Fuzzy logic is a form of logic that deals with reasoning that is approximate rather than fixed and exact. It was introduced in 1965 with the proposal of fuzzy set theory by Lotfi Zadeh. Fuzzy logic uses fuzzy sets and membership functions to deal with imprecise or uncertain inputs and allows for reasoning that allows for partial truth of inputs between fully true and fully false. Fuzzy controllers combine fuzzy logic with control theory to control complex systems. They involve fuzzification of inputs, applying fuzzy rules through inference, and defuzzification of outputs to obtain a crisp control action.
This document discusses classical sets and fuzzy sets. It defines classical sets as having distinct elements that are either fully included or excluded from the set. Fuzzy sets allow for gradual membership, with elements having degrees of membership between 0 and 1. Operations like union, intersection, and complement are defined for both classical and fuzzy sets, with fuzzy set operations accounting for degrees of membership. Properties of classical and fuzzy sets and relations are also covered, noting differences like fuzzy sets not following the law of excluded middle.
This document provides an overview of fuzzy logic. It begins by defining fuzzy as not being clear or precise, unlike classical sets which have clear boundaries. It then explains fuzzy logic allows for partial set membership rather than binary membership. The document outlines fuzzy logic's ability to model imprecise or nonlinear systems using natural language-based rules. It details the key concepts of fuzzy logic including linguistic variables, membership functions, fuzzy set operations, fuzzy inference systems and the 5-step fuzzy inference process of fuzzifying inputs, applying fuzzy operations and implications, aggregating outputs and defuzzifying results.
Fuzzy relations, fuzzy graphs, and the extension principle are three important concepts in fuzzy logic. Fuzzy relations generalize classical relations to allow partial membership and describe relationships between objects to varying degrees. Fuzzy graphs describe functional mappings between input and output linguistic variables. The extension principle provides a procedure to extend functions defined on crisp domains to fuzzy domains by mapping fuzzy sets through functions. These concepts form the foundation of fuzzy rules and fuzzy arithmetic.
Defuzzification is the process of producing a quantifiable result in Crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is typically needed in fuzzy control systems.
How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1
The document introduces fuzzy set theory as an extension of classical set theory that allows for elements to have varying degrees of membership rather than binary membership. It discusses key concepts such as fuzzy sets, membership functions, fuzzy logic, fuzzy rules, and fuzzy inference. Fuzzy set theory provides a framework for modeling imprecise and uncertain concepts that are common in human reasoning.
Fuzzy logic is a form of multivalued logic that allows intermediate values between conventional evaluations like true/false, yes/no, or 0/1. It provides a mathematical framework for representing uncertainty and imprecision in measurement and human cognition. The document discusses the history of fuzzy logic, key concepts like membership functions and linguistic variables, common fuzzy logic operations, and applications in fields like control systems, home appliances, and cameras. It also notes some drawbacks like difficulty in tuning membership functions and potential confusion with probability theory.
MATLAB is a numerical computing environment and programming language. It allows matrix manipulations, plotting of functions and data, implementation of algorithms, and interfacing with programs in other languages. MATLAB can be used for applications like signal processing, image processing, control systems, and computational finance. It offers advantages like ease of use, platform independence, and predefined functions. However, it can sometimes be slow and is commercial software. The MATLAB interface includes a command window, current directory, workspace, and command history. Arrays are fundamental data types in MATLAB and can be vectors, matrices, or multidimensional. Variables are used to store information in the workspace and can represent different data types. Common operations include arithmetic, functions, and following the
This document discusses classical sets and fuzzy sets. It defines classical sets as having distinct elements that are either fully included or excluded from the set. Fuzzy sets allow for gradual membership, with elements having degrees of membership between 0 and 1. Operations like union, intersection, and complement are defined for both classical and fuzzy sets, with fuzzy set operations accounting for degrees of membership. Properties of classical and fuzzy sets and relations are also covered, noting differences like fuzzy sets not following the law of excluded middle.
This document provides an overview of fuzzy logic. It begins by defining fuzzy as not being clear or precise, unlike classical sets which have clear boundaries. It then explains fuzzy logic allows for partial set membership rather than binary membership. The document outlines fuzzy logic's ability to model imprecise or nonlinear systems using natural language-based rules. It details the key concepts of fuzzy logic including linguistic variables, membership functions, fuzzy set operations, fuzzy inference systems and the 5-step fuzzy inference process of fuzzifying inputs, applying fuzzy operations and implications, aggregating outputs and defuzzifying results.
Fuzzy relations, fuzzy graphs, and the extension principle are three important concepts in fuzzy logic. Fuzzy relations generalize classical relations to allow partial membership and describe relationships between objects to varying degrees. Fuzzy graphs describe functional mappings between input and output linguistic variables. The extension principle provides a procedure to extend functions defined on crisp domains to fuzzy domains by mapping fuzzy sets through functions. These concepts form the foundation of fuzzy rules and fuzzy arithmetic.
Defuzzification is the process of producing a quantifiable result in Crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is typically needed in fuzzy control systems.
How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1
The document introduces fuzzy set theory as an extension of classical set theory that allows for elements to have varying degrees of membership rather than binary membership. It discusses key concepts such as fuzzy sets, membership functions, fuzzy logic, fuzzy rules, and fuzzy inference. Fuzzy set theory provides a framework for modeling imprecise and uncertain concepts that are common in human reasoning.
Fuzzy logic is a form of multivalued logic that allows intermediate values between conventional evaluations like true/false, yes/no, or 0/1. It provides a mathematical framework for representing uncertainty and imprecision in measurement and human cognition. The document discusses the history of fuzzy logic, key concepts like membership functions and linguistic variables, common fuzzy logic operations, and applications in fields like control systems, home appliances, and cameras. It also notes some drawbacks like difficulty in tuning membership functions and potential confusion with probability theory.
MATLAB is a numerical computing environment and programming language. It allows matrix manipulations, plotting of functions and data, implementation of algorithms, and interfacing with programs in other languages. MATLAB can be used for applications like signal processing, image processing, control systems, and computational finance. It offers advantages like ease of use, platform independence, and predefined functions. However, it can sometimes be slow and is commercial software. The MATLAB interface includes a command window, current directory, workspace, and command history. Arrays are fundamental data types in MATLAB and can be vectors, matrices, or multidimensional. Variables are used to store information in the workspace and can represent different data types. Common operations include arithmetic, functions, and following the
Fuzzy sets allow for gradual membership of elements in a set, rather than binary membership as in classical set theory. Membership is described on a scale of 0 to 1 using a membership function. Fuzzy sets generalize classical sets by treating classical sets as special cases where membership values are restricted to 0 or 1. Fuzzy set theory can model imprecise or uncertain information and is used in domains like bioinformatics. Examples of fuzzy sets include sets like "tall people" where membership in the set is a matter of degree.
