# Degree of truth

The degree of truth denotes the extent to which a proposition is true.

For example, in standard mathematics, the proposition zero belongs to the set { 0 } has a degree of truth of 1 (true), while proposition one belongs to the set { 0 } has a degree of truth of 0 (false). In fuzzy logic, the degree of truth of a proposition may be any real number between 0 and 1, inclusive. It is possible to build a fuzzy set F so that the proposition zero belongs to F has a degree of truth of 1/2.

Degree of truth should not be confused with a probability; it is not correct to say that zero has a 50% chance of being in F and a 50% chance of not being in F. Flipping a coin has a 50% chance of being heads and a 50% chance of being tails, but one side definitively appears; therefore a coin flip's result has a degree of truth 1 even though it is a random event. Neither should a degree of truth be confused with an unknown or varying truth value. Consider the sentence July 4, 1897 was a sunny day in New York City. Even if its truth value is not 1 (a completely cloudless day) or 0 (a completely cloudy day) it is still a definite value; the sunniness does not change with repeated observations of the day.

## Applications

Degrees of truth are often significant in artificial intelligence models where an agent deals with fuzzy concepts. An artificial weather reporter asked "Is it sunny out?" may piece together fuzzy data such as cloud cover, time of day (even a little sun at midnight may be considered sunny), location, season, and so on, to come up with a final yes or no answer.

Similar mathematical techniques can also be used to model uncertainty in non-fuzzy data (such as the aforementioned coin flip); this is usually called a degree of belief rather than of truth.

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