Quality function deployment is a cross-functional decision-making tool that converts customer needs into technical attributes of new products. Fuzzy numbers are usually adopted to evaluate the customer need importance and the customer need–technical attribute relationships. However, the weighted normalized customer need–technical attribute relationship matrix is not always full rank. If the different fuzzy numbers of two technical attributes are defined as the fuzzy negative ideal solutions, both the closeness coefficients are 0, and the traditional technique for order preference by similarity to an ideal solution cannot prioritize the two technical attributes. Actually, the rankings of different fuzzy numbers are not identical. To solve this problem, we present a new technique for order preference by similarity to an ideal solution to prioritize technical attributes in the fuzzy quality function deployment. The fuzzy positive ideal solution, fuzzy negative ideal solution, and distance measurement of the new technique for order preference by similarity to an ideal solution are improved. As a result, the proposed method not only prioritizes various forms of numbers without considering the lower and upper limits, the median, and boundary interval but also deals with the nonfull rank matrix. Besides, the Theory of Inventive Problem Solving is used to solve technical conflicts which are identified by the line-fitting method. The prioritization results from the proposed method can help to reasonably allocate design and manufacturing resources. Finally, a case on phone shell is given to illustrate the application of the proposed quality function deployment method.