Abstract: Fuzzy controllers can be regarded as a fuzzy mappinq from the set of linguistic variables describing the observed object to that of linguistic variables describing the controlled objects. Therefore, it is of great importance, both theoretically and practically, to the research of fuzzy mapping.
The extension principle developed by Zadeh as a definition can be deduced from the definition of fuzzy mapping discussed in this paper.
In the paper, the α level relation of fuzzy mapping is also defined, and three resolution theorems are proved on the basis of α level set and α level relation.
Given a fuzzy mapping T:X→Y and a fuzzy set B in Y, we raise the problem:Under what Condition can we find such a fuzzy set A in X that T(A)=B? The two sufficient and necessary conditions given in the paper are the answer to the problem.