It is difficult to make arguments for certain theories if it can't be shown to perform alongside existing and accepted theories. Things like propositional logic are exact. If a statement in propositional logic could be illustrated with fuzzy logic...and fuzzy logic did it better, then maybe fuzzy would be more widely accepted.

Fuzzy logic cannot be used for unsolvable problems. This seems fairly reasonable, but its perception of being a guessing game may lead people to believe that it can be used for anything.

An obvious drawback to fuzzy logic is that it's not always accurate. The results are perceived as a guess, so it may not be as widely trusted as an answer from classical logic. Certainly, though, some chances need to be taken. How else can dressmakers succeed in business by assuming the average height for women is 5'6"?

Fuzzy logic can be easily confused with probability theory, and the terms used interchangeably. While they are similar concepts, they do not say the same things. Probability is the likelihood that something is true. Fuzzy logic is the degree to which something is true (or within a membership set).

Classical logicians argue that fuzzy logic is unnecessary. Anything that fuzzy logic is used for can be easily explained using classic logic. For example, True and False are discrete. Fuzzy logic claims that there can be a gray area between true and false. But classic logic says that the definition of terms is inaccurate, as opposed to the actual truth of the statement.

Fuzzy logic has traditionally low respectability. That is probably its biggest problem. While fuzzy logic may be the superset of all logic, people don't believe it. Classical logic is much easier to agree with because it delivers precision. Openmindedness on the part of those who use logic is needed in order to change the acceptance of fuzzy logic.

Contrary to popular belief, fuzzy logic can be used to solve the same types of problems that classical logic does. See the subject of crisp sets on our Sets page. So it is less that fuzzy logic has actual limitations and more that it has perceived limitations.

Arguments about Limitations of Fuzzy Logic

Haack, a formal logician, has some criticisms about fuzzy logic. She states that there are only two areas where fuzzy logic is "needed". (But, in each case, Haack can show that ultimately classical logic can substitute for fuzzy logic.)

The following are Haack's two cases that may require fuzzy logic:

• Nature of Truth and Falsity- Haack argues that True and False are discrete terms. In classical logic, any fuzziness that arises from a statement is due to an imprecise definition of terms. But, Haack says that if it can be shown that fuzzy values are indeed fuzzy (meaning not discrete), then a need for fuzzy logic would be demonstrated.

  For example, is this rectangle blue?

  It's difficult to say whether it blue or not. Because it's partially blue, but it is also partially green. Well, classical logicians would say that the term blue was not defined precisely enough. A more precise question would be: is this rectangle composed of 0/255 parts red, 0/255 parts green, and 0/255 parts blue? With the the terms more precisely defined, the answer is FALSE because this rectangle has the following color components: 0/255 parts red, 128/255 parts green, and 128/255 parts blue.

• Utility of Fuzzy Logic- Haack says if it can be shown that generalizing classic logic to include fuzzy logic would aid calculations, then fuzzy logic would be needed. But, Haack argues that data manipulation in a fuzzy system actually becomes more complex. So, fuzzy logic is not necessary.

So, ultimately, Haack believes fuzzy logic is not necessary because the calculations are more involved and partial membership values can be eliminated by defining terms more precisely.

Fox has responded to Haack's objections. He believes that the following three areas can benefit from fuzzy logic:

• "Requisite" Apparatus- Use fuzzy logic to describe real-world relationships that are inherently fuzzy.
• "Prescriptive" Apparatus- Use fuzzy logic because some data is inherently fuzzy and needs fuzzy calculus.
• "Descriptive" Apparatus- Use fuzzy logic because some inferencing systems are inherently fuzzy.

Fox argues that fuzzy and classical logic should not be seen as competitive but as complementary. Fox also states that fuzzy logic has found its way into the world of practical applications and has proved successful there. He says this is reason enough to continue development in the field of fuzzy logic.

Again we had some help from numerous Fuzzy Logic sites, namely #11 & #12 on our References page.