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Frontiers of Engineering Management

Front. Eng    2020, Vol. 7 Issue (2) : 196-203     https://doi.org/10.1007/s42524-019-0038-z
RESEARCH ARTICLE
Improved approach to quality function deployment based on Pythagorean fuzzy sets and application to assembly robot design evaluation
Huchang LIAO, Yinghan CHANG, Di WU, Xunjie GOU()
Business School, Sichuan University, Chengdu 610064, China
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Abstract

Quality function deployment (QFD) is an effective method that helps companies analyze customer requirements (CRs). These CRs are then turned into product or service characteristics, which are translated to other attributes. With the QFD method, companies could design or improve the quality of products or services close to CRs. To increase the effectiveness of QFD, we propose an improved method based on Pythagorean fuzzy sets (PFSs). We apply an extended method to obtain the group consensus evaluation matrix. We then use a combined weight determining method to integrate former weights to objective weights derived from the evaluation matrix. To determine the exact score of each PFS in the evaluation matrix, we develop an improved score function. Lastly, we apply the proposed method to a case study on assembly robot design evaluation.

Keywords quality function deployment      Pythagorean fuzzy sets      group consensus      combined weights      assembly robot design     
Corresponding Author(s): Xunjie GOU   
Just Accepted Date: 29 April 2019   Online First Date: 30 May 2019    Issue Date: 27 May 2020
 Cite this article:   
Huchang LIAO,Yinghan CHANG,Di WU, et al. Improved approach to quality function deployment based on Pythagorean fuzzy sets and application to assembly robot design evaluation[J]. Front. Eng, 2020, 7(2): 196-203.
 URL:  
http://journal.hep.com.cn/fem/EN/10.1007/s42524-019-0038-z
http://journal.hep.com.cn/fem/EN/Y2020/V7/I2/196
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Huchang LIAO
Yinghan CHANG
Di WU
Xunjie GOU
ωj A 1 A 2 A 3 A 4 A 5 A 6 A 7
0.15 C 1 P(0.8,0.3) P(0.8,0.3) P(0.7,0.2) P(0.8,0.2) P(1,0) P(0.8,0.5) P(0.5,0.8)
0.2 C 2 P(0,1) P(1,0) P(0,1) P(0,1) P(0.8,0.1) P(0.9,0.3) P(0.2,0.9)
0.2 C 3 P(0,1) P(0.9,0.2) P(0,1) P(0,1) P(1,0) P(0.1,0.8) P(0.2,0.9)
0.14 C 4 P(0.7,0.2) P(0.6,0.2) P(0.9,0.2) P(0.9,0.1) P(0.2,0.7) P(0,1) P(0.2,0.6)
0.16 C 5 P(0.4,0.6) P(0.7,0.6) P(0.5,0.5) P(0,1) P(0.8,0.4) P(0.6,0.6) P(1,0)
0.15 C6 P(0.6,0.4) P(0.7,0.4) P(0.7,0.3) P(0.7,0.2) P(0.9,0.3) P(0.7,0.4) P(1,0)
Tab.1  Evaluation matrix of expert e1
ωj A 1 A 2 A 3 A 4 A 5 A 6 A 7
0.15 C 1 P(0.7,0.2) P(0.9,0.3) P(0.7,0.1) P(0.9,0.1) P(0.8,0.2) P(0.6,0.5) P(0.6,0.7)
