional membership functions like cylindrical extensions and projections of fuzzy sets.
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Reference Books:
1. T. J. Ross, "Fuzzy Logic with Engineering Applications", 2/e, John Wiley & Sons,England, 2004.
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Lecture 4 neural networksParveenMalik18 This document provides information about neural networks from Parveen Malik, an Assistant Professor at KIIT University. It defines a neural network as a massively parallel distributed processor made up of simple processing units that has a natural ability to store experiential knowledge and make it available for use, similar to the human brain. Neural networks can be used for applications like object detection, image captioning, time series modelling, and more. The document also discusses the structure and function of biological neurons and their equivalence to artificial neurons in neural networks.
Lecture 3 fuzzy inference system
Lecture 3 fuzzy inference systemParveenMalik18 The document discusses fuzzy inference systems (FIS). It defines FIS as a fuzzy-rule based system that uses a rule base, database with membership functions, and reasoning mechanism. The basic structure and block diagram of a FIS are provided. Applications of FIS include data classification, automatic control, expert systems, time-series prediction, pattern recognition and robotics. Different types of FIS are mentioned such as Mamdani, Sugeno, and Tsukamoto fuzzy inference systems.
Chapter8
Chapter8ParveenMalik18 The document discusses a spectrum analyzer and function generator. A spectrum analyzer is used to display and measure frequency by mixing the input signal with a voltage controlled oscillator, filtering at an intermediate frequency, and using a detector and vertical amplifier to display the pulse output only at the input signal frequency. A function generator generates different signal types like sine, square, and triangular waves, with adjustable frequency from Hz to MHz. It uses positive feedback oscillators like RC, LC, Wien bridge, and phase shift oscillators. The block diagram of each is also included.
Chapter6
Chapter6ParveenMalik18 The document discusses the cathode ray oscilloscope. It describes the cathode ray oscilloscope as an electronic voltmeter used to display and measure peak voltage, frequency, phase difference, pulse width, delay time, rise time, and fall time. It outlines the topics of cathode ray tube construction, electrostatic lens, electrostatic deflection, and phase and frequency measurement. Lissajous patterns are discussed for measuring phase differences and frequencies.
Chapter5
Chapter5ParveenMalik18 This document discusses various types of electronic instruments used to measure voltage, including voltmeters, Q-meters, and digital voltmeters. It describes the limitations of traditional mechanical voltmeters and how electronic circuits overcome these limitations with high input impedance, low output impedance, and voltage amplification. Circuit diagrams and working principles are provided for different types of DC and AC voltmeters using transistors and op-amps. Thermocouple-based true RMS voltmeters are explained as well as Q-meters for measuring coil and capacitor characteristics and digital voltmeters that directly provide a numerical voltage output.
Chapter3
Chapter3ParveenMalik18 This document discusses the classification and operating principles of various analog measurement instruments for voltage and current. It covers classifications based on measured quantity, output representation, construction type, and data presentation. Key instrument types discussed include permanent magnet moving coil (PMMC), galvanometer, moving iron, electrodynamometer, and electrostatic meters. For each type, it describes the operating forces, torque equations, sources of error, and advantages/disadvantages. The document provides detailed information on analog measurement instrument fundamentals.
Chapter2
Chapter2ParveenMalik18 This document discusses the measurement of electrical components like resistance, inductance, and capacitance. It begins by classifying resistances into low, medium, and high ranges. Methods for measuring medium resistances include the ammeter and voltmeter method, substitution method, and Wheatstone bridge. The Wheatstone bridge provides highly accurate measurements. Kelvin's double bridge is discussed for measuring low resistances. Megaohm bridges and megaohmmeters are described for measuring high resistances. Bridges like Maxwell, Hay's, and Anderson are covered for measuring inductance, while Schering's and Wein's bridges are summarized for measuring capacitance and frequency. Potential sources of error in bridge circuits are also outlined.
Electrical and Electronic Measurement
Electrical and Electronic MeasurementParveenMalik18 This document provides an overview of electrical and electronic measurement. It discusses:
1. Measurement and its significance in engineering processes like design, operation, and maintenance.
2. Methods of measurement including direct and indirect methods. It also defines what constitutes an instrument.
3. Classification of instruments into mechanical, electrical, and electronic types. As well as categories like absolute/secondary, deflection/null, and indicating/recording/controlling.