Classical relations and fuzzy relationsBaran Kaynak
This document discusses classical and fuzzy relations. It begins by introducing relations and their importance in fields like engineering, science, and mathematics. It then contrasts classical/crisp relations with fuzzy relations. Classical relations have binary relatedness between elements, while fuzzy relations have degrees of relatedness on a continuum between completely related and not related. The document provides examples and explanations of crisp relations, fuzzy relations, Cartesian products, compositions, and equivalence/tolerance relations. It demonstrates these concepts with examples involving sets of cities and bacteria strains.
This document discusses defuzzification in fuzzy logic. It defines defuzzification as the process of converting fuzzy quantities into crisp quantities. There are several reasons for and applications of defuzzification, such as converting fuzzy controller outputs into crisp values for applications. The document outlines the defuzzification process and several common defuzzification methods, including the centroid method, weighted average method, and max membership principle. It also discusses the lambda-cut and alpha-cut methods for deriving crisp values from fuzzy sets and relations.
Fuzzification transforms crisp quantities into fuzzy quantities by identifying deterministic values as uncertain and represented by membership functions, such as describing a temperature of 45°C as "favorable", "hot", or "cold". Defuzzification is the inverse process, converting fuzzy results back into crisp results by mapping a possibility distribution of an inferred fuzzy control action into a nonfuzzy control action.
The document provides an overview of fuzzy logic concepts including types of fuzzy systems, membership functions, fuzzy inference, fuzzification and defuzzification methods. It discusses knowledge-based and rule-based fuzzy systems, types of membership functions like triangular, trapezoidal and Gaussian. Examples of fuzzy logic applications in autonomous driving cars and methods for defuzzification like weighted average, centroid, max-membership and centre of sums are also summarized.
Fuzzy logic is a flexible machine learning technique that mimics human thought by allowing intermediate values between true and false. It provides a mechanism for interpreting and executing commands based on approximate or uncertain reasoning. Unlike binary logic which can only have true or false values, fuzzy logic uses linguistic variables and degrees of membership to represent concepts that may have a partial truth. Fuzzy systems find applications in automatic control, prediction, diagnosis and user interfaces.
- Fuzzy logic was developed by Lotfi Zadeh to address applications involving subjective or vague data like "attractive person" that cannot be easily analyzed using binary logic. It allows for partial truth values between completely true and completely false.
- Fuzzy logic controllers mimic human decision making and involve fuzzifying inputs, applying fuzzy rules, and defuzzifying outputs. This allows systems to be specified in human terms and automated.
- Fuzzy logic has many applications from industrial process control to consumer products like washing machines and microwaves. It offers an intuitive way to model real-world ambiguities compared to mathematical or logic-based approaches.
This document discusses the application of fuzzy logic to optimal capacitor placement in distribution systems. It begins with definitions of fuzzy logic and fuzzy sets. It then describes the key components of a fuzzy logic system including fuzzification, fuzzy inference rules, and defuzzification. It proposes using power loss reduction index and bus voltage as input variables, and capacitor placement suitability index as the output variable, to determine the optimal locations and sizes of capacitors. The goal is to minimize power losses and maximize annual savings using fuzzy logic techniques.
This document introduces fuzzy sets. It defines a fuzzy set as a set where elements have gradual membership rather than binary membership. Fuzzy sets allow membership values between 0 and 1. Operations on fuzzy sets like union, intersection, and complement are defined. An example fuzzy set distinguishes young and adult ages on a scale rather than a binary classification. Fuzzy sets permit ambiguous or uncertain boundaries unlike classical sets.
This document provides an overview of fuzzy logic concepts for a course on soft computing. It discusses key fuzzy logic topics like membership functions, fuzzy sets, linguistic variables, fuzzy rules, fuzzy inference, and neuro-fuzzy systems. The document also provides examples of commonly used membership functions like triangular, trapezoidal, and Gaussian functions. It explains how fuzzy logic allows for approximate reasoning using natural language terms and multivalent logic with membership values between 0 and 1.
This document provides an introduction to fuzzy logic and fuzzy sets. It discusses key concepts such as fuzzy sets having degrees of membership between 0 and 1 rather than binary membership, and fuzzy logic allowing for varying degrees of truth. Examples are given of fuzzy sets representing partially full tumblers and desirable cities to live in. Characteristics of fuzzy sets such as support, crossover points, and logical operations like union and intersection are defined. Applications mentioned include vehicle control systems and appliance control using fuzzy logic to handle imprecise and ambiguous inputs.
- Fuzzy logic is an extension of classical logic that accounts for partial truth values between "true" and "false". It allows for gradual transitions between values in a membership function.
- Fuzzy logic has been applied to many areas including control systems, decision making, pattern recognition and other areas involving uncertainty. It uses fuzzy "if-then" rules to model imprecise human reasoning.
- The document discusses fuzzy sets, fuzzy relations, applications of fuzzy logic and provides biographical information about Lotfi Zadeh, the founder of fuzzy logic.
Fuzzy logic is a form of logic that accounts for partial truth and vagueness. It is used in control systems and decision support systems. The document discusses the history of fuzzy logic and its applications in areas like automotive, robotics, manufacturing, medical, and more. Fuzzy logic controllers combine fuzzy linguistic variables and rules to automate tasks like speed control in vehicles and temperature control in air conditioners and washing machines.
This document provides an overview of fuzzy logic, including its origins, key concepts, and applications. It discusses how fuzzy logic allows for approximate reasoning and decision making under uncertainty by using linguistic variables and fuzzy set theory. Membership functions are used to characterize fuzzy sets and assign degrees of truth between 0 and 1 rather than binary true/false values. Common fuzzy logic operations like intersection, union, and complement are also covered. Finally, some examples of fuzzy logic control systems are presented, including how they are designed using fuzzy rule bases and inference methods like Mamdani and Sugeno.
The document discusses fuzzy logic systems. It describes how fuzzy logic systems resemble human reasoning by using intermediate values between yes and no rather than binary logic. It explains the typical architecture of a fuzzy logic system including fuzzification, a knowledge base, an inference engine, and defuzzification. An example is provided of a fuzzy logic air conditioning system that adjusts temperature based on room temperature and a target value. Advantages and disadvantages of fuzzy logic systems are also summarized.
This document provides an overview of fuzzy logic and fuzzy set theory with examples from image processing. Some key points:
- Fuzzy set theory was coined by Lofti Zadeh in 1965 and allows for degrees of membership rather than binary true/false values. Almost all real-world classes are fuzzy.
- Fuzzy logic handles imprecise concepts like "tall person" through membership functions and handles inferences through generalized modus ponens.
- Fuzzy logic has been applied to fields like image processing, where concepts like "light blue" are fuzzy, and speech recognition by assigning fuzzy values to phonemes.
