Rating TAs in fuzzy QFD by objective penalty function and fuzzy TOPSIS based on weighted Hamming distance

Quality function deployment (QFD) is an useful tool to solve Multi-criteria decision making, which can translate customer requirements (CRs) into the technical attributes (TAs) of a product and helps maintain a correct focus on true requirements and minimizes misinterpreting customer needs. In applying quality function deployment, rating technical attributes from input variables is a crucial step in fuzzy environments. In this paper, a new approach is developed, which rates technical attributes by objective penalty function and fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) based on weighted Hamming distance under the case of uncertain preference characteristics of decision makers in fuzzy quality function deployment. A pair of nonlinear programming models with constraints and a relevant pair of nonlinear programming models with unconstraints called objective penalty function models are proposed to gain the fuzzy important numbers of technical attributes. Then, this paper compares the fuzzy numbers by fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) method based on weighted Hamming distance in consideration of the uncertain preference characteristics of decision makers. To end with, the developed method is examined with the numerical examples.

An Objective Penalty Function-Based Method for Inequality Constrained Minimization Problem

For inequality constrained minimization problem, we first propose a new exact nonsmooth objective penalty function and then apply a smooth technique to the penalty function to make it smooth. It is shown that any minimizer of the smoothing objective penalty function is an approximated solution of the original problem. Based on this, we develop a solution method for the inequality constrained minimization problem and prove its global convergence. Numerical experiments are provided to show the efficiency of the proposed method.