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Lecture 1 computational intelligence
- 1. Computational Intelligence Parveen Malik Assistant Professor School of Electronics Engineering KIIT University
- 2. Outline • Soft Computing Constituents • Fuzzy Set Theory • Set Theoretic Operations • Two Dimensional MFs
- 3. Soft Computing Constituents • Neural Network • Fuzzy Set Theory • Derivative Free Optimization( Genetic Algorithms) • Conventional AI Text Book : Chuen-Tsai Sun, Eiji Mizutani, and Jyh-Shing Roger Jang. “Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence”
- 4. Hidden Layer Output Layer Input Layer Neural Network
- 5. Fuzzy Set Theory Degree of Belief Fuzzy Hot Cold Degree of Belief Non-Fuzzy (Crisp) 1.0 0.0 Cold Hot 1.0 0.0 𝟒𝟏𝟎𝑪 𝟑𝟗𝟎𝑪 𝟒𝟎𝟎 𝑪 𝟐𝟎𝟎𝑪 𝟏𝟐𝟎𝑪 𝟑𝟎𝟎𝑪 𝟐𝟓𝟎 𝑪 𝟒𝟏𝟎𝑪 𝟑𝟗𝟎𝑪 𝟒𝟎𝟎 𝑪 𝟐𝟎𝟎𝑪 𝟏𝟐𝟎𝑪 𝟑𝟎𝟎𝑪 𝟐𝟓𝟎 𝑪
- 6. History of Conventional AI approaches
- 7. Fuzzy Set Theory Vs Classical Set Theory Classical Set Theory : • Crisp, clear or unambiguous boundary 𝐴 = 𝑥 𝑥 > 6} • Important tool for mathematic and computer science. • Sharp Transition between “Inclusion” and Exclusion”. • Incapable of addressing human concepts and thoughts which tend to be abstract and imprecise. A=“Tall Person” x =“Height” B= Water is hot” C=“Temp. is High”
- 8. Fuzzy Set Theory Vs Classical Set Theory Fuzzy Set Theory : • Introduced by “L.A.Zadeh” in 1965 paper “Fuzzy Sets” • Unclear or ambiguous boundary • Capable of addressing human concepts and thoughts which tend to be abstract and imprecise. A=“Tall Person” x =“Height” B= Water is hot” C=“Temp. is High” • Introduction of membership function • Gradual Transition from “Belong to a set” To “Not belong to set”.
- 9. Fuzzy Set Theory Definition 1.1 : Fuzzy Set and membership functions If X is a collection of objects denoted generically by x, then a fuzzy set A in X is defined as a set of ordered pairs: A= 𝒙, 𝝁𝑨(𝒙) | 𝒙 ∈ 𝑿 Where 𝜇𝐴(𝑥) is the membership function for the fuzzy set A Definition 1.2 : support The support of A fuzzy set A is the set of all points x in X such that 𝜇𝐴(𝑥) >0 support(A)= 𝒙 | 𝝁𝑨 𝒙 > 𝟎 Definition 1.3 : core The core of A fuzzy set A is the set of all points x in X such that 𝜇𝐴(𝑥) =1 core(A)= 𝒙|𝝁𝑨 𝒙 = 𝟎 Definition 1.4 : Normality A fuzzy set A is normal if its core is non-empty.
