Читать книгу Introduction to Fuzzy Logic - James K. Peckol - Страница 59

Over the years, fuzzy logic has been found to be extremely beneficial and useful to people involved in research and development in numerous fields including engineers, computer software developers, mathematicians, medical researchers, and natural scientists. As we begin, with all those people involved, we raise the question: What is fuzzy?

Originally, the word fuzz described the soft feathers that cover baby chicks. In English, the word means indistinct, imprecise, blurred, not focused, or not sharp. In French, the word is flou and in Japanese, it is pronounced “aimai.” In academic or technical worlds, the word fuzz or fuzzy is used in an attempt to describe the sense of ambiguity, imprecision, or vagueness often associated with human concepts.

Revisiting an earlier example, trying to teach someone to drive a car is a typical example of real‐life fuzzy teaching and fuzzy learning. As the student approaches a red light or intersection, what do you tell him or her? Do you say, “Begin to brake 25 m or 75 ft from the intersection?” Probably not. More likely, we would say something more like “Apply the brakes soon” or “Start to slow down in a little bit.” The first case is clearly too precise to be implemented or executed by the driver. How can one determine exactly when one is 25 m or 75 ft from an intersection? Streets and roads generally do not have clearly visible and accurate millimeter‐ or inch‐embedded gradations. The second vague instruction is the kind of expression that is common in everyday language.

Children learn to understand and to manipulate fuzzy instructions at an early age. They quite easily understand phrases such as “Go to bed about 10:00.” Perhaps with children, they understand too well. They are adept at turning such a fuzzy expression into one that is very precise. At 9:56, determined to stay up longer, they declare, “It's not 10:00 yet.”

In daily life, we find that there are two kinds of imprecision: statistical and nonstatistical. Statistical imprecision is that which arises from such events as the outcome of a coin toss or card game. Nonstatistical imprecision, on the other hand, is that which we find in instructions such as “Begin to apply the brakes soon.” This latter type of imprecision is called fuzzy, and qualifiers such as very, quickly, slowly or others on such expressions are called hedges in the fuzzy world.

Another important concept to grasp is the linguistic form of variables. Linguistic variables are variables with more qualitative rather than numerical values, comprising words or phrases in a natural or potentially an artificial language. That is, whether simple or complex, such variables are linguistic rather than numeric. Simple examples of such variables are very, slightly, quickly, and slowly. Other examples may be generated from a set of primary terms such as young or its antonym old or tall with its antonym short.

The first practical noteworthy applications of fuzzy logic and fuzzy set theory began to appear in the 1970s and 1980s. To effectively design modern everyday systems, one must be able to recognize, represent, interpret, and manipulate statistical and nonstatistical uncertainties. One should also learn to work with hedges and linguistic variables. One should use statistical models to capture and quantify random imprecision and fuzzy models to capture and to quantify nonrandom imprecision.