Soft Computing

, Volume 22, Issue 17, pp 5603–5615 | Cite as

Establishing the relationship matrix in QFD based on fuzzy regression models with optimized h values

  • Yuanyuan Liu
  • Yulin Han
  • Jian Zhou
  • Yizeng Chen
  • Shuya Zhong


In quality function deployment (QFD), establishing the relationship matrix is quite an important step to transform ambiguous and qualitative customer requirements into concrete and quantitative technical characteristics. Owing to the inherent imprecision and fuzziness of the matrix, the fuzzy linear regression (FLR) is gradually applied into QFD to establish it. However, with regard to an FLR model, the h value is a critical parameter whose setting is always an aporia and it is commonly determined by decision makers. To a certain extent, this subjective assignment fades the effectiveness of FLR in the application of QFD. Aiming to this problem, FLR models with optimized parameters h obtained by maximizing system credibility are introduced into QFD in this paper, in which relationship coefficients are assumed as asymmetric triangular fuzzy numbers. Moreover, a systematic approach is developed to identify the relationship matrix in QFD, whose application is demonstrated through a packing machine example. The final results show that FLR models with optimized h values can always achieve a more reliable relationship matrix. Besides, a comparative study on symmetric and asymmetric cases is elaborated detailedly.


Quality function deployment Relationship matrix Fuzzy linear regression Optimized h value Asymmetric triangular fuzzy number 



The authors would like to acknowledge the gracious support of this work by “Shuguang Program” from Shanghai Education Development Foundation and Shanghai Municipal Education Commission (Grant No. 15SG36).

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Yuanyuan Liu
    • 1
  • Yulin Han
    • 2
  • Jian Zhou
    • 2
  • Yizeng Chen
    • 3
  • Shuya Zhong
    • 1
  1. 1.Logistics Institute-Asia PacificNational University of SingaporeSingaporeSingapore
  2. 2.School of ManagementShanghai UniversityShanghaiChina
  3. 3.School of ManagementShenzhen PolytechnicShenzhenChina

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