- 10. Fuzzy Set Theory Definition 1.5 : Cross Over Points A crossover point of a fuzzy set A is a point 𝑥 ∈ 𝑋 at which 𝜇𝐴(𝑥) = 0.5. crossover(A)= 𝒙|𝝁𝑨 𝒙 = 𝟎. 𝟓 Where 𝜇𝐴(𝑥) is the membership function for the fuzzy set A. Definition 1.6 : Fuzzy singleton A fuzzy set whose support is a single point in X with 𝜇𝐴(𝑥) = 1 is called a Fuzzy Singleton. Definition 1.7 : α-cut, strong α-cut α-cut, α-level set of a fuzzy set A is crisp set defined by 𝑨𝜶= 𝒙|𝝁𝑨 𝒙 ≥ 𝟎 Strong α-cut, strong α-level set of a fuzzy set A is defined by 𝑨𝜶 ′ = 𝒙|𝝁𝑨 𝒙 > 𝟎
- 11. Fuzzy Set Theory Definition 1.8 : Convexity A fuzzy set A is convex if and only if for any 𝑥1, 𝑥2 ∈ 𝑋 𝑎𝑛𝑑 for any λ ∈ 0,1 𝝁𝑨(𝝀𝒙𝟏 + (𝟏 − 𝝀)𝒙𝟐) ≥ Min 𝝁𝑨 𝒙𝟏 , 𝝁𝑨 𝒙𝟐 Alternatively, A is convex if all its 𝛼 − 𝑠𝑒𝑡𝑠 are convex. Definition 1.9 : Fuzzy numbers A fuzzy number A is a fuzzy set in the real line that satisfies the conditions for Normality and convexity. Definition 1.10 : Bandwidths of normal and convex fuzzy sets For a normal and convex fuzzy set, the bandwidth or width is defined as the distance between the two unique crossover points: 𝒘𝒊𝒅𝒕𝒉 𝑨 = 𝒙𝟐 − 𝒙𝟏 Where 𝝁𝑨 𝒙𝟏 = 𝝁𝑨(𝒙𝟐)=0.5
- 12. Fuzzy Set Theory Definition 1.11 : Symmetry A fuzzy set A is symmetric if its MF is symmetric around a certain point x=c , 𝝁𝑨 𝒄 + 𝒙 = 𝝁𝑨 𝒄 − 𝒙 for all 𝒙 ∈ 𝑿 Definition 1.12 : Open left, Open right, closed A fuzzy set A is open left if 𝒍𝒊𝒎𝒙→−∞𝝁𝑨 𝒙 =1 and 𝒍𝒊𝒎𝒙→+∞𝝁𝑨 𝒙 = 0 open right if 𝒍𝒊𝒎𝒙→−∞𝝁𝑨 𝒙 =0 and 𝒍𝒊𝒎𝒙→+∞𝝁𝑨 𝒙 = 1 Closed if 𝒍𝒊𝒎𝒙→−∞𝝁𝑨 𝒙 =𝒍𝒊𝒎𝒙→+∞𝝁𝑨 𝒙 =0
- 13. Set Theoretic Operations Definition 2.1 : Containment or Subset Fuzzy set A is contained in Fuzzy set B if and only if 𝑨 ⊆ 𝑩 ⇔ 𝝁𝑨 𝒙 ≤ 𝝁𝑩 𝒙 Definition 2.2 : Union (Disjunction) The union of two sets A and B is a set C (𝐴 ∪ B) whose MF is related by 𝝁 𝒙 = max {𝝁𝑨 𝒙 , 𝝁𝑩 𝒙 } = 𝝁𝑨 𝒙 ˅ 𝝁𝑩 𝒙 Definition 2.3 : Intersection (Conjunction) The intersection of two sets A and B is a set C (𝐴 ∩ B) whose MF is related by 𝝁 𝒙 = min {𝝁𝑨 𝒙 , 𝝁𝑩 𝒙 } = 𝝁𝑨 𝒙 ˄ 𝝁𝑩 𝒙
- 14. Set Theoretic Operations Definition 2.4 : Complement (Negation) The complement of Fuzzy set A is ഥ 𝐀 ¬𝐀 𝐨𝐫 𝐍𝐎𝐓 𝐀 𝝁ഥ 𝑨 𝒙 = 𝟏 − 𝝁𝑨 𝒙 Definition 2.5 : Cartesian product and co-product Let A and B be fuzzy sets in X and Y respectively. The Cartesian product of A and B denoted by 𝑨 × 𝑩 , 𝝁𝑨×𝑩 𝒙, 𝒚 = min {𝝁𝑨 𝒙 , 𝝁𝑩 𝒚 } The Co- product of A and B denoted by A + B, 𝝁𝑨+𝑩 𝒙, 𝒚 = max {𝝁𝑨 𝒙 , 𝝁𝑩 𝒚 }
- 15. Two Dimensional MFs Definition 3.1 : Cylindrical extensions of 1D fuzzy sets If A is a fuzzy set in X, then its cylindrical extension in 𝑿 × 𝒀 is a fuzzy set c(A) defined by 𝒄(𝑨) = න 𝑿×𝒀 𝝁𝑨(𝒙)/(𝒙, 𝒚)
- 16. Two Dimensional MFs Definition 3.1 : Projections of fuzzy sets If R be a two-dimensional fuzzy set on 𝑿 × 𝒀. The projections of R onto X and Y are defined as 𝑹𝑿 = න 𝑋 𝒎𝒂𝒙 {𝝁𝑹(𝒙, 𝒚)} /𝒙 𝑹𝒀 = න 𝑌 𝒎𝒂𝒙 {𝝁𝑹(𝒙, 𝒚)} /𝒚