Improved approach to quality function deployment based on Pythagorean fuzzy sets and application to assembly robot design evaluation

doi:10.1007/s42524-019-0038-z

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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

最新录用日期: 在线预览日期: 发布日期: 2020-05-27

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	Huchang LIAO
	Yinghan CHANG
	Di WU
	Xunjie GOU

引用本文:

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.

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https://journal.hep.com.cn/fem/EN/10.1007/s42524-019-0038-z OR https://journal.hep.com.cn/fem/EN/Y2020/V7/I2/196

$ω ″ j$		$A 1$	$A 2$	$A 3$	$A 4$	$A 5$	$A 6$	$A 7$
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	$C 6$	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

e 1

$ω ″ j$		$A 1$	$A 2$	$A 3$	$A 4$	$A 5$	$A 6$	$A 7$
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	$C 6$	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

e 2

$ω ″ j$		$A 1$	$A 2$	$A 3$	$A 4$	$A 5$	$A 6$	$A 7$
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	$C 6$	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

e 3

$ω ″ j$		$A 1$	$A 2$	$A 3$	$A 4$	$A 5$	$A 6$	$A 7$
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	$C 6$	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

		$A 1$	$A 2$	$A 3$	$A 4$	$A 5$	$A 6$	$A 7$
Similarity degree	$e 1$	0.8074	0.8280	0.8757	0.9134	0.8701	0.7966	0.8930
	$e 2$	0.7990	0.7961	0.8968	0.9254	0.8991	0.7979	0.8643
	$e 3$	0.8400	0.8321	0.9023	0.9419	0.9011	0.7930	0.8796
Deviation	$e 1$	0.0081	0.0093	0.0159	0.0135	0.0200	0.0008	0.0140
	$e 2$	0.0164	0.0226	0.0052	0.0015	0.0090	0.0021	0.0147
	$e 3$	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
$C 6$	-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
$C 6$						1

Tab.7 Correlation coefficients between each pair of different demands

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