A novel IVIF QFD considering both the correlations of customer requirements and the ranking uncertainty of technical attributes

Abstract

Quality function deployment (QFD) is a planning and problem-solving tool that is gaining acceptance for translating customer requirements into the technical attributes. Deriving the rating of technical attributes (TAs) is a crucial step in QFD. However, the prioritization of TAs may be misleading in conventional QFD because of the uncertainty in linguistic data and result randomness. This study proposes a novel method to rate TAs based on interval-valued intuitionistic fuzzy sets, continuous ordered weighted averaging aggregation operator, Choquet integral, K-additive measures, and mixed integer programming. Firstly, the continuous ordered weighted averaging aggregation operator is proposed under interval-valued intuitionistic fuzzy environment to reflect individuals’ risk attitudes. Then, K-additive measures and Choquet integral are integrated to consider the correlation among customer requirements. Finally, the mixed integer programming is employed to prioritize technical attributes when maximizing the utility of design company and minimizing the group disagreements. The proposed method could rank TAs more robustly. An example of robot perception system design is cited to demonstrate the application of the method.

Appendix

According to Möbius transformation, we could get the fuzzy measures of CRs.

$$\begin{aligned}&W_{\varnothing }=\frac{1}{2}\sum _{i\in {N}}W_{i}-\frac{1}{6}\sum _{i,j\in {N}}I_{ij}\\&\qquad =\frac{1}{2}-\frac{1}{6}\times {(0.3+0.2+0.1)}=0.4\\&a(\varnothing )=W_{\varnothing }-\frac{1}{2}\sum _{i\in {N}}W_{i}+\frac{1}{6}\sum _{i,j\in {N}}I_{ij}=0\\&a(1)=W_{1}-\frac{1}{2}\sum _{j\in {N/1}}I_{1j}\\&\qquad \,=0.42-\frac{1}{2}\times {(0.3+0.1)}=0.22 a(2)\\&\qquad \,=W_{2}-\frac{1}{2}\sum _{j\in {N/2}}I_{2j}=0.28-\frac{1}{2}\times {(0.3+0.2)}\\&\qquad \,=0.03\\&a(3)=W_{3}-\frac{1}{2}\sum _{j\in {N/3}}I_{3j}=0.30-\frac{1}{2}\times {(0.2+0.1)}\\&\qquad \,\,=0.15\\&a(12)=I_{12}=0.3,a(13)=I_{13}=0.1,a(23)=I_{23}=0.2\\&\varphi {(CR_1)}=a(\varnothing )+a(1)=0.22,\varphi {(CR_2)}=a(\varnothing )+a(2)\\&\qquad \quad \,\,\,\,\,=0.03\\&\varphi {(CR_3)}=a(\varnothing )+a(3)=0.15,\varphi {(CR_1,CR_2)}=a(\varnothing )\\&\quad \qquad \qquad \quad +a(1)+a(2)+a(12)=0.55\\&\varphi {(CR_1,CR_3)}=a(\varnothing )+a(1)+a(3)+a(13)=0.47\\&\varphi {(CR_3,CR_2)}=a(\varnothing )+a(2)+a(3)+a(23)=0.38\\ \end{aligned}$$