- Techniques discussed include fuzzy membership functions, aggregation operations, alpha cuts, linguistic
Fuzzy logic is a form of logic that deals with reasoning that is approximate rather than precise. It allows intermediate values to be defined between conventional evaluations like true/false, and uses a continuum of truth values between 0 and 1. Fuzzy logic is useful for problems with imprecise or uncertain data, and can represent human reasoning that uses approximate terms like "warm" or "fast". It has been applied in various systems to control variables like temperature, speed, and focus based on fuzzy linguistic rules.
This document discusses fuzzy logic, beginning with its origins in ancient Greece and formalization in 1965 by Lotfi Zadeh. It explains fuzzy logic represents concepts with overlapping membership functions rather than binary logic. Fuzzy logic and neural networks both model human reasoning but fuzzy logic uses linguistic rules while neural networks learn from examples. Fuzzy logic has applications in control systems like temperature controllers and anti-lock braking systems to handle nonlinear dynamics. It is used in other fields like business and expert systems to represent subjective concepts.
The document discusses fuzzy logic and artificial neural networks. It provides an overview of fuzzy logic, including fuzzy sets, membership functions, fuzzy linguistic variables, fuzzy rules and fuzzy control. It also covers artificial neural networks, including the biological inspiration from the human brain, basic neuron models, multi-layer feedforward networks, training algorithms like gradient descent, and examples of neural networks solving problems like XOR classification. Hardware implementations on systems like DSpace and Opal RT are also briefly mentioned.
The document provides an overview of fuzzy logic and fuzzy sets. It discusses how fuzzy logic can handle imprecise data unlike classical binary sets. Membership functions assign degrees of membership values between 0 and 1. Fuzzy logic systems use if-then rules and linguistic variables. An example shows how fuzzy logic is used to estimate project risk levels based on funding and staffing levels. Fuzzy logic has been applied in various domains due to its ability to model human reasoning.
Fuzzy sets allow for gradual membership of elements in a set, rather than binary membership as in classical set theory. Membership is described on a scale of 0 to 1 using a membership function. Fuzzy sets generalize classical sets by treating classical sets as special cases where membership values are restricted to 0 or 1. Fuzzy set theory can model imprecise or uncertain information and is used in domains like bioinformatics. Examples of fuzzy sets include sets like "tall people" where membership in the set is a matter of degree.
Classical relations and fuzzy relationsBaran Kaynak
This document discusses classical and fuzzy relations. It begins by introducing relations and their importance in fields like engineering, science, and mathematics. It then contrasts classical/crisp relations with fuzzy relations. Classical relations have binary relatedness between elements, while fuzzy relations have degrees of relatedness on a continuum between completely related and not related. The document provides examples and explanations of crisp relations, fuzzy relations, Cartesian products, compositions, and equivalence/tolerance relations. It demonstrates these concepts with examples involving sets of cities and bacteria strains.
This document discusses defuzzification in fuzzy logic. It defines defuzzification as the process of converting fuzzy quantities into crisp quantities. There are several reasons for and applications of defuzzification, such as converting fuzzy controller outputs into crisp values for applications. The document outlines the defuzzification process and several common defuzzification methods, including the centroid method, weighted average method, and max membership principle. It also discusses the lambda-cut and alpha-cut methods for deriving crisp values from fuzzy sets and relations.
Fuzzification transforms crisp quantities into fuzzy quantities by identifying deterministic values as uncertain and represented by membership functions, such as describing a temperature of 45°C as "favorable", "hot", or "cold". Defuzzification is the inverse process, converting fuzzy results back into crisp results by mapping a possibility distribution of an inferred fuzzy control action into a nonfuzzy control action.
The document provides an overview of fuzzy logic concepts including types of fuzzy systems, membership functions, fuzzy inference, fuzzification and defuzzification methods. It discusses knowledge-based and rule-based fuzzy systems, types of membership functions like triangular, trapezoidal and Gaussian. Examples of fuzzy logic applications in autonomous driving cars and methods for defuzzification like weighted average, centroid, max-membership and centre of sums are also summarized.
Fuzzy logic is a flexible machine learning technique that mimics human thought by allowing intermediate values between true and false. It provides a mechanism for interpreting and executing commands based on approximate or uncertain reasoning. Unlike binary logic which can only have true or false values, fuzzy logic uses linguistic variables and degrees of membership to represent concepts that may have a partial truth. Fuzzy systems find applications in automatic control, prediction, diagnosis and user interfaces.
- Fuzzy logic was developed by Lotfi Zadeh to address applications involving subjective or vague data like "attractive person" that cannot be easily analyzed using binary logic. It allows for partial truth values between completely true and completely false.
- Fuzzy logic controllers mimic human decision making and involve fuzzifying inputs, applying fuzzy rules, and defuzzifying outputs. This allows systems to be specified in human terms and automated.
- Fuzzy logic has many applications from industrial process control to consumer products like washing machines and microwaves. It offers an intuitive way to model real-world ambiguities compared to mathematical or logic-based approaches.
This document discusses the application of fuzzy logic to optimal capacitor placement in distribution systems. It begins with definitions of fuzzy logic and fuzzy sets. It then describes the key components of a fuzzy logic system including fuzzification, fuzzy inference rules, and defuzzification. It proposes using power loss reduction index and bus voltage as input variables, and capacitor placement suitability index as the output variable, to determine the optimal locations and sizes of capacitors. The goal is to minimize power losses and maximize annual savings using fuzzy logic techniques.
This document introduces fuzzy sets. It defines a fuzzy set as a set where elements have gradual membership rather than binary membership. Fuzzy sets allow membership values between 0 and 1. Operations on fuzzy sets like union, intersection, and complement are defined. An example fuzzy set distinguishes young and adult ages on a scale rather than a binary classification. Fuzzy sets permit ambiguous or uncertain boundaries unlike classical sets.
This document provides an overview of fuzzy logic concepts for a course on soft computing. It discusses key fuzzy logic topics like membership functions, fuzzy sets, linguistic variables, fuzzy rules, fuzzy inference, and neuro-fuzzy systems. The document also provides examples of commonly used membership functions like triangular, trapezoidal, and Gaussian functions. It explains how fuzzy logic allows for approximate reasoning using natural language terms and multivalent logic with membership values between 0 and 1.
This document provides an introduction to fuzzy logic and fuzzy sets. It discusses key concepts such as fuzzy sets having degrees of membership between 0 and 1 rather than binary membership, and fuzzy logic allowing for varying degrees of truth. Examples are given of fuzzy sets representing partially full tumblers and desirable cities to live in. Characteristics of fuzzy sets such as support, crossover points, and logical operations like union and intersection are defined. Applications mentioned include vehicle control systems and appliance control using fuzzy logic to handle imprecise and ambiguous inputs.
