# Fuzzy Logic

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## Definition: Fuzzy Logic

Fuzzy Logic is type of logic that involves more than simple true and false values. This means that propositions can be represented with degrees of truthfulness and falsehood. For example the statement It is a cloudy morning might be 100% true if the sky is full of clouds, 80% true if there are many clouds , 50% true if it's hazy and 0% true if the sun is out. Fuzzy logic is based on qualitative description used in day to day language and hence it is easy to understand.

The AND, NOT and OR operators used in Boolean Logic is also used in fuzzy logic. They are usually defined as the minimum, maximum, and complement are called the Zadeh operators. So for the fuzzy variables x and y:

NOT X = (1 – Truth(Y))

X AND Y = Minimum (truth(X), truth(Y))

X OR Y = Maximum (truth(X), truth(Y))

There are other operators known as hedges are applied in fuzzy logic and are mostly adverbs such as "very", "somewhat", which changes the meaning of a fuzzy set using mathematical formulas. Fuzzy logic and probability theory addresses different kinds of uncertainty. While both represent degrees of various kinds of subjective belief, probability theory uses the concept of subjective probability, i.e., how probable is it that a variable is included in a set (uncertainty is necessarily present) and fuzzy set theory uses the concept of fuzzy set membership, i.e., how much a variable is present in a set (may or may not be uncertainty).

Fuzzy logic has proved to be very useful in expert system and various other artificial intelligence applications. It is also used in spell checkers to suggest a list of probable words which could replace a misspelled one.

An example of fuzzy logic could be a temperature controller where the temperature can be defined as cold, cool, hot and warm and the humidity level can be low, medium and high. A fuzzy set can be defined using this.

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