How can a logic which is "fuzzy" be useful?
As humans, we often rely on imprecise expressions like "usually", "expensive", or "far". But the comprehension of a computer is limited to a black-white, everything-or-nothing, or true-false mode of thinking. Within conventional logic, terms can be only "true" or "false" i.e. either 0 or 1. Fuzzy logic allows a generalization of conventional logic. It provides for terms between "true" and "false" like "almost true" or "partially false". Therefore, fuzzy logic cannot be directly processed on computers but must be emulated by special code. The binary logic of modern computers often falls short when describing the vagueness of the real world. Fuzzy logic offers more graceful alternatives. Computers do not reason as brains do. Computers "reason" when they manipulate precise facts that have been reduced to strings of zeros and ones and statements that are either true or false. The human brain can reason with vague assertions or claims that involve uncertainties or value judgments: The air is cool," or "That speed is fast" or "She is young." Unlike computers, humans have common sense that enables them to reason in a world where things are only partially true. Fuzzy logic is a branch of machine intelligence that helps computers paint gray, commonsense pictures of an uncertain world. Logicians in the 1920s first broached its key concept: everything is a matter of degree.
�Fuzzy logic manipulates such vague concepts as "warm" or "still dirty" and so helps engineers to build air conditioners, washing machines and other devices that judge how fast they should operate or shift from one setting to another even when the criteria for making those changes are hard to define. When mathematicians lack specific algorithms that dictate how a system should respond to inputs, fuzzy logic can control or describe the system by using "commonsense" rules that refer to indefinite quantities. No known mathematical model can back up a truck-and-trailer rig from a parking lot to a loading dock when the vehicle starts from a random spot. Both humans and fuzzy systems can perform this nonlinear guidance task by using practical but imprecise rules such as "If the trailer turns a little to the left, then turn it a little to the right." Fuzzy systems often glean their rules from experts. When no expert gives the rules, adaptive fuzzy systems learn the rules by observing how people regulate real systems. Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. Fuzzy logic relies on a set of defined rules to be determined as being true or false. It relies on creating quantitative measurements of already pre-defined binary states. It can be thought of as the application side of fuzzy set theory dealing with well thought out real world expert values for a complex problem. Fuzzy logic allows for set membership values to range (inclusively) between 0 and 1, and in its linguistic form, imprecise concepts like "slightly", "quite" and "very". Specifically, it allows partial membership in a set. It is related to fuzzy sets and possibility theory. Basically, fuzzy logic allows a continuous range of truth values instead of just true and false. In fuzzy, set values strictly between 0 and 1 characterize the fuzzy members. Fuzzy logic is indeed a purely quantitative system and not the qualitative system many seem to assume is its key benefit.
Fuzzy logic is the same as "imprecise logic".
Fuzzy logic is not any less precise than any other form of logic: it is an organized and mathematical method of handling inherently imprecise concepts. The concept of "coldness" cannot be expressed in an equation, because although temperature is a quantity, "coldness" is not. However, people have an idea of what "cold" is, and agree that there is no sharp cutoff between "cold" and "not cold", where...