The fuzzy number intuitionistic fuzzy group was defined and its some operations through fuzzy number intuitionistic set was discussed, then studied its some properties and gave its prove. Then in the sense of homomorphism between two nonempty limited classical groups, it proved that the image of this kind of fuzzy number intuitionistic fuzzy group also is a fuzzy number intuitionistic fuzzy group.

A new fuzzy number intuitionistic fuzzy sets distance was defined. A distance formula used to calculate an example was give and proved. Finally, the formula was used to calculate an instance. The result calculated example shows that the commodity prices can be assessed through the fuzzy estimation and calculation using the distance formula under the absence of accurate data.

Lagrange operator（Ln）and Bernstein operator（Bn）are two important operators used to deal with polynomial approximation and fitting problems, and they have advantages and disadvantages of their own. As to how to avoid weaknesses of these two operators, scholars have made unremitting efforts. One of the most famous is the French mathematician Sablonniere P, who introduced and studied a kind of new quasi-Bernstein interpolation operators in 1992. This kind of operators have given dual attention to the Lagrange operator and the Bernstein operator merit, and have avoided the two's deficiency. After giving the expression of operators B (k) n in detail when n=3. How to make use of these operators to conduct design of polynomial curve satisfying certain given conditions was proposed.