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Back to Subjects - Mathematics

Fuzzy logic

Fuzzy logic Fuzzy Logic is a term used to identify a new trend of quantifying partial truths. One disadvantage of most rule sets that they cannot process inconsistent data. Fuzzy logic is a superset of conventional logic that has been extended to handle the concept of partial truth, being values that lie between "completely true" and "completely untrue". Dr. Lotfi Zadeth of UC/Berkley first introduced it in the 1960s as a means of modeling the uncertainty of natural language. All this works by using expanding on Boolean logic and the concept of subsets. In classical set theory, a subset X of a set Y can be defined as a mapping from the elements of Y to the elements of the set (0,1), X: Y --* (0,1). This mapping can be represented by a set of ordered pairs, with one ordered pair present for each element of the set X, and the second element is an element of the set (0,1). The value 0 represents non-membership, and the value 1 is used to represent membership. This approach is limited to only two opposing possible outcomes. If a variable z is in X, then the statement is true if z=1 and false if z=0. Fuzzy logic takes this process a few steps further and quantifies the degree of membership instead of stopping at a positive or negative correlation. A fuzzy subset F of a set Y can be defined as a set of ordered pairs, each with the first element from S, and the second element from the interval [0,1], with exactly one ordered pair present for each element of S. This defines a mapping between elements of the set S and values in the interval [0,1]. The value zero is still used to represent complete non-membership, the value one is used to represent complete membership, and values in between are used to represent intermediate degrees of membership. The set S is referred to as the universe of discourse for the fuzzy subset F. Frequently, the mapping is described as a function, the membership function of F. The degree to which the statement x is in F is true is determined by finding the ordered pair whose first element is x. The degree of truth of the statement is the second element of the ordered pair. To understand this graphically, lets use a Zadeh example that measures tallness. In this case the set S (the universe of discourse) is the set of people. We define a fuzzy subset TALL, which will answer the question "to what degree is person x tall?" Zadeh describes TALL as a linguistic variable, which represents our cognitive category of "tallness". To each person in the universe of discourse, we have to assign a degree of membership in the fuzzy subset TALL. The easiest way to do this is with a membership function based on the person's height. The following figure is how to define this using a graph. tall(x) = { 0, if height(x) * 5 ft., (height(x)-5ft.)/2ft., if 5 ft. *= height (x) *= 7 ft., 1, if height(x) * 7 ft. } 1.0 + +------------------- 0.0 +-------------+-----+------------------- Person Height degree of tallness -------------------------------------- The application of fuzzy logic allows us to go beyond the simple categories of "tall" and "not tall" and apply a real world understanding of other outside variables that are always included when considering humanistic characteristics. If someone were to ask "how tall is Shaq?", you probably wouldn't say "tall", you would probably add a descriptive variable like "really tall". Fuzzy logic is a way of measuring more discrete variables for further understanding. Fuzzy logic is used directly in very few applications. One good example of its application is the Sony Palmtop. This device is one of the new handheld messaging systems that have become very popular of late. With it, you can use a computer light pen to write words on the screen. The computer then uses a form of fuzzy logic to decipher the written text into a chosen computer font. It's an ingenious idea when you take into account the billions of different styles of handwriting. The computer takes in the written information and applies the logic to find which character is the closest match. The need for Fuzzy logic is growing with advancements in robotics and artificial intelligence. Fuzzy CLIPS is an extension of the CLIPS (C Language Integrated Production System) expert system shell from NASA. It was developed by the Integrated Reasoning Group of the Institute for Information Technology of the National Research Council of Canada and has been widely distributed for a number of years. It enhances CLIPS by providing a fuzzy reasoning capability that is fully integrated with CLIPS facts and inference engine allowing one to represent and manipulate fuzzy facts and rules. Fuzzy CLIPS can deal with exact, fuzzy (or inexact), and combined reasoning, allowing fuzzy and normal terms to be freely mixed in the rules and facts of an expert system. The system uses two basic inexact concepts, fuzziness and uncertainty. It has provided a useful environment for developing fuzzy applications but it does require significant effort to update and maintain as new versions of CLIPS are released. There is another application of fuzzy logic in oil drilling. Their goal is to apply fuzzy modeling and genetic algorithm to model infill drilling oil and recovery using data collected from oil wells. Their preliminary results show that this modeling can improve the prediction accuracy of statistical models that were previously