1. Fuzzy Systems. Introduction

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1 1. Fuzzy Systems منظومات ضبابيه (هلاميه) Introduction

2 1.1. What is FUZZY? fuzzy = not sharp, unclear, imprecise, approximate ex: fuzzy statement: I shall return in a few minutes It is the mark of an instructed mind to rest satisfied with that degree of precision which the nature of the subject admits, and not to seek exactness where only an approximation of the truth is possible. Aristotle, BC Ancient Greek philosopher Fuzzy systems are very useful in two general contexts: (1) in situations involving highly complex systems whose behaviors are not well understood, and (2) in situations where an approximate, but fast, solution is warranted

3 1.2. What are Fuzzy Sets? Crisp Sets use sharp distinctions. It forces us to draw lines between members of a class and non-members. For instance, we may say, Aly is tall because his height is 181 cm. If we drew a line at 180 cm, we would find that Samir, who is 179 cm, is small. Is Samir really a small man or we have just drawn an arbitrary line in the sand? That an element can (exclusively) either belong to set or not belong to a set, makes it highly impossible to represent much of human Verbal expressions (large profit, high pressure, tall man, moderate temperature) Can we represent expert knowledge that uses vague and ambiguous terms in a computer? YES, WE CAN; through Fuzzy Sets

4 What are Fuzzy Sets? (Contd.) Temperature, height, speed, distance, beauty all come on a sliding scale. Fuzzy logic is based on the idea to express things imprecisely. Examples: The motor is running really hot. Esmat is a very tall guy. Since knowledge can be expressed in a more natural way by using fuzzy sets, many engineering and decision problems can be greatly simplified

5 1.3. What is FUZZY Control? Manual Control of water Level in a tank

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7 1.4. Bit of History In 1964 Lotfi Zadeh, was to present a paper on pattern recognition at a conference. The thought occurred to him that, recognizing patterns means deciding whether an object or its points match or at least closely resemble a pattern. Such a decision is often not a simple one to make it is much easier not to commit with 100% certainty but instead just to give an approximate answer. This, in turn, means gradually evaluating the membership of points to a pattern and replacing the yes/no decision with a softer, vague, unsharp statement. From this small idea, Zadeh developed a mathematical theory whose basic modules are sets with elements that are capable of belonging to the sets to only a certain degree and functions that give these elements their degrees of membership to the sets

8 In 1965 Lotfi Zadeh, published his famous paper Fuzzy sets. Zadeh extended the work on possibility theory into a formal system of mathematical logic, and introduced a new concept for applying natural language terms. This new logic for representing and manipulating fuzzy terms was called fuzzy logic

9 1.5. Fuzzy Applications Theory of fuzzy sets and fuzzy logic has been applied to problems in a variety of fields: topology; linguistics; logic; automata theory; game theory; pattern recognition; medicine; law; decision support; Information retrieval; etc. and more recently fuzzy machines have been developed including: automatic train control; tunnel digging machinery; washing machines; rice cookers; vacuum cleaners; air conditioners, etc

Example Washing Machine: Typically, fuzzy logic controls the washing process, water intake, water temperature, wash time, rinse performance, and spin speed.

10 Example Washing Machine: Typically, fuzzy logic controls the washing process, water intake, water temperature, wash time, rinse performance, and spin speed. This optimises the life span of the washing machine. More sophisticated machines weigh the load (so you can t overload the washing machine), advise on the required amount of detergent, assess cloth material type and water hardness, and check whether the detergent is in powder or liquid form. Some machines even learn from past experience, memorising programs and adjusting them to minimise running costs

11 1. Water Amount: Fuzzy Logic detects the type and amount of laundry in the drum and allows only as much water to enter the machine as is really needed for the loaded amount. And less water will heat up quicker which means less energy consumption. 2. Foam detection: If Fuzzy Logic detects the formation of too much foam in the rinsing spin cycle, it simply activates an additional rinse cycle. 3. An optical sensor measures the clarity of the wash water, and the controller estimates how long it would take a stain to dissolve in the wash water. 4. Some machines use a load sensor to trigger changes in the agitation rate or water temperature. Others shoot bubbles into the wash to help dissolve dirt and detergent

12 Course Contents 1. Introduction 2. Classical and Fuzzy Sets 3. Crisp & Fuzzy Relations 4. Membership Functions 5. Fuzzy Numbers, Arithmetic, Vectors and the extension Principle 6. Fuzzy Rules 7. Decision Making 8. Classification and Pattern Recognition 9. Fuzzy Control Systems

Fuzzy Logic and Fuzzy Systems

Fuzzy Logic and Fuzzy Systems Xin Yao Some material adapted from slides by B. Vrusias, University of Surrey, and by G. Cheng, West Virginia University. Fall 2017 Artificial Intelligence: Fuzzy Logic and