- Fuzzy logic is an extension of classical logic that accounts for partial truth values between "true" and "false". It allows for gradual transitions between values in a membership function.
- Fuzzy logic has been applied to many areas including control systems, decision making, pattern recognition and other areas involving uncertainty. It uses fuzzy "if-then" rules to model imprecise human reasoning.
- The document discusses fuzzy sets, fuzzy relations, applications of fuzzy logic and provides biographical information about Lotfi Zadeh, the founder of fuzzy logic.
Fuzzy logic is a form of logic that accounts for partial truth and vagueness. It is used in control systems and decision support systems. The document discusses the history of fuzzy logic and its applications in areas like automotive, robotics, manufacturing, medical, and more. Fuzzy logic controllers combine fuzzy linguistic variables and rules to automate tasks like speed control in vehicles and temperature control in air conditioners and washing machines.
This document provides an overview of fuzzy logic, including its origins, key concepts, and applications. It discusses how fuzzy logic allows for approximate reasoning and decision making under uncertainty by using linguistic variables and fuzzy set theory. Membership functions are used to characterize fuzzy sets and assign degrees of truth between 0 and 1 rather than binary true/false values. Common fuzzy logic operations like intersection, union, and complement are also covered. Finally, some examples of fuzzy logic control systems are presented, including how they are designed using fuzzy rule bases and inference methods like Mamdani and Sugeno.
The document discusses fuzzy logic systems. It describes how fuzzy logic systems resemble human reasoning by using intermediate values between yes and no rather than binary logic. It explains the typical architecture of a fuzzy logic system including fuzzification, a knowledge base, an inference engine, and defuzzification. An example is provided of a fuzzy logic air conditioning system that adjusts temperature based on room temperature and a target value. Advantages and disadvantages of fuzzy logic systems are also summarized.
This document provides an overview of fuzzy logic and fuzzy set theory with examples from image processing. Some key points:
- Fuzzy set theory was coined by Lofti Zadeh in 1965 and allows for degrees of membership rather than binary true/false values. Almost all real-world classes are fuzzy.
- Fuzzy logic handles imprecise concepts like "tall person" through membership functions and handles inferences through generalized modus ponens.
- Fuzzy logic has been applied to fields like image processing, where concepts like "light blue" are fuzzy, and speech recognition by assigning fuzzy values to phonemes.
- Techniques discussed include fuzzy membership functions, aggregation operations, alpha cuts, linguistic
Fuzzy logic is a form of logic that deals with reasoning that is approximate rather than precise. It allows intermediate values to be defined between conventional evaluations like true/false, and uses a continuum of truth values between 0 and 1. Fuzzy logic is useful for problems with imprecise or uncertain data, and can represent human reasoning that uses approximate terms like "warm" or "fast". It has been applied in various systems to control variables like temperature, speed, and focus based on fuzzy linguistic rules.
This document discusses fuzzy logic, beginning with its origins in ancient Greece and formalization in 1965 by Lotfi Zadeh. It explains fuzzy logic represents concepts with overlapping membership functions rather than binary logic. Fuzzy logic and neural networks both model human reasoning but fuzzy logic uses linguistic rules while neural networks learn from examples. Fuzzy logic has applications in control systems like temperature controllers and anti-lock braking systems to handle nonlinear dynamics. It is used in other fields like business and expert systems to represent subjective concepts.
The document discusses fuzzy logic and artificial neural networks. It provides an overview of fuzzy logic, including fuzzy sets, membership functions, fuzzy linguistic variables, fuzzy rules and fuzzy control. It also covers artificial neural networks, including the biological inspiration from the human brain, basic neuron models, multi-layer feedforward networks, training algorithms like gradient descent, and examples of neural networks solving problems like XOR classification. Hardware implementations on systems like DSpace and Opal RT are also briefly mentioned.
The document provides an overview of fuzzy logic and fuzzy sets. It discusses how fuzzy logic can handle imprecise data unlike classical binary sets. Membership functions assign degrees of membership values between 0 and 1. Fuzzy logic systems use if-then rules and linguistic variables. An example shows how fuzzy logic is used to estimate project risk levels based on funding and staffing levels. Fuzzy logic has been applied in various domains due to its ability to model human reasoning.
Fuzzy logic is an approach to logic that allows intermediate values between conventional assessments like true/false, yes/no, high/low. It uses membership functions that assign values between 0 and 1 to indicate the degree to which an item belongs to a set. This resembles how natural language uses imprecise terms. Fuzzy logic is used in control systems, business, and finance to model complex systems using approximate reasoning rather than binary logic. A fuzzy expert system uses fuzzy rules and membership functions to reason about input data and produce output, mimicking how humans handle imprecision.
Fuzzy logic provides a method to formalize reasoning with vague terms by allowing membership functions and degrees of truth rather than binary true/false values. It can be used to model problems involving linguistic variables like "poor", "good", and "excellent".
The document discusses a tipping example to demonstrate fuzzy logic. It defines fuzzy rules for tip amounts based on the quality of service and food. For example, one rule is that if service is poor or food is rancid, the tip should be cheap. Membership functions are then used to evaluate the fuzzy rules and determine appropriate tip amounts based on varying degrees of service and food quality.
Fuzzy logic provides a more intuitive way to model problems involving vague
It is known as two-valued logic because it have only two values Ramjeet Singh Yadav
This document discusses fuzzy logic and its applications. It begins by explaining classical logic and crisp sets, which have binary membership. It then introduces fuzzy logic, which was developed by Lotfi Zadeh in 1965 and allows partial set membership between 0 and 1. This allows fuzzy logic to handle concepts involving degrees of truth. The key concepts of fuzzy logic discussed include fuzzy sets and membership functions, fuzzy operations like union and intersection, fuzzy relations, fuzzy rules, and fuzzy inference systems. Real-world applications of fuzzy inference systems are also mentioned, such as automatic control, expert systems, and medical engineering.
This document provides an overview of fuzzy logic and fuzzy set theory. It discusses how fuzzy sets allow for partial membership rather than crisp binary membership in sets. Various membership functions are described, including triangular, trapezoidal, Gaussian, and sigmoidal functions. Properties of fuzzy sets like support, convexity, and symmetry are defined. Finally, fuzzy set operations analogous to classical set operations are mentioned.
Artificial Intelligence lecture notes. AI summarized notes on uncertainty and handling it through fuzzy logic, tipping problem scenarios are seen in it, for reading and may be for self-learning, I think.
1) The document discusses the bias-variance trade-off in machine learning models. It explains that models with high complexity can overfit limited data, while simpler models may not capture important patterns.
2) Regularization can control overfitting by limiting model complexity. The bias-variance decomposition shows that prediction error can be decomposed into bias, variance, and noise terms as a function of the model.
