Abstarct: The subject of this thesis is evaluate the fuzzy eigenvalues and it’s applications. To find the fuzzy eigenvalues of the two different methods are used. On a method of using the α-cut, fuzzy eigenvalues ￿￿and corresponding fuzzy eigenvectors are calculated by fully fuzzy linear system and Another method is baxsed on fuzzy number that is assigned the membershipfunctionisobtainedbyusingthedeterminant. Inthefirstchapterthehistory of the subject is expressed. The second chapter contains a variety of concepts related to the eigenvalues ￿￿of the graph and some bounds for the energy graphs is investigated. The thirdandfourthchapterscontaintwodifferentmethodsforfindingfuzzyeigenvalues￿￿and fuzzy eigenvectors of fuzzy numbers using the parameter mode. Chapter five contains the graph Laplacian energy and some bounds of this type of energy. This energy is also extended to the fuzzy case. Moreover, some bounds of eigenvalues ￿￿and energy of fuzzy graphs are calculated. For further understanding in each section, in first of each of these subjects in crisp mode and then fuzzy mode is expressed.