developed. Another application is in highway traffic research. They hope to apply fuzzy logic to detect traffic incidents on diamond interchanges. This is part of a major research endeavor toward the development of intelligent and scalable traffic management systems conducted at Intelligent Vehicle Highway System Research Center. The Intelligent Tutoring Systems (ITS) program is supposed to design, develop, test, evaluate, document, deliver, and maintain an aircraft maintenance troubleshooting skills tutors. This project will utilize the state-of-the-art cognitive science and software development techniques. It is being conducted for the US Air Force Human Systems Program office. Fresno Industrial Technology professor Matthew Yen is exploring agricultural applications of a new technology that mimics human thought patterns in controlling industrial equipment operations. Professor Yen's research is focused on the application of fuzzy logic in the control of equipment such as heaters, motors, pumps, valves and sprinklers used in the food processing industry and other automated agricultural operations. In order to automate these processes, temperature, motor speed, liquid level, pressure, humidity, flow rate and other variables must be constantly monitored and adjusted according to prescribed schedule. Some more real life applications of fuzzy logic have proven to be beneficial: - Tokio Electric Power: uses FL for automatic control of dam gates for hydroelectric power - Hirota, Fuji Electric, Toshiba, and Omron: use it for simplified control of robots - Omron: uses FL for automated camera aiming for the telecast of sporting events - Hitachi: substitution of an expert for the assessment of stock exchange activities - Mitsubishi: preventing unwanted temperature fluctuations in air-conditioning systems - Nissan: Efficient and stable control of car engines and better cruise control - Aptronix: Improved efficiency and optimized function of industrial control applications - Canon - positioning of water - steppers in the production of semiconductors - Toshiba: Optimize planning of bus time tables - Mitsubishi: archiving system for documents - Kawasaki Medical School: cancer diagnosis - Matsu*censored*a: Combination of fuzzy logic and Neural nets - Sony: Recognition of handwritten symbols with pocket computers - Canon - Recognition of motives in pictures with video cameras - Matsushi: Automatic motor control for vacuum cleaners with recognition of surface condition and degree of soiling - Sanyo: black light control for camcorders - Matsu*censored*a: Compensation against vibrations in camcorders, single button control for washing machines - Sugeno: flight aid for helicopters - Nagoy University: simulation for legal proceedings - Harima: Software design for industrial processes - NKK: controlling of machinery speed and temperature for steel works - Hitachi: controlling of subway systems in order to improve driving comfort, precision of halting and power economy - NOK: Improved fuel - consumption for automobiles - Toshiba: Improved sensitiveness and efficiency for elevator control - Bernard: Improved safety for nuclear reactors When we began this project, we hoped to find a deeper understanding of fuzzy logic and its applications. While we gathered information, it became very apparent that fuzzy logic is the foundation for next level computer software development. Its applications will frontier artificial intelligence and other program knowledge's. In order to figure out a cost estimate for this project, we must estimate the time lost from doing other things we enjoy or need to do. While doing research, we could have been doing any number of relaxing or hobby like activities. We also could have been studying or finishing assignments for our other classes. Taking into account these facts, we have decided that we are happy to have spent the time doing this project. It is as informative as any other required assignment we have had and we were even given a choice of topics, which these days are a rarity. Feb. 2 - gathered research for milestone 1 Feb. 5 - gathered information for milestone 1 Feb. 14 - gathered information for Milestone 2 Mar. 20 - gathered information for milestone 3 Apr. 10 - started putting together final project Upon completion of this project, we have a deeper understanding and respect for the emerging technology and possible applications for fuzzy logic. It is one of the most exciting frontiers in so many areas because of the almost infinite application possibilities. We have learned where the original theory came from and where it is going. Fuzzy logic will be a staple in future technologies ranging from computer applications on data sets to airline navigation to stock market predictions. It will be the mother of AI and the stepping-stone for super advanced data processing systems. We might have expanded a little on the mathematical explanation of fuzzy logic. It is a very complex application when it comes to large number sets and quantification of extremely diverse rule sets. Other than that, we might have explained how exactly some of the fuzzy logic systems are adapted to some of the real life applications being used today. www.cs.cmu.edu/Groups/AI/html/faqs/ai/fuzzy/part1/faq.html www.ortech-engr.com/fuzzy/reservoir.html www.emsl.pnl.gov:2080/proj/neuron/fuzzy/what.html www.wolfram.com/products/applications/fuzzylogic Bibliography:

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