3) For regression, the optimal prediction minimizes expected squared loss and is given by the conditional mean. The bias-variance decomposition is then applied to regression to relate expected prediction error to model complexity through the bias and variance terms.
---TABLE OF CONTENT---
Introduction
Differences between crisp sets & Fuzzy sets
Operations on Fuzzy Sets
Properties
MF formulation and parameterization
Fuzzy rules and Fuzzy reasoning
Fuzzy interface systems
Introduction to genetic algorithm
Lambda-cut method converts a fuzzy set (or relation) into a crisp set (or relation) by defining membership values above a specified lambda value. It works by determining the crisp values where the membership is greater than or equal to lambda. The output of a fuzzy system can be a single fuzzy set or a union of multiple output fuzzy sets, depending on the number of rules.
Fuzzy logic allows for modeling of imprecise concepts using fuzzy sets and fuzzy rules. A fuzzy set is characterized by a membership function that assigns a degree of membership between 0 and 1 to elements of a universe of discourse. Common fuzzy set operations include intersection, union, and complement. Fuzzy rules relate fuzzy propositions through an if-then structure. A fuzzy associative matrix maps the antecedent fuzzy set to the consequent fuzzy set to perform fuzzy inference using max-min composition. Fuzzy logic provides a framework for approximate reasoning about vague or uncertain concepts.
Fuzzy set theory is an extension of classical set theory that allows for partial membership in a set rather than crisp boundaries. In fuzzy set theory, elements have degrees of membership in a set represented by a membership function between 0 and 1. This allows for modeling of imprecise concepts like "young" where the boundary is ambiguous. Fuzzy set theory is useful for modeling human reasoning and systems that can handle unreliable or incomplete information. Key concepts include fuzzy rules in an if-then format and fuzzy inference using methods like Mamdani inference involving fuzzification, rule evaluation, aggregation, and defuzzification.
This document describes fuzzy logic controllers and their components. It discusses:
- The architecture of a fuzzy logic controller including fuzzification, inference engine, rule base, and defuzzification.
- Membership functions and linguistic variables which are used to quantify fuzzy sets and linguistic terms between 0 and 1. Different types of membership functions are described including triangular, trapezoidal, and Gaussian.
- An example fuzzy logic controller for an air conditioning system that adjusts temperature based on rules relating current and target temperatures.
- Implementation of a Mamdani fuzzy logic controller in MATLAB with two inputs, membership functions, a rule base, and one output to control a process.
Fuzzy logic is a method for representing uncertainty and imprecision in logic and reasoning. It involves fuzzy sets that assign a degree of membership between 0 and 1 rather than crisp true/false values. Fuzzy logic control uses fuzzy membership functions, fuzzy rules, and defuzzification to map inputs to outputs based on linguistic variables like "temperature is warm." An example is a speed controller that uses speed, acceleration, and distance as inputs to determine engine power output based on fuzzy rules.
Fuzzy logic is a form of logic that accounts for partial truth and intermediate values between true and false. It extends conventional binary logic which has only true and false values. Fuzzy logic is used in fuzzy expert systems where rules use linguistic variables and fuzzy membership functions rather than binary logic. A fuzzy expert system fuzzifies inputs, applies inference rules to fuzzy subsets assigned by rules, composes the fuzzy subsets into single fuzzy subsets for outputs, and may defuzzify outputs into crisp values.
Fuzzy logic was introduced in 1965 by Lofti Zadeh based on fuzzy set theory. It allows for intermediate values between 0 and 1, unlike boolean logic which only considers true or false. A fuzzy logic system uses fuzzification to convert crisp inputs to fuzzy values, applies a rule base and inference engine to the fuzzy values, and then uses defuzzification to convert the fuzzy output to a crisp value. Fuzzy logic is useful for approximate reasoning and has applications in areas like control systems, decision making, and pattern recognition.
The document discusses various methods for representing knowledge, including:
- Using categories, objects, and properties to represent knowledge about the world in first-order logic
- Representing actions, events, and how objects and properties change over time using the situation calculus
- Addressing challenges like the frame and qualification problems by developing successor state axioms that characterize how fluents change with actions
We consider the problem of model estimation in episodic Block MDPs. In these MDPs, the decision maker has access to rich observations or contexts generated from a small number of latent states. We are interested in estimating the latent state decoding function (the mapping from the observations to latent states) based on data generated under a fixed behavior policy. We derive an information-theoretical lower bound on the error rate for estimating this function and present an algorithm approaching this fundamental limit. In turn, our algorithm also provides estimates of all the components of the MDP.
We apply our results to the problem of learning near-optimal policies in the reward-free setting. Based on our efficient model estimation algorithm, we show that we can infer a policy converging (as the number of collected samples grows large) to the optimal policy at the best possible asymptotic rate. Our analysis provides necessary and sufficient conditions under which exploiting the block structure yields improvements in the sample complexity for identifying near-optimal policies. When these conditions are met, the sample complexity in the minimax reward-free setting is improved by a multiplicative factor $n$, where $n$ is the number of contexts.
Real Time System Validation using Hardware in Loop (HIL) Digital PlatformSHIMI S L
Dr. Shimi S.L presents information on real time system validation using hardware-in-the-loop (HIL) digital platforms. HIL allows testing embedded systems by interacting them with simulated plant models in real time. This enables testing systems in unlimited scenarios without risks to actual hardware. Applications include controller design and testing, closed-loop testing of devices, SCADA systems studies, microgrid studies, and protection scheme design. DSpace and OPAL-RT are popular HIL platforms that interface simulated plant models with physical controllers using computation units and I/O interfaces. HIL provides an effective method for rigorous real-time testing of systems before deployment.
This document outlines the vision, mission, program objectives, and curriculum for an Electrical Engineering department. The vision is to be a center of excellence for electrical engineering education, training, and research. The mission includes offering continuing education programs, developing curricula, instructional materials, and undertaking research and consultancy. The program objectives are to develop technical and research skills, and generic skills. The curriculum spans 4 semesters and includes courses in various electrical engineering topics, laboratory courses, and a thesis. Program outcomes are defined and mapped to the curriculum and graduate attributes. Stakeholder feedback is incorporated into revising the curriculum and objectives. Student performance metrics like admissions, success rate, academic performance and placements are provided.
The document discusses laboratories and facilities available at an Electrical Engineering department. It notes that laboratories are well-equipped and maintained, with 3-4 students allotted per experimental setup. Preventive maintenance is carried out each semester. Laboratories have necessary equipment, white/blackboards, and manuals. Labs are established per university curriculum. Equipment is maintained and available for experiments beyond the curriculum. Facilities support mini projects and final theses. Laboratories include specialized equipment to support attainment of program outcomes in areas like power electronics, advanced power electronics, and a simulation center of excellence in collaboration with ABB India. Safety measures and additional training have been provided. Admission rates have been over 90% in recent years, with 100% of admitted
This document summarizes the facilities and technical support available in the Electrical Engineering department at NITTTR Chandigarh.
