# Fuzzy Logic

##### Course Outline

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I. Introduction to Fuzzy Logic Systems

A. Overview and Understanding of Fuzzy Logic Systems

B. History and Evolution of Fuzzy Logic

C. Comparison: Fuzzy Logic vs Classical Logic

II. Basics of Fuzzy Logic

A. Understanding Fuzzy Sets

B. Operations on Fuzzy Sets

C. Fuzzy Relations and Fuzzy Graphs

III. Fuzzy Logic and Linguistic Variables

A. Introduction to Linguistic Variables

B. Fuzzification and Defuzzification Processes

C. Fuzzy if-then Rules

IV. Fuzzy Logic Controllers

A. Architecture of Fuzzy Logic Controllers

B. Designing a Fuzzy Logic Controller: Case Study

C. Applications of Fuzzy Logic Controllers

V. Fuzzy Decision Making

A. Fuzzy Decision Making and Evaluation Processes

B. Multi-Criteria Decision Making with Fuzzy Logic

C. Case Study: Fuzzy Decision Making in Practice

VI. Fuzzy Logic and Artificial Intelligence

A. Fuzzy Logic in Expert Systems

B. Fuzzy Logic in Machine Learning

C. Fuzzy Logic in Artificial Neural Networks

VII. Fuzzy Logic in Engineering and Sciences

A. Fuzzy Logic in Control Systems and Automation

B. Fuzzy Logic in Data Analysis and Data Mining

C. Fuzzy Logic in Medical Sciences

VIII. Advanced Topics in Fuzzy Logic

A. Type-2 Fuzzy Logic Systems

B. Adaptive Neuro-Fuzzy Inference System (ANFIS)

C. Fuzzy Logic and Uncertainty Modeling

IX. Challenges and Limitations of Fuzzy Logic Systems

A. Overview of the Criticisms of Fuzzy Logic Systems

B. Current Research and Future Trends in Fuzzy Logic Systems

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Textbook: "Fuzzy Logic with Engineering Applications" by Timothy J. Ross.

##### 1. Introduction to Fuzzy Logic Systems

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We will discuss the overview of fuzzy logic, its history and evolution, and draw a comparison between fuzzy logic and classical logic.

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A. Overview and Understanding of Fuzzy Logic Systems

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Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" (1 or 0) binary logic on which the modern computer is based. It was introduced by Dr. Lotfi Zadeh of UC/Berkeley in the 1960s as a means to model the uncertainty in natural languages.

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Fuzzy logic presents a different approach to formulating decisions, essentially by allowing partial membership in a set. In the simplest sense, a thing can be a member, not a member, or partly a member of a set.

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For example, consider the statement "Today is sunny." In binary (classical) logic, the day is either sunny or it isn't. But in fuzzy logic, it might be 0.3 rainy (because there are some clouds in the sky) and 0.7 sunny (because the sun is mostly visible).

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B. History and Evolution of Fuzzy Logic

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Fuzzy logic started in 1965 when Lotfi Zadeh, a professor at the University of California, Berkeley, proposed a mathematical definition of fuzzy sets as an extension of classical set theory. He extended it to a fuzzy logic system in 1973.

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Fuzzy logic got its big break in modern industry in the '80s in Japan, where it was used to control the speed of the subway in Sendai, resulting in energy savings. It then got popularized in consumer electronics like cameras and washing machines. It's used today in a variety of applications ranging from controlling autonomous vehicles to managing climate control systems.

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C. Comparison: Fuzzy Logic vs Classical Logic

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In classical binary set theory, a element either belongs to a set or it doesn’t. But, in fuzzy logic, the set membership is a possibility and can be any value between 0 and 1. It's this feature that allows fuzzy logic to model the uncertainty and vagueness in human reasoning.

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For example, in classical logic, a person could be classified as tall if they are over 6 feet, and not tall if they are below. But what about someone who is exactly 6 feet? Are they tall or not tall? Fuzzy logic allows us to handle such scenarios more effectively by assigning a degree of membership to the person's tallness, like this person is 0.7 tall.