0.2 C 2 P(0,1) P(1,0) P(0,1) P(0,1) P(1,0) P(0.8,0.3) P(0,1)
0.2 C 3 P(0,1) P(0.7,0.2) P(0,1) P(0,1) P(1,0) P(0.1,0.8) P(0.1,0.9)
0.14 C 4 P(0.9,0.2) P(0.5,0.3) P(1,0) P(1,0) P(0.2,0.7) P(0,1) P(0.2,0.8)
0.16 C 5 P(0.6,0.5) P(0.4,0.6) P(0.4,0.6) P(0.2,0.8) P(0.7,0.4) P(0.6,0.6) P(1,0)
0.15 C6 P(0.5,0.6) P(0.8,0.4) P(0.8,0.3) P(0.6,0.3) P(0.9,0.2) P(0.8,0.5) P(0.9,0.1)
Tab.2  Evaluation matrix of expert e2
ωj A 1 A 2 A 3 A 4 A 5 A 6 A 7
0.15 C 1 P(0.9,0.2) P(0.8,0.2) P(0.8,0.3) P(0.9,0.2) P(0.9,0.2) P(0.6,0.6) P(0.4,0.7)
0.2 C 2 P(0,1) P(1,0) P(0,1) P(0,1) P(0.9,0.1) P(0.8,0.2) P(0.1,0.9)
0.2 C 3 P(0,1) P(0.8,0.4) P(0,1) P(0,1) P(1,0) P(0.2,0.9) P(0.3,0.9)
0.14 C 4 P(0.8,0.3) P(0.6,0.3) P(0.9,0.1) P(1,0) P(0.2,0.9) P(0,1) P(0.4,0.7)
0.16 C 5 P(0.6,0.3) P(0.6,0.4) P(0.5,0.6) P(0.1,0.8) P(0.6,0.3) P(0.4,0.7) P(1,0)
0.15 C6 P(0.5,0.4) P(0.8,0.2) P(0.8,0.2) P(0.7,0.3) P(0.8,0.2) P(0.8,0.3) P(0.9,0.2)
Tab.3  Evaluation matrix of expert e3
ωj A 1 A 2 A 3 A 4 A 5 A 6 A 7
0.15 C 1 P(0.80,0.23) P(0.83,0.27) P(0.73,0.20) P(0.87,0.17) P(0.90,0.13) P(0.67,0.53) P(0.50,0.73)
0.2 C 2 P(0.00,1.00) P(1.00,0.00) P(0.00,1.00) P(0.00,1.00) P(0.90,0.07) P(0.83,0.27) P(0.10,0.93)
0.2 C 3 P(0.00,1.00) P(0.80,0.27) P(0.00,1.00) P(0.00,1.00) P(1.00,0.00) P(0.13,0.83) P(0.20,0.90)
0.14 C 4 P(0.80,0.23) P(0.57,0.27) P(0.93,0.1) P(0.97,0.03) P(0.20,0.77) P(0.00,1.00) P(0.27,0.70)
0.16 C 5 P(0.53,0.47) P(0.57,0.53) P(0.47,0.57) P(0.10,0.87) P(0.70,0.37) P(0.57,0.63) P(1.00,0.00)
0.15 C6 P(0.53,0.47) P(0.77,0.33) P(0.77,0.27) P(0.67,0.27) P(0.87,0.23) P(0.77,0.40) P(0.93,0.10)
Tab.4  Integrated matrix
A1 A2 A3 A4 A5 A6 A7
Similarity degree e1 0.8074 0.8280 0.8757 0.9134 0.8701 0.7966 0.8930
e2 0.7990 0.7961 0.8968 0.9254 0.8991 0.7979 0.8643
e3 0.8400 0.8321 0.9023 0.9419 0.9011 0.7930 0.8796
Deviation e1 0.0081 0.0093 0.0159 0.0135 0.0200 0.0008 0.0140
e2 0.0164 0.0226 0.0052 0.0015 0.0090 0.0021 0.0147
e3 0.0245 0.0133 0.0107 0.0150 0.0110 0.0029 0.0007
Tab.5  Similarity degrees and deviations of experts
A 1 A 2 A 3 A 4 A 5 A 6 A 7
C 1 0.294 0.405 0.086 0.511 0.626 -0.102 -0.516
C 2 -1.000 1.000 -1.000 -1.000 0.622 0.405 -0.984
C 3 -1.000 0.296 -1.000 -1.000 1.000 -0.971 -0.932
C 4 0.294 -0.348 0.746 0.869 -0.931 -1.000 -0.871
C 5 -0.427 -0.356 -0.571 -0.984 -0.004 -0.438 1.000
C6 -0.427 0.194 0.191 -0.098 0.517 0.195 0.746
Tab.6  Score values of all elements of the integrated matrix
C 1 C 2 C 3 C 4 C 5 C 6
C 1 1 0.338 0.569 0.343 -0.646 0.442
C 2 1 0.693 -0.562 -0.012 -0.234
C 3 1 -0.430 0.142 -0.373
C 4 1 -0.637 0.635
C 5 1 -0.772
C6 1
Tab.7  Correlation coefficients between each pair of different demands
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