Fuzzy Logic

Fuzzy logic is a system of logic in which statements can vary in degrees of truthfulness rather than be confined to true or false answers. The human brain operates on fuzzy logic as it breaks down information into areas of probability. The idea was first developed in the 1960s by a computer scientist trying to discover a way to make computers mimic the human decision-making process. Fuzzy logic is widely used in the field of artificial intelligence (AI), with its more practical applications in consumer products such as air conditioners, cameras, and washing machines.

Background

The standard form of logic is often referred to as Boolean logic, named after nineteenth-century English mathematician George Boole. It is a system based on absolute values such as yes or no, true or false. In computing, this form of logic is applied to the binary values used in machine language. Binary values consist of 1s and 0s, which correspond to true or false, or on or off within a computer's circuitry.

The task of processing information within the human brain does not operate on an absolute system. It uses a method that closely resembles fuzzy logic to arrive at a result within a degree of uncertainty between a range of possibilities. For example, five people of varying heights can be standing in a line. Standard logic would answer the question "Is a person tall?" with a yes or no response. Six feet may be considered tall, while five feet, eleven inches would not be. Fuzzy logic allows for a number of responses between yes and no. A person may be considered tall, or somewhat tall, short or somewhat short. It also allows for personal interpretation, as six feet may be considered tall if a person is standing alone but not if he or she is standing next to an individual who is seven feet.

Overview

In 1965, professor Lotfi Zadeh at the University of California, Berkeley, developed the concept of fuzzy logic while attempting to find a way for computers to understand human language. Because humans do not think or communicate in 0s and 1s, Zadeh created a data set that assigned objects within the set values between 0 and 1. The values of 0 and 1 were included in the set but marked its outlying borders. For example, instead of a computer categorizing a person as old or young, it was assigned values that allowed it to classify a person as a percentage of young. Age five may be considered 100 percent young, while age twenty may be 50 percent young. Instead of determining data in absolutes, computers that used fuzzy logic measured the degree of probability that a statement was correct.

A concept important in fuzzy logic is the idea of a fuzzy set. A fuzzy set is a data set without a crisp, easily defined boundary. It is in contrast to a classical set in which the elements can clearly be placed within defined parameters. For example, it is easy to find a classical data set for months of the year from a list that includes June, Monday, July, Tuesday, August, Wednesday, and September. The answer is obviously June, July, August, and September. However, change the data set to summer months and it becomes a fuzzy set. While June, July, and August are often associated with summer, only about ten June days occur after the summer solstice. Conversely, the majority of September, which is often considered a fall month, actually corresponds with the end of summer. As a result, fuzzy logic holds that July and August are 100 percent summer months, while June is roughly 33 percent summer and September is 66 percent summer.

Fuzzy logic also involves an input of information that is run through a series of "if-then" statements called rules to produce an output of information. In order to achieve a valid result, all the variables must be defined prior to the input of information. A program designed to detect temperature changes in a room and adjust the air-conditioning accordingly must first be told what values constitute hot, warm, and cold and the proper air-conditioning output corresponding to those values. Then the program will run through a series of rules such as "if the temperature value is a certain percentage of hot and rising, then increase air conditioner output," or "if temperature value is a percentage of cold and falling, then decrease output."

While Zadeh developed fuzzy logic in the 1960s, it took almost a decade of advances in computer technology to allow it to be used in practical applications. Fuzzy logic applications became more common in Japan than in the United States, where the computing concept was slow to catch on. Because it tries to replicate the human thought process, fuzzy logic is often used in the field of artificial intelligence and robotics. It has found a more practical application, however, on lower-level AI systems such as those found in smart consumer and industrial products. Fuzzy logic is the process that allows vacuum cleaners to detect the amount of dirt on a surface and adjust its suction power to compensate. It allows cameras to adjust to the proper amounts of light or darkness in an environment, microwaves to coordinate cooking time with the amount of food, or washing machines to compensate for added volume of laundry. Fuzzy logic programs are also very flexible and continue to function if they encounter an unexpected value. They are also easily fine-tuned, often needing only an input of a new set of values to change the system's production.

Bibliography

Cintula, Petr, et al. "Fuzzy Logic." Stanford Encyclopedia of Philosophy, 15 Nov. 2016, plato.stanford.edu/entries/logic-fuzzy/. Accessed 24 Jan. 2017.

Dingle, Norm. "Artificial Intelligence: Fuzzy Logic Explained." Control Engineering, 4 Nov. 2011, www.controleng.com/single-article/artificial-intelligence-fuzzy-logic-explained/8f3478c13384a2771ddb7e93a2b6243d.html. Accessed 24 Jan. 2017.

"Foundations of Fuzzy Logic." MathWorks, www.mathworks.com/help/fuzzy/foundations-of-fuzzy-logic.html. Accessed 24 Jan. 2017.

"Fuzzy Logic Introduction." Imperial College London, www.doc.ic.ac.uk/~nd/surprise‗96/journal/vol2/jp6/article2.html. Accessed 24 Jan. 2017.

Kaehler, Steven D. "Fuzzy Logic – An Introduction." Seattle Robotics Society, www.seattlerobotics.org/encoder/mar98/fuz/fl‗part1.html#INTRODUCTION. Accessed 24 Jan. 2017.

McNeill, Daniel, and Paul Freiberger. Fuzzy Logic: The Revolutionary Computer Technology That Is Changing Our World. Touchstone, 1993.

Ross, Timothy J. Fuzzy Logic with Engineering Applications. 3rd ed., Wiley, 2010.

Scott, Gordon. "Fuzzy Logic: Definition, Meaning, Examples, and History." Investopedia, 10 Aug. 2022, www.investopedia.com/terms/f/fuzzy-logic.asp. Accessed 18 Jan. 2023.

Tang, Hooi Hung and Nur Syazreen Ahmed. "Fuzzy Logic Approach for Controlling Uncertain and Nonlinear Systems: A Comprehensive Review of Applications and Advances." Systems Science & Control Engineering, vol. 12, no. 1, 24 Aug. 2024, doi.org/10.1080/21642583.2024.2394429. Accessed 19 Nov. 2024.

"What Is 'Fuzzy Logic'? Are There Computers That Are Inherently Fuzzy and Do Not Apply the Usual Binary Logic?" Scientific American, www.scientificamerican.com/article/what-is-fuzzy-logic-are-t/. Accessed 24 Jan. 2017.