It describes the laboratories available including the Virtual Instruments Lab and Power Electronics Lab. Details are provided on the equipment available, batch sizes, weekly utilization, and technical staff support. Additional simulation facilities have been created including a Simulation Center of Excellence and a solar PV training kit.
Maintenance of laboratory equipment is discussed, including regular checks, repairs, and expenditures. Safety measures across laboratories are outlined. Academic audits are conducted by an Internal Quality Assurance Cell to monitor teaching quality and student performance. Actions are taken based on results to improve attainment of program outcomes and objectives. Placement, higher education and
This document discusses the processes used to assess attainment of course and program outcomes at an engineering program. It describes how course outcomes are defined and mapped to program outcomes. Assessment tools like assignments, exams, and projects are mapped to outcomes. Attainment is calculated based on student performance and surveys. First year courses contribute to early outcome assessment. Actions are taken like improving questions and tutorials if outcomes are not fully attained.
Selective harmonic elimination in a solar powered multilevel inverterSHIMI S L
The document discusses harmonic elimination in solar powered multilevel inverters. It describes different inverter topologies and compares their weight, cost, power loss and ability to eliminate harmonics. Cascaded H-bridge inverters have advantages of lighter weight and lower cost. Selective harmonic elimination technique uses firing angle optimization to eliminate specific harmonics like 5th, 7th and 11th. Block diagram shows the harmonic elimination system connected to grid via an 11-level cascaded H-bridge inverter. Mathematical equations are provided for calculating the firing angles to eliminate desired harmonics from the output voltage waveform.
The document discusses maximum power point tracking (MPPT) techniques for solar photovoltaic systems. It describes two basic approaches for maximizing power extraction: using an automatic sun tracker or searching for maximum power point (MPP) conditions using methods like perturb and observe, incremental conductance or artificial intelligence methods. The document provides details on selective harmonic elimination in solar powered multilevel inverters, comparing topologies based on weight, cost, power loss and harmonic reduction capabilities. Equations for the selective harmonic elimination technique are also presented.
Genetic algorithms are a type of evolutionary algorithm that mimics natural selection. They operate on a population of potential solutions applying operators like selection, crossover and mutation to produce the next generation. The algorithm iterates until a termination condition is met, such as a solution being found or a maximum number of generations being produced. Genetic algorithms are useful for optimization and search problems as they can handle large, complex search spaces. However, they require properly defining the fitness function and tuning various parameters like population size, mutation rate and crossover rate.
1. A state variable representation uses state variables, inputs, and outputs to model dynamic systems. The state variables provide information about the internal state of the system.
2. The behavior of a system can be described by state equations that relate the time derivatives of the state variables to the inputs, state variables, and outputs.
3. Eigenvalues and eigenvectors, which are derived from state variable models, have many applications including vibration analysis, image recognition, and determining communication channel capacities.
There are two broad classes of power system stability:
1) Steady state stability - The ability of a system to maintain equilibrium after a small disturbance.
2) Transient stability - The ability to maintain synchronism during large disturbances like faults.
Factors influencing transient stability include generator loading, fault conditions, clearing time, reactances, and inertia. Methods to improve it include high-speed excitation, series capacitors, fault clearing and independent pole operation.
Solar energy application for electric power generationSHIMI S L
The document discusses various topics related to solar energy generation including:
- Solar energy is generated through nuclear fusion reactions inside the sun and can be harnessed using technologies like solar cells, solar heat collectors, and solar power plants.
- Applications of solar energy include generating electricity at utility-scale solar power plants as well as powering vehicles, heating homes and water, and providing power in remote locations.
- Maximizing the power extracted from solar panels requires techniques like automatic sun tracking and searching for maximum power point conditions.
- Emerging solar technologies include solar farms in space that beam microwave energy to receivers on Earth and solar panels integrated into buildings.
Modern trends in electric drives involve replacing fixed speed drives with more efficient variable speed drives using power electronic converters and control. Variable speed drives allow optimizing motor speed for different applications and loads. Power electronic converters are used in electric drive systems to convert electric energy from AC sources like the grid to regulated DC or AC for electric motors. Modern drive systems use intelligent controllers and sensors for improved performance. Common electric motors used in drive systems include DC motors, induction motors, and permanent magnet synchronous motors.
This document discusses interfacing MATLAB with Arduino and provides details on:
1. Using a gyroscope module connected to an Arduino Uno board to measure orientation in three axes.
2. The specifications of the Arduino Uno microcontroller including flash memory size, SRAM, clock speed, and number of analog and digital input/output pins.
3. A link to a MATLAB package called ArduinoIO that provides Arduino support within MATLAB.
This document discusses different types of choppers and cycloconverters used in DC-DC conversion. It describes the basic operation and characteristics of various classes of choppers (A, B, C, D, E) and explains step-down, step-up, and buck-boost chopper configurations. The document also covers cycloconverter types, components, waveforms, and applications. Advantages include direct AC-AC conversion in a single stage while disadvantages are their complexity and limited output frequency range.
Power electronics devices operate at high power levels and require high efficiency compared to linear electronics. Some key power electronic devices include thyristors, IGBTs, MOSFETs, and integrated power circuits. Thyristors can be turned on through forward voltage triggering or gate triggering and turned off through natural commutation in AC circuits or forced commutation using resonant circuits, complementary devices, or external pulses. Proper protection of power devices includes using snubber circuits, overvoltage and overcurrent protection, and gate protection.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
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KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
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Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
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ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
2. The term "fuzzy logic" was introduced with
the 1965 proposal of fuzzy set
theory by Lotfi A. Zadeh.
Fuzzy logic is a form
of many-valued logic; it
deals with reasoning that is
approximate rather than
fixed and exact.
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
3. Fuzzy Controllers
The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant:
Fuzzification Inference Defuzzification
IFtemp=low
ANDP=high
THENA=med
IF...
Variables
Measured Variables
Plant
Command
4. Conventional (Boolean) Set Theory:
Fuzzy Set Theory
“Strong Fever”
40.1°C
42°C
41.4°C
39.3°C
38.7°C
37.2°C
38°C
Fuzzy Set Theory:
40.1°C
42°C
41.4°C
39.3°C
38.7°C
37.2°C
38°C
“More-or-Less” Rather Than “Either-Or” !
“Strong Fever”
5. Fuzzy Set vs Crisp Set
• X is a set of all real numbers from 1 to 10
• Universe of Discourse
• A is a set of real numbers between 5 and 8
• Crisp or Classical Set
• Membership Value 1 or 0
6. Fuzzy Set vs Crisp Set
• B is a set of young people
• Membership values between 0 and 1 – Fuzzy Set
Age 65 27 17 32 22 25
B 0 0.3 1 0 0.8 0.5
7. Fuzzy Set
• Another example of Fuzzy
Set
• What season is it right now?
