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The fundamental difference is that in fuzzy set theory permits the gradual assessment of the membership of elements in a set and this is described with the aid of a membership function valued in the real unit interval [0, 1]. Better, the degree of membership of the elements of a set can take values ranging between 0 and 1 allowing for a ranking of membership. Conversely, crisp set theory is a classical bivalent set so that the membership function only takes values 0 or 1. In this case, one can know only if an element of the set have or not a particular characteristic and a ranking of membership is not possible.
Classical theory is a reference to established theory. Fuzzy set theory is a reference to theories that are not widely accepted.
prove the intersction for crisp set theory
None. A set is a collection and a collection is a set.
The difference between the greatest and least numbers in a set of data is called the range.