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Student Corner: Fuzzy Logic

| On 03, Dec 2007

By Abram Teplitskiy

Is experience the best judge of paradoxes? Broadly speaking, it is not. Logic and experience can “trick” minds. Understanding the different types of logic and opportunities for confusion can help avoid the traps people regularly face.

By applying dialectic logic, people observed that changes between contradicting features often have no definite boundary. As such, a new category of logic was developed – fuzzy. Consider the following experiment: Begin with a bag of pieces of grain. Pick one grain and put it down on a table. Begin to add grains one by one on the table. When you can say that the person has a heap? This answer will be different for different individuals depending upon how they define a “heap.”

While dialectic logic analyzes systems as “black or white,” fuzzy logic considers systems in degrees as “possibly white, probably white, possibly black, probably black.” Another example illustrates the challenge of trying to estimate what turns an apple to not-an-apple when eating. Without a clear definition, the answer remains fuzzy.

Figure 1: Eating an Apple

Courtesy of Merle and Kelly Cunningham

In some cases, an “expert system” needs to be developed – sometimes based on databases and computer programs (e.g., certain medical examinations, lie detectors). Public opinion polls and juries are such “expert” systems that try to un-fuzzy information and turn it into dialectic logic, with a clear answer.

In a story by Russian writer Anton Chekhov, a priest was the defendant in a criminal trial facing a jury. The prosecutor claimed that the priest was guilty and asked jury members for support. The defense attorney’s speech comprised only a few sentences. He said that the priest, during long years of his service, had forgiven a lot of people for a lot of sins. Now, the jury members must return the debt. The jury, using, presumably, fuzzy logic, decided a verdict of “not guilty.”

Figure 2: A “Fuzzy” Jury

Courtesy of Merle and Kelly Cunningham

There are three types of logic: classic logic deals with two opposite poles (black or white); dialectic logic unites these poles in a system (black and white), which exhibits each pole separately in time or space; and fuzzy logic consider process of changing features from one pole to another, like the process of transforming one grain to a heap. Despite their differences, all three types of logic use the same tools: premise and conclusion; identification; classification; inductive and deductive syllogisms; analysis and synthesis.

In logic, a thesis or claim is called a conclusion and the evidence is called a premise. Consider the two following conclusions:

  1. It rains, therefore ground is wet.
  2. If the ground is wet, then it is raining.

The first conclusion is valid, but the second conclusion is not true in all cases, because the ground could be wet because of many different reasons (e.g., sprinkler systems).

The opportunities for logical thinking are often not consciously considered. Readers should spend a few days looking for examples of classic, dialectic and fuzzy logic. Please share the results with other Student Corner readers. The topic of logic will continue in the next Student Corner.

Happy inventing!