Chapter 10. Fuzzy Logic

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Chapter 10. Fuzzy Logic In 1965 Lotfi Zadeh, a professor at the University of California Berkeley, wrote his original paper laying out fuzzy set theory. We find no better way of explaining what fuzzy logic is than by quoting the father of fuzzy logic himself. In a 1994 interview of Zadeh conducted by Jack Woehr of Dr. Dobbs Journal, Woehr paraphrases Zadeh when he says "fuzzy logic is a means of presenting problems to computers in a way akin to the way humans solve them." Zadeh later goes on to say that "the essence of fuzzy logic is that everything is a matter of degree." We'll now elaborate on these two fundamental principles of fuzzy logic. What does the statement "problems are presented to computers in a way similar to how humans solve them" really mean? The idea here is that humans very often analyze situations, or solve problems, in a rather imprecise manner. We might not have all the facts, the facts might be uncertain, or perhaps we can only generalize the facts without the benefit of precise data or measurements. For example, say you're playing a friendly game of basketball with your buddies. When sizing up an opponent on the court to decide whether you or someone else should guard him, you might base your decision on the opponent's height and dexterity. You might decide the opponent is tall and quick, and therefore, you'd be better off guarding someone else. Or perhaps you'd say he is very tall but somewhat slow, so you might do fine against him. You normally wouldn't say to yourself something such as, "He's 6 feet 5.5 inches tall and can run the length of the court in 5.7 seconds." Fuzzy logic enables you to pose and solve problems using linguistic terms similar to what you might use; in theory you could have the computer, using fuzzy logic, tell you whether to guard a particular opponent given that he is very tall and slow, and so on. Although this is not necessarily a practical application of fuzzy logic, it does illustrate a key point�fuzzy logic enables you to think as you normally do while using very precise tools such as computers. The second principle, that everything is a matter of degree, can be illustrated using the same basketball opponent example. When you say the opponent is tall versus average or very tall, you don't necessarily have fixed boundaries in mind for such distinctions or categories. You can pretty much judge that the guy is tall or very tall without having to say to yourself that if he is more than 7 feet, he's very tall, whereas if he is less than 7 feet, he's tall. What about if he is 6 feet 11.5 inches tall? Certainly you'd still consider that to be very tall, though not to the same degree as if he were 7 feet 4 inches. The border defining your view of tall versus very tall is rather gray and has some overlap. Traditional Boolean logic forces us to define a point above which we'd consider the guy very tall and below which we'd consider the guy just tall. We'd be forced to say he is either very tall or not very tall. You can circumvent this true or false/on or off characteristic of traditional Boolean logic using fuzzy logic. Fuzzy logic allows gray areas, or degrees, of being very tall, for example. In fact, you can think of everything in terms of fuzzy logic as being true, but to varying degrees. If we say that something is true to degree 1 in fuzzy logic, it is absolutely true. A truth to degree 0 is an absolute false. So, in fuzzy logic we can have something that is either absolutely true, or absolutely false, or anything in between�something with a degree between 0 and 1. We'll look at the mechanisms that enable us to quantify degrees of truth a little later. Another aspect of the ability to have varying degrees of truth in fuzzy logic is that in control applications, for example, responses to fuzzy input are smooth. Using traditional Boolean logic forces us to switch response states to some given input in an abrupt manner. To alleviate very abrupt state transitions, we'd have to discretize the input into a larger number of sufficiently small ranges. We can avoid these problems using fuzzy logic because the response will vary smoothly given the degree of truth, or strength, of the input condition. Let's consider an example. A standard home central air conditioner is equipped with a thermostat, which the homeowner sets to a specific temperature. Given the thermostat's design, it will turn on when the temperature rises higher than the thermostat setting and cut off when the temperature reaches or falls lower than the thermostat setting. Where we're from in Southern Louisiana, our air conditioner units constantly are switching on and off as the temperature rises and falls due to the warming of the summer sun and subsequent cooling by the air conditioner. Such switching is hard on the air conditioner and often results in significant wear and tear on the unit. One can envision in this scenario a fuzzy thermostat that modulates the cooling fan so as to keep the temperature about ideal. As the temperature rises the fan speeds up, and as the temperature drops the fan slows down, all the while maintaining some equilibrium temperature right around our prescribed ideal. This would be done without the unit having to switch on and off constantly. Indeed, such systems do exist, and they represent one of the early applications of fuzzy control. Other applications that have benefited from fuzzy control include train and subway control and robot control, to name a few. Fuzzy logic applications are not limited to control systems. You can use fuzzy logic for decision-making applications as well. One typical example includes stock portfolio analysis or management, whereby one can use fuzzy logic to make buy or sell decisions. Pretty much any problem that involves decision making based on subjective, imprecise, or vague information is a candidate for fuzzy logic. Traditional logic practitioners argue that you also can solve these problems using traditional rules-based approaches and logic. That might be true; however, fuzzy logic affords us the use of intuitive linguistic terms such as near, far, very far, and so on, when setting up the problem, developing rules, and assessing output. This usually makes the system more readable and easier to understand and maintain. Further, Timothy Masters, in his book Practical Neural Network Recipes in C++, (Morgan Kauffman) reports that fuzzy-rules systems generally require 50% to 80% fewer rules than traditional rules systems to accomplish identical tasks. These benefits make fuzzy logic well worth taking a look at for game AI that is typically replete with if-then style rules and Boolean logic. With this motivation, let's consider a few illustrative examples of how we can use fuzzy logic in games.

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