The correct answer is A. Fuzzy logic is an extension of crisp set theory with an extension of handling the concept of partial truth.
Crisp set theory is a mathematical theory that deals with sets of objects that have a clear-cut membership. In crisp set theory, an object either belongs to a set or it does not. For example, the set of all red objects would include objects that are clearly red, such as a red ball or a red apple. It would not include objects that are not clearly red, such as a pink ball or a red-orange apple.
Fuzzy set theory is an extension of crisp set theory that allows for objects to have a partial membership in a set. In fuzzy set theory, an object can have a membership value that is between 0 and 1, where 0 indicates that the object does not belong to the set at all and 1 indicates that the object belongs to the set completely.
For example, the set of all red objects in fuzzy set theory might include objects that have a membership value of 0.9, such as a very red ball, and objects that have a membership value of 0.1, such as a slightly red apple.Fuzzy logic is a type of logic that is based on fuzzy set theory. Fuzzy logic allows for the use of partial truth in reasoning. For example, in fuzzy logic, it is possible to say that a statement is “mostly true” or “somewhat true”. This is in contrast to crisp logic, where a statement is either true or false.
Fuzzy logic has been used in a variety of applications, including control systems, pattern recognition, and decision making. It has also been used in artificial intelligence, where it has been used to develop systems that can reason in a more human-like way.