• Using the astronomical
definitions for season, we
get sharp boundaries.
• What we experience as
seasons varies more or less
continuously
8. Traditional Representation of Logic
Slow Fast
Speed = 0 Speed = 1
bool speed;
get the speed
if ( speed == 0) {
// speed is slow
}
else {
// speed is fast
}
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
9. Fuzzy Logic Representation
Every problem must be
represent in terms of
fuzzy sets.
What are fuzzy sets?
Slowest
Fastest
Slow
Fast
[ 0.0 – 0.25 ]
[ 0.25 – 0.50 ]
[ 0.50 – 0.75 ]
[ 0.75 – 1.00 ]
10. Fuzzy Logic Representation
Slowest Fastest
float speed;
get the speed
if ((speed >= 0.0)&&(speed < 0.25)) {
// speed is slowest
}
else if ((speed >= 0.25)&&(speed < 0.5))
{
// speed is slow
}
else if ((speed >= 0.5)&&(speed < 0.75))
{
// speed is fast
}
else // speed >= 0.75 && speed < 1.0
{
// speed is fastest
}
Slow Fast
11.
12. 12
Fuzzy Linguistic Variables
• Fuzzy Linguistic Variables are used to
represent qualities spanning a particular
spectrum
• Temp: {Freezing, Cool, Warm, Hot}
• Membership Function
• Question: What is the temperature?
• Answer: It is warm.
• Question: How warm is it?
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
13. 13
Membership Functions
• Temp: {Freezing, Cool, Warm, Hot}
• Degree of Truth or "Membership“
• Each of these linguistic terms is associated
with a fuzzy set defined by a corresponding
membership function.
50 70 90 1103010
Temp. (F°)
Freezing Cool Warm Hot
0
1
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
14. Membership Functions
• Membership function (MF) is a curve that defines
how each point in the input space is mapped to a
membership value (or degree of membership)
between 0 and 1 and is often given the designation
of µ.
• µA(x) is called the membership function (or MF) of x
in A.
• Thus membership functions are subjective measures
for linguistic terms.
• There are many types of membership functions.
16. 16
Membership Functions
• How cool is 36 F° ?
50 70 90 1103010
Temp. (F°)
Freezing Cool Warm Hot
0
1
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
17. 17
Membership Functions
• How cool is 36 F° ?
• It is 30% Cool and 70% Freezing
50 70 90 1103010
Temp. (F°)
Freezing Cool Warm Hot
0
1
0.7
0.3
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
18. 18
Fuzzy Logic
• How do we use fuzzy membership
functions in predicate logic?
• Fuzzy logic Connectives:
– Fuzzy Conjunction,
– Fuzzy Disjunction,
• Operate on degrees of membership
in fuzzy sets
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
19. 19
Fuzzy Disjunction (Union)
• AB max(A, B)
• AB = C "Quality C is the
disjunction of Quality A and B"
0
1
0.375
A
0
1
0.75
B
(AB = C) (C = 0.75)
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
20. 20
Fuzzy Conjunction (Intersection)
• AB min(A, B)
• AB = C "Quality C is the
conjunction of Quality A and B"
0
1
0.375
A
0
1
0.75
B
(AB = C) (C = 0.375)
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
21.
22. Fuzzy Set Operations
• There are three basic operation on fuzzy sets: negation, intersection,
and union
• Negation
membership_value(not x)= 1- membership_value(x)
where x is the fuzzy set being negated
• Intersection
membership_value(x and y) = minimum{membership_value(x),
membership_value(y)}
where x and y are the fuzzy sets involved in the intersection
• Union
membership_value(x or y) = maximum{membership_value(x),
membership_value(y)}
where x and y are the fuzzy sets involved in the union
• minimum operator for intersection and the
maximum operator for union
23. Fuzzy Set Operations
• Let A be a fuzzy interval between 5 and 8
• B be a fuzzy number about 4.
27. Fuzzy Relations
• A crisp relation between two sets X, Y is a
binary relation.
• Binary relations are represented by relation
matrices and also by sagittal diagrams.
• R={(1,a) (2,c) (3,b) (4,c)}
• Sagittal Diagram
• Relation Matrix
1004
0103
1002
0011
cba
28. Fuzzy Relations
• Relation between two or more fuzzy sets is
obtained by the Cartesian product.
yxyxyx BAAxBR ,min,,
321 x
1
+
x
50
+
x
20
=A
..
21 y
90
+
y
30
=B
..
9030x
5030x
2020x
yy
3
2
1
21
..
..
..
29. Fuzzy Relations
• Let us describe the relationship between the
colour of a fruit, x and the grade of maturity, y.
• x= {green, yellow, red}
y={verdant, half-mature, mature}
• Considering the relation between the linguistic
terms red and mature, and representing them
by the membership functions, a fruit can be
characterized by the property of red and
mature.
31. 4.08.0
5.07.0=
2
1
21
x
x
yy
R
Fuzzy Compositions
T = R o S - max-min composition
T = R S - max-product composition
Chain-strength analogy for max-min composition
5.07.01.0
2.06.09.0=
2
1
321
y
y
zzz
S
( ) ( ) ( )( ){ }zyyxzx SRT ,,,minmax=,
( ) ( ) ( )( ){ }zyyxzx SRT ,•,max=,
36. Fuzzy Relations
• Three variables of interest in power transistors are the
amount of current that can be switched, the voltage that can
be switched, and the cost. The following membership
functions for power transistors were developed from
hypothetical components catalog:
• Average current
• Average voltage
• Power is defined by the algebraic operation P = VI
(a) Let us find the Cartesian Product P = VxI.
{ }
21
60
+
11
80
+
1
1
+
90
70
+
80
40
=
.
.
.
.
.
.
.
.
I
{ }
90
70
+
75
90
+
60
1
+
45
80
+
30
20
=
....
V
37. Fuzzy Relations
• The Cartesian Product expresses the relationship between
Vi and Ij , where Vi and Ij are individual elements in the
fuzzy set V and I.
• Now let us define a fuzzy set for the cost C in rupees, of a
transistor
(b)Using a fuzzy Cartesian Product, find T = IxC.
(c) Using max-min composition find E = PoT
(d) Using max-product composition find E = PoT
{ }
70
50
+
60
1
+
50
40
=
.
.
..
.
C
38. Fuzzy Control
Using a procedure originated by Ebrahim Mamdani
in the late 70s, three steps are taken to create a
fuzzy controlled machine:
Fuzzification (Using membership functions to
graphically describe a situation)
Rule Evaluation (Application of fuzzy rules)
Defuzzification (Obtaining the crisp results)
39. Fuzzy Control
Fuzzification is the process of making a crisp quantity
fuzzy.
Membership functions characterize the fuzziness in a
fuzzy set.
Six procedures to build membership functions
Intuition
Inference
Rank Ordering
Neural Networks
Genetic Algorithm
Inductive Reasoning
40. Fuzzy Control
Defuzzification is the conversion of a fuzzy quantity to a
precise quantity.
Output of a fuzzy process can be the logical union of two or
more fuzzy membership functions defined on the universe of
discourse. .
Methods of defuzzification
Max-membership principle
Centroid method
Weighted average method
Mean max membership
Center of sums
Center of largest area
First (or last) of maxima
41. 41
Fuzzy Control
• Fuzzy Control combines the use of
fuzzy linguistic variables with fuzzy
logic
• Example: Speed Control
• How fast am I going to drive today?
• It depends on the weather.
• Disjunction of Conjunctions
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
44. 44
Rules
• If it's Sunny and Warm, drive Fast
Sunny(Cover)Warm(Temp) Fast(Speed)
• If it's Cloudy and Cool, drive Slow
Cloudy(Cover)Cool(Temp) Slow(Speed)
• Driving Speed is the combination of
output of these rules...
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
45. 45
Example Speed Calculation
• How fast will I go if it is
– 65 F°
– 25 % Cloud Cover ?
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
51. ● Artificial neural network (ANN) is a machine
learning approach that models human brain and
consists of a number of artificial neurons.
● An Artificial Neural Network is specified by:
− neuron model: the information processing unit
of the NN,
− an architecture: a set of neurons and links
connecting neurons. Each link has a weight,
− a learning algorithm: used for training the NN
by modifying the weights in order to model a
particular learning task correctly on the
training examples.
● The aim is to obtain a NN that is trained and
generalizes well.
● It should behaves correctly on new instances of
the learning task.
52. The Biological Neural Network
Characteristics of Human Brain
• Ability to learn from experience
• Ability to generalize the knowledge it possess
• Ability to perform abstraction
• To make errors.
53. • A neuron fires when the sum of its collective
inputs reaches a threshold
• There are about 10^11 neurons per person
• Each neuron may be connected with up to
10^5 other neurons
Consists of three
sections
cell body
dendrites
axon
54. • Nerve impulses which pass down the axon, jump
from node to node, thus saving energy.
• There are about 10^16 synapses. Usually no
physical or electrical connection made at the
synapse.
55.
56. Human neurons Artificial neurons
Neurons Neurons
Axon, Synapse Wkj (weight)
Synaptic terminals
to next neuron
output terminals
Synaptic terminals
taking input
input terminals (Xj)
human response time=1 ms silicon chip response time=1ns
58. Neuron
● The neuron is the basic information processing unit of a
NN. It consists of:
1 A set of links, describing the neuron inputs, with weights W1, W2,
…, Wm
2 An adder function (linear combiner) for computing the weighted
sum of the inputs:
(real numbers)
3 Activation function for limiting the amplitude of the neuron
output. Here ‘b’ denotes bias.
m
1
jjxwu
j
)(uy b
59. Bias of a Neuron
● The bias b has the effect of applying a transformation to
the weighted sum u
v = u + b
● The bias is an external parameter of the neuron. It can be
modeled by adding an extra input.
● v is called induced field of the neuron
bw
xwv j
m
j
j
0
0
60.
61. Activation Function
● The choice of activation function determines the
neuron model.
Examples:
● step function:
● ramp function:
● sigmoid function with z,x,y parameters
● Gaussian function:
2
2
1
exp
2
1
)(
v
v
)exp(1
1
)(
yxv
zv
otherwise))/())(((
if
if
)(
cdabcva
dvb
cva
v
cvb
cva
v
if
if
)(
62. Training
Training is accomplished by sequentially applying input vectors while
adjusting network weights according to a predetermined procedures.
Supervised Training
requires the pairing of each input vector with a target vector representing
the desired output.
Unsupervised Training
requires no target vector for the output and no comparisons to
predetermined ideal responses. The training algorithm modifies network
weights to produce output vectors that are consistent. Also called self-
organizing networks.
65. These two classes (true and false) cannot be separated using a
line. Hence XOR is non linearly separable.
Input Output
X1 X2 X1 XOR X2
0 0 0
0 1 1
1 0 1
1 1 0
X1
1 true false
false true
0 1 X2
66. Multi layer feed-forward NN (FFNN)
● FFNN is a more general network architecture, where there are
hidden layers between input and output layers.
● Hidden nodes do not directly receive inputs nor send outputs to
the external environment.
● FFNNs overcome the limitation of single-layer NN.
● They can handle non-linearly separable learning tasks.
Input
layer
Output
layer
Hidden Layer
3-4-2 Network
67. FFNN for XOR
● The ANN for XOR has two hidden nodes that realizes this non-linear
separation and uses the sign (step) activation function.
● Arrows from input nodes to two hidden nodes indicate the directions of
the weight vectors (1,-1) and (-1,1).
● The output node is used to combine the outputs of the two hidden
nodes.
Input nodes Hidden layer Output layer Output
H1 –0.5
X1 1
–1 1
Y
–1 H2
X2 1 1
68. Inputs OutputofHiddenNodes Output
Node
X1XORX2
X1 X2 H1 H2
0 0 0 0 –0.50 0
0 1 –10 1 0.5 1 1
1 0 1 –10 0.5 1 1
1 1 0 0 –0.50 0
Since we are representing two states by 0 (false) and 1 (true), we
will map negative outputs (–1, –0.5) of hidden and output layers
to 0 and positive output (0.5) to 1.
Input nodes Hidden layer Output layer Output
H1 –0.5
X1 1
–1 1
Y
–1 H2
X2 1 1
73. • Human can identify a person through thoughts.which means humans neurons are getting trained
itself. Therefore through Artificial Neural Network we can train artificial neurons using computer
programming . using neural network we are trying to build a network between neurons to transfer
the electrical signals.which are consists of neural commands .
• usually Computer response time is 10^6 times faster than humans response time because of the
silicon Integrated chips.
• silicon chip response time :- 1 nanosecond
• human response time :- 1 millisecond
•
• but human can perform faster than chips because human has massively parallel neural structure. If
we consider human neuron structure it has synaptic terminals, cell body(neurons), basal dendrite
and axon. Each components has some function to transfer signal to
neurons.
74. • Bias neurons are added to neural networks to
help them learn patterns. A bias neuron is
nothing more than a neuron that has a
constant output of one. Because the bias
neurons have a constant output of one they
are not connected to the previous layer. The
value of one, which is called the bias
activation, can be set to values other than
one. However, one is the most common bias
activation.