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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.
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What is the difference between classical set theory and fuzzy set theory?
Classical theory is a reference to established theory. Fuzzy set theory is a reference to theories that are not widely accepted.
Difference between crisp logic and fuzzy logic?
Crisp :Binary logicIt may be occur or non occurindicator functionFuzzy logicContinuous valued logicmembership functionConsider about degree of membership
What is the Difference between fuzzy logic and probability?
The difference between probability and fuzzy logic is clear when we consider the underlying concept that each attempts to model. Probability is concerned with the undecidability in the outcome of clearly defined and randomly occurring events, while fuzzy logic is concerned with the ambiguity or undecidability inherent in the description of the event itself. Fuzziness is often expressed as ambiguity rather than imprecision or uncertainty and remains a characteristic of perception as well as concept.
Different between crisp set and fuzzy set?
In short, for a crisp set (subset) elements of the set definitely do belong to the set, while in a fuzzy set (subset) elements of the set have a degree of membership in the set. To make things clearer:Suppose we have a reference set X={x_1, ...} and a subset Y={y_1, ...} of X. If Y represents a crisp subset of X, then for all x_n belonging to X, x_n either belongs or Y or does not belong to Y. We can write this by assigning a function C which takes each member of X to 1 iff it belongs to Y, and 0 iff it does not belong to Y. E. G. Suppose we have the set {1, 2, 3, 4, 5}. For the crisp subset {1, 2, 4} we could write this in terms of a function C which takes 1 to 1, 2 to 1, 3 to 0, 4 to 1, and 5 to 0, or we can write {(1, 1), (2, 1), (3, 0), (4, 1), (5, 1)}.For a fuzzy subset F of a reference set X the elements of F may belong to F to a degree in between 0 and 1 (as well as may belong to F to degree 0 or 1). We can write this by assigning a function M which takes each member of X to a number in the interval of real numbers from 0 to 1, [0, 1] to represent its degree of membership. Here "larger" numbers represent a greater degree of membership in the fuzzy subset F. For example, for the reference set {1, 2, 3, 4, 5} we could have a function M which takes 1 to .4, 2 to 1, 3 to .6, 4 to .2, and 5 to 0, or {(1, .4), (2, 1), (3, .6), (4, .2), (5, 0)}, with 3 having a greater degree of membership in F than 4 does, since .6>.2.
Why is fuzzy logic not best in solving uncertainty?
Certainly fuzzy logic is not the best in solving uncertainty, but..... it is on of the best alternatives to that exists to model uncertainty.
