The fuzzy structured element theory of fuzzy number is adopted to give a definition of fuzzy number that is non-linear and is categorized into exponent and sine fuzzy number. Based on the method of order-preserving transform of bounded monotone functions on the symmetric interval [ - 1,1 ] , four fundamental operations of exponent and sine fuzzy number are discussed and put forward the membership function formula according to results of the four fundamental operations. The methods and achievements will play a referential role in having a research on the swift-calculation of fuzzy number of other forms.