Information about 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.
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.
See Also:
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.
See Also:
proposition is the content of an assertion, that is, it is true-or-false and defined by the meaning of a particular piece of language. The proposition is independent of the of communication.
..... Click the link for more information.
..... Click the link for more information.
Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
..... Click the link for more information.
..... Click the link for more information.
Fuzzy Logic may refer to:
Fuzzy logic
..... Click the link for more information.
- Fuzzy Logic (album), the debut album by the Super Furry Animals
- Fuzzy logic, an application of fuzzy set theory
- For the music album, see Fuzzy Logic (album)
Fuzzy logic
..... Click the link for more information.
In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339…. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as π and
..... Click the link for more information.
..... Click the link for more information.
Probability is the likelihood that something is the case or will happen. Probability theory is used extensively in areas such as statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of
..... Click the link for more information.
..... Click the link for more information.
artificial intelligence (or AI) is "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions which maximizes its chances of success.
..... Click the link for more information.
..... Click the link for more information.
intelligent agent (IA) is a software agent that assists users and will act on their behalf, in performing non-repetitive computer-related tasks. An agent in the sense of the word is like an insurance agent or travel agent.
..... Click the link for more information.
..... Click the link for more information.
vagueness. One example of a vague concept is the concept of a heap. Two or three grains of sand is not a heap, but a thousand is. How many grains of sand does it take to make a heap? There is no clear line. (See the paradox of the heap.
..... Click the link for more information.
..... Click the link for more information.
This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus
