基于熵权法和灰色关联度分析法综合评价谷子品种的农艺性状及产量与品质

doi:10.6048/j.issn.1001-4330.2024.12.005

新疆农业科学 ›› 2024, Vol. 61 ›› Issue (12): 2902-2912.DOI: 10.6048/j.issn.1001-4330.2024.12.005

• 种质资源·分子遗传学·耕作栽培·生理生化·微生物 • 上一篇下一篇

基于熵权法和灰色关联度分析法综合评价谷子品种的农艺性状及产量与品质

郝曦煜¹^,²(), 刘婷婷³, 王辉³, 冷静文³, 宫世航³, 刘伟³(), 梁杰¹()

1.吉林省农业科学院/中国农业科技东北创新中心,长春 130033
2.黑龙江飞鹤乳业有限公司,北京 10015
3.吉林省白城市农业科学院,吉林白城 137000

收稿日期:2024-05-11 出版日期:2024-12-20 发布日期:2025-01-16
通信作者: 刘伟(1974-),男,吉林白城人,研究员,研究方向为蓖麻育种与栽培,(E-mail)jlhyliuwei@126.com;
梁杰(1973-),女,吉林白城人,研究员,研究方向为作物育种与栽培,(E-mail) liangjie9669@163.com
作者简介:郝曦煜(1990-),男,辽宁铁岭人,副研究员,硕士,研究方向为食用豆育种与栽培,(E-mail)haoxiyu1990@foxmail.com
基金资助:
国家现代农业产业技术体系(CARS-06)

Comprehensive evaluation of foxtail millet varieties based on entropy weight method and grey relational analysis

HAO Xiyu¹^,²(), LIU Tingting³, WANG Hui³, LENG Jingwen³, GONG Shihang³, LIU Wei³(), LIANG Jie¹()

1. Northeast Agricultural Research Center of China /Jilin Academy of Agricultural Sciences, Changchun 130033,China
2. Heilongjiang Feihe Dairy Co., Ltd., Beijing 100015, China
3. Baicheng Academy of Agricultural Sciences, Baicheng Jilin 137000, China

Received:2024-05-11 Published:2024-12-20 Online:2025-01-16
Supported by:
China Agriculture Research System(CARS-06)

摘要/Abstract

摘要：

【目的】 筛选不同选择目标下最适宜的谷子品种,综合评价适宜不同选择目标的最佳谷子品种。【方法】 2021~2022年分析对比20份谷子新品种的25个农艺性状、产量和品质指标,利用熵权法对各指标赋权,采用DTOPSIS法、灰色关联度分析法评价对不同品种的农艺性状及产量与品质。【结果】 除千粒重外,其余24个指标的谷子品种间差异均达极显著水平。2种分析方法的排序结果与产量排序结果的吻合程度更高,即灰色关联度分析较DTOPSIS法更注重评价产量。C_i最大差异值为30.01%,r_i最大差异值为7.71%,γ最大差异值为11.85%,DTOPSIS法更能体现出各谷子品种的差异性。【结论】 DTOPSIS法和熵权法赋权的加权灰色关联度分析法适用于综合评价谷子品种。半干旱生产区应选择张杂谷16号;各性状更平衡的品种应选择金苗K₂;兼顾产量和各性状平衡的品种应选择济谷22号。

关键词: 谷子; 综合评价; 灰色关联度; DTOPSIS法; 熵值

Abstract:

【Objective】 It is necessary to determine the most suitable variety under different selection goals and the best comprehensive evaluation method for different selection goals of millet varieties.【Methods】 In this study from 2021 to 2022, 25 agronomic traits, yield, and quality indicators of 20 new millet varieties were analyzed and compared.Meanwhile, the entropy weight method was used to assign weights to each indicator, and DTOPSIS method and grey relational degree analysis method were used to evaluate different varieties.【Results】 Except for thousand-grain weight, the differences between varieties in the other 24 indicators reached a highly significant level.The ranking results of the two analytical methods, DTOPSIS and grey relational analysis, showed a higher degree of agreement with the yield ranking results.This indicated that grey relational analysis payed more attention to the evaluation of yield than the DTOPSIS method.The maximum difference value of Ci was 30.01%, the maximum difference value of ri was 7.71%, and the maximum difference value of γ was 11.85%, indicating that the DTOPSIS method could better demonstrate the differences between varieties.【Conclusion】 The DTOPSIS method and the weighted grey relational analysis method based on entropy weight are suitable for the comprehensive evaluation of millet varieties.In semi-arid production areas, if higher yield varieties are needed, Zhangzagu 16 should be selected; if varieties with more balanced traits are needed, Jinmiao K₂ should be chosen; if varieties with a balance between yield and various traits are needed, Jigu 22 should be selected.

Key words: foxtail millet; comprehensive evaluation; grey relational degree analysis; dtopsis method; entropy

中图分类号:

S515

郝曦煜, 刘婷婷, 王辉, 冷静文, 宫世航, 刘伟, 梁杰. 基于熵权法和灰色关联度分析法综合评价谷子品种的农艺性状及产量与品质[J]. 新疆农业科学, 2024, 61(12): 2902-2912.

HAO Xiyu, LIU Tingting, WANG Hui, LENG Jingwen, GONG Shihang, LIU Wei, LIANG Jie. Comprehensive evaluation of foxtail millet varieties based on entropy weight method and grey relational analysis[J]. Xinjiang Agricultural Sciences, 2024, 61(12): 2902-2912.

图/表 10

图1 2021~2022年谷子生育期内各月份平均温度、降雨量与日照时数

Fig.1 Average temperature, rainfall, and sunshine hours per month during the foxtail millet growing period in 2021-2022

表1 参试品种

Tab.1 Test cultivars

品种编号 Varieties No.	名称 Names	来源 Source
V₁	公谷88号	吉林省农科院作物资源研究所
V₂	黄金苗	赤峰市农牧科学研究所
V₃	山西红谷	赤峰市农牧科学研究所
V₄	金苗K2	赤峰市农牧科学研究所
V₅	赤优金苗1号	赤峰市农牧科学研究所
V₆	陇谷13号	甘肃省农业科学院作物所
V₇	冀谷168	河北省农林科学院谷子研究所
V₈	冀谷39号	河北省农林科学院谷子研究所
V₉	张杂谷16号	河北省张家口市农业科学院
V₁₀	豫谷18号	河南省安阳市农业科学院
V₁₁	豫谷35号	河南省安阳市农业科学院
V₁₂	嫩选18号	黑龙江省农科院齐齐哈尔分院
V₁₃	嫩选15号	黑龙江省农科院齐齐哈尔分院
V₁₄	龙谷38号	黑龙江省农科院作物资源研究所
V₁₅	九谷23号	吉林省吉林市农业科学院
V₁₆	朝谷58号	辽宁省旱地农林研究所
V₁₇	济谷22号	山东省农业科学院作物研究所
V₁₈	大同29号	山西省农业科学院高寒作物所
V₁₉	中谷9号	中国农业科学院作物科学研究所
V₂₀	中谷2号	中国农业科学院作物科学研究所

表2 参试品种各指标方差变化

Tab.2 Comparisons of variance of each indicator for the tested varieties

指标 Indexes	平方和Sum of squares			自由度Degree of freedom			均方Mean square		F	显著性 signifi- cance
指标 Indexes	品种间 Intra- cultivars	品种内 Inter- cultivars	总变异 Total	品种间 Intra- cultivars	品种内 Inter- cultivars	总变异 Total	品种间 Intra- cultivars	品种内 Inter- cultivars	F	显著性 signifi- cance
M₁	2 636.100	53.333	2 689.433	19	40	59	138.742	1.333	104.057	0.000
M₂	11.250	0.533	11.783	19	40	59	0.592	0.013	44.408	0.000
M₃	134.850	13.333	148.183	19	40	59	7.097	0.333	21.292	0.000
M₄	105.000	13.333	118.333	19	40	59	5.526	0.333	16.579	0.000
M₅	0.556	0.533	1.090	19	40	59	0.029	0.013	2.196	0.018
M₆	0.757	0.533	1.290	19	40	59	0.040	0.013	2.989	0.002
M₇	1.409	0.533	1.942	19	40	59	0.074	0.013	5.562	0.000
M₈	18.600	13.333	31.933	19	40	59	0.979	0.333	2.937	0.002
M₉	107.250	13.333	120.583	19	40	59	5.645	0.333	16.934	0.000
M₁₀	99.000	13.333	112.333	19	40	59	5.211	0.333	15.632	0.000
M₁₁	2 204.119	53.333	2257.452	19	40	59	116.006	1.333	87.005	0.000
M₁₂	959.753	160.000	1 119.753	19	40	59	50.513	4.000	12.628	0.000
M₁₃	979.912	53.333	1 033.245	19	40	59	51.574	1.333	38.681	0.000
M₁₄	2.070	2.133	4.203	19	40	59	0.109	0.053	2.042	0.029
M₁₅	2.513	2.133	4.646	19	40	59	0.132	0.053	2.480	0.008
M₁₆	5.849	2.133	7.982	19	40	59	0.308	0.053	5.772	0.000
M₁₇	28 471.697	1 333.333	29 805.030	19	40	59	1 498.510	33.333	44.955	0.000
M₁₈	486.184	53.333	539.517	19	40	59	25.589	1.333	19.191	0.000
M₁₉	5.408	4.800	10.208	19	40	59	0.285	0.120	2.372	0.011
M₂₀	538.794	120.000	658.794	19	40	59	28.358	3.000	9.453	0.000
M₂₁	444.431	120.000	564.431	19	40	59	23.391	3.000	7.797	0.000
M₂₂	2.184	3.333	5.517	19	40	59	0.115	0.083	1.379	0.192
M₂₃	71 241.616	1 333.333	72 574.950	19	40	59	3 749.559	33.333	112.487	0.000
M₂₄	67.075	13.333	80.409	19	40	59	3.530	0.333	10.591	0.000
M₂₅	18.625	3.333	21.959	19	40	59	0.980	0.083	11.763	0.000

表2 参试品种各指标方差变化

Tab.2 Comparisons of variance of each indicator for the tested varieties

指标 Indexes	平方和Sum of squares			自由度Degree of freedom			均方Mean square		F	显著性 signifi- cance
指标 Indexes	品种间 Intra- cultivars	品种内 Inter- cultivars	总变异 Total	品种间 Intra- cultivars	品种内 Inter- cultivars	总变异 Total	品种间 Intra- cultivars	品种内 Inter- cultivars	F	显著性 signifi- cance
M₁	2 636.100	53.333	2 689.433	19	40	59	138.742	1.333	104.057	0.000
M₂	11.250	0.533	11.783	19	40	59	0.592	0.013	44.408	0.000
M₃	134.850	13.333	148.183	19	40	59	7.097	0.333	21.292	0.000
M₄	105.000	13.333	118.333	19	40	59	5.526	0.333	16.579	0.000
M₅	0.556	0.533	1.090	19	40	59	0.029	0.013	2.196	0.018
M₆	0.757	0.533	1.290	19	40	59	0.040	0.013	2.989	0.002
M₇	1.409	0.533	1.942	19	40	59	0.074	0.013	5.562	0.000
M₈	18.600	13.333	31.933	19	40	59	0.979	0.333	2.937	0.002
M₉	107.250	13.333	120.583	19	40	59	5.645	0.333	16.934	0.000
M₁₀	99.000	13.333	112.333	19	40	59	5.211	0.333	15.632	0.000
M₁₁	2 204.119	53.333	2257.452	19	40	59	116.006	1.333	87.005	0.000
M₁₂	959.753	160.000	1 119.753	19	40	59	50.513	4.000	12.628	0.000
M₁₃	979.912	53.333	1 033.245	19	40	59	51.574	1.333	38.681	0.000
M₁₄	2.070	2.133	4.203	19	40	59	0.109	0.053	2.042	0.029
M₁₅	2.513	2.133	4.646	19	40	59	0.132	0.053	2.480	0.008
M₁₆	5.849	2.133	7.982	19	40	59	0.308	0.053	5.772	0.000
M₁₇	28 471.697	1 333.333	29 805.030	19	40	59	1 498.510	33.333	44.955	0.000
M₁₈	486.184	53.333	539.517	19	40	59	25.589	1.333	19.191	0.000
M₁₉	5.408	4.800	10.208	19	40	59	0.285	0.120	2.372	0.011
M₂₀	538.794	120.000	658.794	19	40	59	28.358	3.000	9.453	0.000
M₂₁	444.431	120.000	564.431	19	40	59	23.391	3.000	7.797	0.000
M₂₂	2.184	3.333	5.517	19	40	59	0.115	0.083	1.379	0.192
M₂₃	71 241.616	1 333.333	72 574.950	19	40	59	3 749.559	33.333	112.487	0.000
M₂₄	67.075	13.333	80.409	19	40	59	3.530	0.333	10.591	0.000
M₂₅	18.625	3.333	21.959	19	40	59	0.980	0.083	11.763	0.000

表3 参试品种各指标差异比较

Tab.3 Comparisons of differences in each indicator among the tested varieties

品种编号 Varieties number	M₁	M₂	M₃	M₄	M₅	M₆	M₇	M₈	M₉	M₁₀	M₁₁	M₁₂	M₁₃
V₁	111.7^fF	4.1^bB	11.3^cdCD	14.3^cdCD	1.1^abcdeAB	1.1^bcdeABC	1.1^bcdeABC	10.3^aA	12.3^cdCD	13.3^cdCD	58.9^bBC	58.9^bBC	63.4^abABC
V₂	107.7^gG	5.1^aA	10.3^deDE	13.3^deDE	1.0^bcdeAB	1.1^cdeBC	1.1^cdeBC	10.3^aA	12.3^cdCD	13.3^cdCD	53.7^eEFG	53.7^eEFG	64.9^aA
V₃	117.7^cdDE	5.1^aA	11.3^cdCD	13.3^cdCD	1.0^bcdeAB	1.1^cdeBC	1.1^cdeBC	10.3^aA	12.3^cdCD	13.3^cdCD	53.4^eFG	53.4^eFG	61.9^bcBCD
V₄	115.2^eE	4.1^bB	11.3^cdCD	13.3^cdCD	0.9^cdeB	1.0^cdeC	1.0^cdeC	9.3^abAB	12.3^cdCD	13.3^cdCD	44.3^ijJK	44.3^ijJK	51.7^fgG
V₅	115.2^eE	4.1^bB	13.3^abAB	12.3^abAB	1.0^bcdeAB	1.1^bcdeABC	1.1^bcdeABC	9.3^abAB	12.3^cdCD	15.3^abAB	50.1^fH	50.1^fH	62.7^bcABC
V₆	119.7^bcCD	4.1^bB	11.3^cdCD	12.3^cdCD	1.1^abcdAB	1.2^bcdABC	1.2^bcdABC	9.3^abAB	10.3^eE	11.3^eE	55.9^cdDEF	55.9^cdDEF	62.7^bcABC
V₇	111.7^fF	5.1^aA	12.3^bcBC	12.3^bcBC	1.1^bcdeAB	1.1^cdeBC	1.1^cdeBC	10.3^aA	14.3^bAB	15.3^abAB	53.0^eG	53.0^eG	59.3^deDEF
V₈	117.2^deDE	5.1^aA	12.3^bcBC	12.3^bcBC	1.0^bcdeAB	1.1^bcdeABC	1.1^bcdeABC	9.3^abcAB	11.3^deDE	13.3^cdCD	52.7^eG	52.7^eG	59.7^deDEF
V₉	112.2^fF	4.1^bB	12.3^bcBC	12.3^bcBC	1.0^bcdeAB	1.0^cdeBC	1.0^cdeBC	10.3^aA	10.3^eE	13.3^cdCD	59.7^bAB	59.7^bAB	58.4^eEF
V₁₀	100.7^hH	4.1^bB	9.3^fE	12.3^fE	0.9^deB	1.0^deC	1.0^deC	9.3^abAB	10.3^eE	11.3^eE	54.7^deEFG	54.7^deEFG	53.2^fG
V₁₁	117.2^deDE	4.1^bB	13.3^abAB	12.3^abAB	1.1^bcdeAB	1.1^cdeBC	1.1^cdeBC	9.3^abAB	11.3^deDE	15.3^abAB	53.7^eEFG	53.7^eEFG	60.7^cdCDE
V₁₂	97.2^iI	4.1^bB	13.3^abAB	11.3^abAB	0.9^abcAB	0.9^eC	0.9^eC	10.3^aA	13.3^bcBC	13.3^cdCD	48.7^fgH	48.7^fgH	61.9^bcBCD
V₁₃	123.2^aAB	4.1^bB	7.3^gF	11.3^gF	1.0^bcdeB	1.0^cdeBC	1.0^cdeBC	9.3^abAB	10.3^eE	12.3^deDE	37.7^kL	37.7^kL	52.9^fG
V₁₄	118.2^cdCD	4.1^bB	12.3^bcBC	11.3^bcBC	1.1^bcdeAB	1.1^bcdeABC	1.1^bcdeABC	9.3^abAB	12.3^cdCD	14.3^bcBC	56.4^cdCDE	56.4^cdCDE	60.7^cdCDE
V₁₅	120.7^bBC	4.1^bB	11.3^cdCD	11.3^cdCD	1.1^abcAB	1.3^abAB	1.3^abAB	10.3^aA	13.3^bcBC	14.3^bcBC	57.7^bcBCD	57.7^bcBCD	63.8^abAB
V₁₆	124.7^aA	5.1^aA	12.3^bcBC	11.3^bcBC	1.0^bcdeAB	1.1^bcdeABC	1.1^bcdeABC	9.3^abAB	11.3^deDE	16.3^aA	45.7^hiIJ	45.7^hiIJ	60.7^cdCDE
V₁₇	115.2^eE	4.1^bB	12.3^bcBC	11.3^bcBC	0.9^eB	1.1^cdeBC	1.1^cdeBC	9.3^abAB	11.3^deDE	14.3^bcBC	47.7^ghHI	47.7^ghHI	57.7^eF
V₁₈	118.2^cdCD	4.1^bB	14.3^aA	10.3^aA	1.3^aA	1.4^aA	1.4^aA	9.3^abAB	15.3^aA	15.3^abAB	47.7^ghHI	47.7^ghHI	59.7^deDEF
V₁₉	117.7^cdDE	4.1^bB	11.3^cdCD	9.3^cdCD	1.2^abAB	1.3^abAB	1.3^abAB	8.3^bdB	13.3^bcBC	14.3^bcBC	62.2^aA	62.2^aA	60.7^cdCDE
V₂₀	118.7^bcdCD	4.1^bB	12.3^bcBC	7.3^bcBC	1.1^abcdeAB	1.2^abcABC	1.2^abcABC	9.3^abAB	11.3^deDE	13.3^cdCD	42.7^jK	42.7^jK	50.7^gG
品种编号 Varieties number	M₁₄	M₁₅	M₁₆	M₁₇	M₁₈	M₁₉		M₂₀	M₂₁	M₂₂	M₂₃	M₂₄	M₂₅
V₁	2.9^abcAB	3.1^bcdeABC	3.1^defgBCDEF	175.5^cBC	21.8^efEFG		2.7^eC	18.0^gH	14.6^iF	3.2^abcA	318.9^nN	11.5^cdefBCD	11.5^cdefBCD
V₂	2.8^abcAB	2.8^cdeBC	2.9^fgEF	186.8^bB	22.0^efEFG		2.8^deABC	19.2^fgFGH	15.5^ghiDEF	2.9^abcA	324.1^mnMN	11.1^defgBCDE	11.7^cdeBC
V₃	2.9^abcAB	3.0^bcdeABC	3.2^defgBCDEF	177.3^bcBC	24.1^cdCDE		3.0^abcdeABC	19.1^fgFGH	15.6^ghiDEF	3.3^abA	331.9^lmLMN	10.6^efghijCDEF	12.3^bcAB
V₄	2.6^cdAB	2.8^deBC	3.0^efgCDEF	152.3^efEF	25.2^cBCD		3.3^abcdeABC	23.6^cdeBCDE	19.8^bcdeBCD	2.8^bcA	382.8^fFG	11.8^cdBC	13.2^abA
V₅	2.7^bcdAB	2.9^cdeBC	2.9^fgDEF	169.3^cdCD	25.5^cBCD		3.3^abcdeABC	23.5^cdeBCDEF	19.5^cdeBCDE	3.0^abcA	372.6^gGH	9.56^jF	12.4^bcAB
V₆	2.7^bcdAB	2.8^cdeBC	3.0^efgDEF	137.4^hG	23.1^deDE		2.9^cdeABC	23.5^cdeBCDEF	19.5^cdeBCDE	3.3^abA	372.0^gGH	10.6^efghiCDEF	10.4^fghijCDEF
V₇	2.4^dB	2.7^eC	2.8^gF	200.3^aA	25.5^cBCD		3.2^abcdeABC	25.1^bcdABCD	20.7^bcdeBC	2.9^abcA	387.5^efEF	13.5^aA	10.1^ghijDEF
V₈	2.8^abcAB	3.1^abcdeABC	3.2^bcdefBCDEF	146.3^fghEFG	18.8^hH		3.5^abcABC	19.0^fgGH	15.2^hiEF	3.1^abcA	328.7^lmnMN	10.0^hijEF	10.6^efghiCDEF
V₉	2.9^abcAB	2.9^bcdeABC	3.2^bcdefBCDEF	159.3^deDE	28.0^abAB		3.7^aA	29.08^aA	25.0^aA	3.3^abA	432.0^aA	11.5^cdefBCD	10.7^efghiCDEF
V₁₀	3.1^abcA	3.1^abcdABC	4.1^aA	150.1^efEFG	29.1^aA		3.5^abcABC	23.2^cdeBCDEFG	19.2^cdefBCDE	3.4^aA	367.3^ghH	11.7^cdeBC	9.88^ijEF
V₁₁	2.9^abcAB	3.1^abcdeABC	3.4^bcdeBCDE	159.2^deDE	20.0^fghFGH		2.7^deBC	22.3^deCDEFGH	18.5^defgBCDEF	3.2^abcA	343.5^jkJKL	12.3^bcAB	11.1^defghBCDE
V₁₂	2.9^abcAB	3.0^bcdeABC	3.2^bcdefBCDEF	168.3^cdCD	21.4^efgEFGH		3.2^abcdeABC	23.2^cdeBCDEFG	19.0^defBCDE	2.9^abcA	361.2^hiHI	13.2^abA	11.1^defgBCDE
V₁₃	3.0^abcA	3.2^abcABC	3.7^bAB	91.5^iH	19.4^ghGH		3.2^abcdeABC	24.4^bcdeBCD	20.9^bcdeABC	3.2^abcA	396.9^deDE	12.4^bcAB	11.0^defghBCDEF
V₁₄	2.9^abcAB	2.9^bcdeABC	3.4^bcdeBCDE	144.9^fghEFG	25.4^cBCD		3.4^abcdABC	22.9^cdeBCDEFG	19.0^cdefBCDE	2.7^cA	352.4^ijIJ	10.4^fghijCDEF	10.6^efghijCDEF
V₁₅	2.9^abcAB	3.0^bcdeABC	3.2^bcdefBCDEF	151.3^efEFG	26.2^bcBC		3.6^aAB	26.8^abAB	22.3^abcABC	3.1^abcA	415.3^bBC	10.1^ghijDEF	11.8^cdBC
V₁₆	2.7^bcdAB	3.0^bcdeABC	3.2^cdefBCDEF	139.2^ghFG	26.2^bcBC		3.6^aAB	26.0^abcABC	21.8^bcdABC	2.8^abcA	411.7^bcC	10.6^efghiCDEF	9.56^jF
V₁₇	2.7^bcdAB	2.9^bcdeBC	3.5^bcdBCD	149.5^efgEFG	25.4^cBCD		3.6^abABC	25.3^bcdABCD	21.1^bcdeABC	2.9^abcA	404.2^cdCD	10.7^efghiCDEF	10.6^efghiCDEF
V₁₈	3.2^abA	3.5^aA	3.6^bcABC	151.3^efEFG	22.4^deEF		3.1^abcdeABC	19.2^fgEFGH	16.1^fghiDEF	3.2^abcA	346.8^jkJK	9.88^ijEF	13.5^aA
V₁₉	3.2^aA	3.3^abAB	3.5^bcdBCD	148.2^fgEFG	25.8^cBCD		2.9^bcdeABC	27.3^abAB	22.8^abAB	3.2^abcA	426.4^aAB	11.1^defghBCDE	10.0^hijEF
V₂₀	2.9^abcAB	3.3^abAB	3.4^bcdeBCDE	141.3^fghFG	20.2^fghFGH		3.1^abcdeABC	21.5^efDEFGH	18.0^efghCDEF	3.1^abcA	337.5^klKLM	11.0^defghBCDEF	11.5^cdefBCD

表3 参试品种各指标差异比较

Tab.3 Comparisons of differences in each indicator among the tested varieties

品种编号 Varieties number	M₁	M₂	M₃	M₄	M₅	M₆	M₇	M₈	M₉	M₁₀	M₁₁	M₁₂	M₁₃
V₁	111.7^fF	4.1^bB	11.3^cdCD	14.3^cdCD	1.1^abcdeAB	1.1^bcdeABC	1.1^bcdeABC	10.3^aA	12.3^cdCD	13.3^cdCD	58.9^bBC	58.9^bBC	63.4^abABC
V₂	107.7^gG	5.1^aA	10.3^deDE	13.3^deDE	1.0^bcdeAB	1.1^cdeBC	1.1^cdeBC	10.3^aA	12.3^cdCD	13.3^cdCD	53.7^eEFG	53.7^eEFG	64.9^aA
V₃	117.7^cdDE	5.1^aA	11.3^cdCD	13.3^cdCD	1.0^bcdeAB	1.1^cdeBC	1.1^cdeBC	10.3^aA	12.3^cdCD	13.3^cdCD	53.4^eFG	53.4^eFG	61.9^bcBCD
V₄	115.2^eE	4.1^bB	11.3^cdCD	13.3^cdCD	0.9^cdeB	1.0^cdeC	1.0^cdeC	9.3^abAB	12.3^cdCD	13.3^cdCD	44.3^ijJK	44.3^ijJK	51.7^fgG
V₅	115.2^eE	4.1^bB	13.3^abAB	12.3^abAB	1.0^bcdeAB	1.1^bcdeABC	1.1^bcdeABC	9.3^abAB	12.3^cdCD	15.3^abAB	50.1^fH	50.1^fH	62.7^bcABC
V₆	119.7^bcCD	4.1^bB	11.3^cdCD	12.3^cdCD	1.1^abcdAB	1.2^bcdABC	1.2^bcdABC	9.3^abAB	10.3^eE	11.3^eE	55.9^cdDEF	55.9^cdDEF	62.7^bcABC
V₇	111.7^fF	5.1^aA	12.3^bcBC	12.3^bcBC	1.1^bcdeAB	1.1^cdeBC	1.1^cdeBC	10.3^aA	14.3^bAB	15.3^abAB	53.0^eG	53.0^eG	59.3^deDEF
V₈	117.2^deDE	5.1^aA	12.3^bcBC	12.3^bcBC	1.0^bcdeAB	1.1^bcdeABC	1.1^bcdeABC	9.3^abcAB	11.3^deDE	13.3^cdCD	52.7^eG	52.7^eG	59.7^deDEF
V₉	112.2^fF	4.1^bB	12.3^bcBC	12.3^bcBC	1.0^bcdeAB	1.0^cdeBC	1.0^cdeBC	10.3^aA	10.3^eE	13.3^cdCD	59.7^bAB	59.7^bAB	58.4^eEF
V₁₀	100.7^hH	4.1^bB	9.3^fE	12.3^fE	0.9^deB	1.0^deC	1.0^deC	9.3^abAB	10.3^eE	11.3^eE	54.7^deEFG	54.7^deEFG	53.2^fG
V₁₁	117.2^deDE	4.1^bB	13.3^abAB	12.3^abAB	1.1^bcdeAB	1.1^cdeBC	1.1^cdeBC	9.3^abAB	11.3^deDE	15.3^abAB	53.7^eEFG	53.7^eEFG	60.7^cdCDE
V₁₂	97.2^iI	4.1^bB	13.3^abAB	11.3^abAB	0.9^abcAB	0.9^eC	0.9^eC	10.3^aA	13.3^bcBC	13.3^cdCD	48.7^fgH	48.7^fgH	61.9^bcBCD
V₁₃	123.2^aAB	4.1^bB	7.3^gF	11.3^gF	1.0^bcdeB	1.0^cdeBC	1.0^cdeBC	9.3^abAB	10.3^eE	12.3^deDE	37.7^kL	37.7^kL	52.9^fG
V₁₄	118.2^cdCD	4.1^bB	12.3^bcBC	11.3^bcBC	1.1^bcdeAB	1.1^bcdeABC	1.1^bcdeABC	9.3^abAB	12.3^cdCD	14.3^bcBC	56.4^cdCDE	56.4^cdCDE	60.7^cdCDE
V₁₅	120.7^bBC	4.1^bB	11.3^cdCD	11.3^cdCD	1.1^abcAB	1.3^abAB	1.3^abAB	10.3^aA	13.3^bcBC	14.3^bcBC	57.7^bcBCD	57.7^bcBCD	63.8^abAB
V₁₆	124.7^aA	5.1^aA	12.3^bcBC	11.3^bcBC	1.0^bcdeAB	1.1^bcdeABC	1.1^bcdeABC	9.3^abAB	11.3^deDE	16.3^aA	45.7^hiIJ	45.7^hiIJ	60.7^cdCDE
V₁₇	115.2^eE	4.1^bB	12.3^bcBC	11.3^bcBC	0.9^eB	1.1^cdeBC	1.1^cdeBC	9.3^abAB	11.3^deDE	14.3^bcBC	47.7^ghHI	47.7^ghHI	57.7^eF
V₁₈	118.2^cdCD	4.1^bB	14.3^aA	10.3^aA	1.3^aA	1.4^aA	1.4^aA	9.3^abAB	15.3^aA	15.3^abAB	47.7^ghHI	47.7^ghHI	59.7^deDEF
V₁₉	117.7^cdDE	4.1^bB	11.3^cdCD	9.3^cdCD	1.2^abAB	1.3^abAB	1.3^abAB	8.3^bdB	13.3^bcBC	14.3^bcBC	62.2^aA	62.2^aA	60.7^cdCDE
V₂₀	118.7^bcdCD	4.1^bB	12.3^bcBC	7.3^bcBC	1.1^abcdeAB	1.2^abcABC	1.2^abcABC	9.3^abAB	11.3^deDE	13.3^cdCD	42.7^jK	42.7^jK	50.7^gG
品种编号 Varieties number	M₁₄	M₁₅	M₁₆	M₁₇	M₁₈	M₁₉		M₂₀	M₂₁	M₂₂	M₂₃	M₂₄	M₂₅
V₁	2.9^abcAB	3.1^bcdeABC	3.1^defgBCDEF	175.5^cBC	21.8^efEFG		2.7^eC	18.0^gH	14.6^iF	3.2^abcA	318.9^nN	11.5^cdefBCD	11.5^cdefBCD
V₂	2.8^abcAB	2.8^cdeBC	2.9^fgEF	186.8^bB	22.0^efEFG		2.8^deABC	19.2^fgFGH	15.5^ghiDEF	2.9^abcA	324.1^mnMN	11.1^defgBCDE	11.7^cdeBC
V₃	2.9^abcAB	3.0^bcdeABC	3.2^defgBCDEF	177.3^bcBC	24.1^cdCDE		3.0^abcdeABC	19.1^fgFGH	15.6^ghiDEF	3.3^abA	331.9^lmLMN	10.6^efghijCDEF	12.3^bcAB
V₄	2.6^cdAB	2.8^deBC	3.0^efgCDEF	152.3^efEF	25.2^cBCD		3.3^abcdeABC	23.6^cdeBCDE	19.8^bcdeBCD	2.8^bcA	382.8^fFG	11.8^cdBC	13.2^abA
V₅	2.7^bcdAB	2.9^cdeBC	2.9^fgDEF	169.3^cdCD	25.5^cBCD		3.3^abcdeABC	23.5^cdeBCDEF	19.5^cdeBCDE	3.0^abcA	372.6^gGH	9.56^jF	12.4^bcAB
V₆	2.7^bcdAB	2.8^cdeBC	3.0^efgDEF	137.4^hG	23.1^deDE		2.9^cdeABC	23.5^cdeBCDEF	19.5^cdeBCDE	3.3^abA	372.0^gGH	10.6^efghiCDEF	10.4^fghijCDEF
V₇	2.4^dB	2.7^eC	2.8^gF	200.3^aA	25.5^cBCD		3.2^abcdeABC	25.1^bcdABCD	20.7^bcdeBC	2.9^abcA	387.5^efEF	13.5^aA	10.1^ghijDEF
V₈	2.8^abcAB	3.1^abcdeABC	3.2^bcdefBCDEF	146.3^fghEFG	18.8^hH		3.5^abcABC	19.0^fgGH	15.2^hiEF	3.1^abcA	328.7^lmnMN	10.0^hijEF	10.6^efghiCDEF
V₉	2.9^abcAB	2.9^bcdeABC	3.2^bcdefBCDEF	159.3^deDE	28.0^abAB		3.7^aA	29.08^aA	25.0^aA	3.3^abA	432.0^aA	11.5^cdefBCD	10.7^efghiCDEF
V₁₀	3.1^abcA	3.1^abcdABC	4.1^aA	150.1^efEFG	29.1^aA		3.5^abcABC	23.2^cdeBCDEFG	19.2^cdefBCDE	3.4^aA	367.3^ghH	11.7^cdeBC	9.88^ijEF
V₁₁	2.9^abcAB	3.1^abcdeABC	3.4^bcdeBCDE	159.2^deDE	20.0^fghFGH		2.7^deBC	22.3^deCDEFGH	18.5^defgBCDEF	3.2^abcA	343.5^jkJKL	12.3^bcAB	11.1^defghBCDE
V₁₂	2.9^abcAB	3.0^bcdeABC	3.2^bcdefBCDEF	168.3^cdCD	21.4^efgEFGH		3.2^abcdeABC	23.2^cdeBCDEFG	19.0^defBCDE	2.9^abcA	361.2^hiHI	13.2^abA	11.1^defgBCDE
V₁₃	3.0^abcA	3.2^abcABC	3.7^bAB	91.5^iH	19.4^ghGH		3.2^abcdeABC	24.4^bcdeBCD	20.9^bcdeABC	3.2^abcA	396.9^deDE	12.4^bcAB	11.0^defghBCDEF
V₁₄	2.9^abcAB	2.9^bcdeABC	3.4^bcdeBCDE	144.9^fghEFG	25.4^cBCD		3.4^abcdABC	22.9^cdeBCDEFG	19.0^cdefBCDE	2.7^cA	352.4^ijIJ	10.4^fghijCDEF	10.6^efghijCDEF
V₁₅	2.9^abcAB	3.0^bcdeABC	3.2^bcdefBCDEF	151.3^efEFG	26.2^bcBC		3.6^aAB	26.8^abAB	22.3^abcABC	3.1^abcA	415.3^bBC	10.1^ghijDEF	11.8^cdBC
V₁₆	2.7^bcdAB	3.0^bcdeABC	3.2^cdefBCDEF	139.2^ghFG	26.2^bcBC		3.6^aAB	26.0^abcABC	21.8^bcdABC	2.8^abcA	411.7^bcC	10.6^efghiCDEF	9.56^jF
V₁₇	2.7^bcdAB	2.9^bcdeBC	3.5^bcdBCD	149.5^efgEFG	25.4^cBCD		3.6^abABC	25.3^bcdABCD	21.1^bcdeABC	2.9^abcA	404.2^cdCD	10.7^efghiCDEF	10.6^efghiCDEF
V₁₈	3.2^abA	3.5^aA	3.6^bcABC	151.3^efEFG	22.4^deEF		3.1^abcdeABC	19.2^fgEFGH	16.1^fghiDEF	3.2^abcA	346.8^jkJK	9.88^ijEF	13.5^aA
V₁₉	3.2^aA	3.3^abAB	3.5^bcdBCD	148.2^fgEFG	25.8^cBCD		2.9^bcdeABC	27.3^abAB	22.8^abAB	3.2^abcA	426.4^aAB	11.1^defghBCDE	10.0^hijEF
V₂₀	2.9^abcAB	3.3^abAB	3.4^bcdeBCDE	141.3^fghFG	20.2^fghFGH		3.1^abcdeABC	21.5^efDEFGH	18.0^efghCDEF	3.1^abcA	337.5^klKLM	11.0^defghBCDEF	11.5^cdefBCD

表4 各指标熵值和权重的变化

Tab.4 Changes of entropy values and weights of each indicator

指标 Indexes	熵值 Entropy	效用值 Utility value	权重系数 Weight coeffecient(%)
M₁	0.999 4	0.000 6	1.22
M₂	0.998 3	0.001 7	3.54
M₃	0.996 9	0.003 1	6.48
M₄	0.998 1	0.001 9	4.13
M₅	0.998 4	0.001 6	3.39
M₆	0.998 1	0.001 9	4.01
M₇	0.997 0	0.003 0	6.32
M₈	0.999 4	0.000 6	1.27
M₉	0.997 9	0.002 1	4.51
M₁₀	0.998 5	0.001 5	3.23
M₁₁	0.997 6	0.002 4	5.10
M₁₂	0.999 1	0.000 9	1.80
M₁₃	0.999 2	0.000 8	1.72
M₁₄	0.999 2	0.000 8	1.66
M₁₅	0.999 2	0.000 8	1.74
M₁₆	0.998 4	0.001 6	3.41
M₁₇	0.996 4	0.003 6	7.65
M₁₈	0.997 4	0.002 6	5.42
M₁₉	0.998 3	0.001 7	3.60
M₂₀	0.996 9	0.003 1	6.56
M₂₁	0.996 2	0.003 8	7.97
M₂₂	0.999 3	0.000 7	1.50
M₂₃	0.998 5	0.001 5	3.10
M₂₄	0.998 5	0.001 5	3.28
M₂₅	0.996 5	0.003 5	7.39

表5 DTOPSIS分析结果

Tab.5 DTOPSIS analysis results

品种编号 Varieties number	D⁺	D^-	C_i	C_i排序 C_i Rank
V₁	0.310	0.246	0.442	18
V₂	0.281	0.269	0.489	10
V₃	0.265	0.270	0.505	8
V₄	0.224	0.293	0.567	2
V₅	0.243	0.282	0.537	4
V₆	0.289	0.237	0.450	17
V₇	0.245	0.339	0.581	1
V₈	0.289	0.255	0.468	12
V₉	0.265	0.296	0.528	5
V₁₀	0.275	0.280	0.505	7
V₁₁	0.330	0.226	0.406	20
V₁₂	0.252	0.300	0.543	3
V₁₃	0.317	0.275	0.465	14
V₁₄	0.272	0.245	0.474	11
V₁₅	0.301	0.249	0.453	16
V₁₆	0.274	0.262	0.489	9
V₁₇	0.261	0.268	0.507	6
V₁₈	0.323	0.254	0.440	19
V₁₉	0.300	0.261	0.465	13
V₂₀	0.283	0.241	0.460	15

表6 灰色关联分析法计算结果

Tab.6 Calculation results of gray correlation analysis

品种编号 Varieties number	r_i	r_i排序 r_i Rank	$r_{i}^{'}$	$r_{i}^{'}$ 排序 $r_{i}^{'}$ Rank
V₁	0.914 4	2	0.866 7	1
V₂	0.915 5	4	0.886 9	2
V₃	0.929 3	5	0.896 7	5
V₄	0.949 0	17	0.983 2	20
V₅	0.956 3	20	0.953 8	13
V₆	0.946 4	16	0.950 1	12
V₇	0.931 6	8	0.935 4	10
V₈	0.934 6	9	0.895 7	3
V₉	0.915 0	3	0.965 8	16
V₁₀	0.942 0	13	0.948 4	11
V₁₂	0.941 3	12	0.909 6	6
V₁₂	0.939 5	11	0.930 3	9
V₁₃	0.882 6	1	0.969 1	17
V₁₄	0.950 6	19	0.910 7	7
V₁₅	0.949 7	18	0.970 2	18
V₁₆	0.931 5	7	0.959 5	14
V₁₇	0.944 6	15	0.977 6	19
V₁₈	0.938 7	10	0.896 5	4
V₁₉	0.931 3	6	0.961 0	15
V₂₀	0.943 5	14	0.915 7	8

表6 灰色关联分析法计算结果

Tab.6 Calculation results of gray correlation analysis

品种编号 Varieties number	r_i	r_i排序 r_i Rank	$r_{i}^{'}$	$r_{i}^{'}$ 排序 $r_{i}^{'}$ Rank
V₁	0.914 4	2	0.866 7	1
V₂	0.915 5	4	0.886 9	2
V₃	0.929 3	5	0.896 7	5
V₄	0.949 0	17	0.983 2	20
V₅	0.956 3	20	0.953 8	13
V₆	0.946 4	16	0.950 1	12
V₇	0.931 6	8	0.935 4	10
V₈	0.934 6	9	0.895 7	3
V₉	0.915 0	3	0.965 8	16
V₁₀	0.942 0	13	0.948 4	11
V₁₂	0.941 3	12	0.909 6	6
V₁₂	0.939 5	11	0.930 3	9
V₁₃	0.882 6	1	0.969 1	17
V₁₄	0.950 6	19	0.910 7	7
V₁₅	0.949 7	18	0.970 2	18
V₁₆	0.931 5	7	0.959 5	14
V₁₇	0.944 6	15	0.977 6	19
V₁₈	0.938 7	10	0.896 5	4
V₁₉	0.931 3	6	0.961 0	15
V₂₀	0.943 5	14	0.915 7	8

表7 不同分析方法的相关性

Tab.7 Correlations analysis of different analysis methods

项目 Items	产量排序 Yield rank	C_i值排序 C_i rank	r_i值排序 r_i rank	$r_{i}^{'}$ 值排序 $r_{i}^{'}$ rank
产量排序 Yield rank	1
C_i值排序 C_i rank	0.33	1
r_i值排序 r_i rank	0.10	0.10	1
$r_{i}^{'}$ 值排序 $r_{i}^{'}$ rank	0.89^**	0.37	0.29	1

表7 不同分析方法的相关性

Tab.7 Correlations analysis of different analysis methods

项目 Items	产量排序 Yield rank	C_i值排序 C_i rank	r_i值排序 r_i rank	$r_{i}^{'}$ 值排序 $r_{i}^{'}$ rank
产量排序 Yield rank	1
C_i值排序 C_i rank	0.33	1
r_i值排序 r_i rank	0.10	0.10	1
$r_{i}^{'}$ 值排序 $r_{i}^{'}$ rank	0.89^**	0.37	0.29	1

图2 各品种不同方法排序分布

Fig.2 Distribution of different method rankings for each cultivar

表8 不同分析方法结果比较

Tab.8 Comparisons of results from different analysis methods

品种编号 Varieties number	产量 Yield		DTOPSIS法 DTOPSIS methods		灰色关联分析 Grey correlation analysis
品种编号 Varieties number	排序 Rank	显著性 Significance	排序 Rank	C_i差异值 Difference value of C_i(%)	排序 Rank	r_i差异值 Difference value of r_i(%)	排序 Rank	$r_{i}^{'}$ 差异值 Difference value of $r_{i}^{'}$ (%)
V₁	20	318.9^nN	18	23.81	19	4.38	20	11.85
V₂	19	324.1^mnMN	10	15.71	17	4.27	19	9.79
V₃	17	331.9^lmLMN	8	13.04	16	2.82	16	8.80
V₄	8	382.8^fFG	2	2.34	4	0.76	1	0.00
V₅	9	372.6^gGH	4	7.46	1	0.00	8	2.99
V₆	10	372.0^gGH	17	22.46	5	1.04	9	3.36
V₇	7	387.5^efEF	1	0.00	13	2.58	11	4.86
V₈	18	328.7^lmnMN	12	19.33	12	2.26	18	8.90
V₉	1	432.0^aA	5	8.98	18	4.31	5	1.77
V₁₀	11	367.3^ghH	7	13.01	8	1.49	10	3.54
V₁₁	15	343.5^jkJKL	20	30.01	9	1.56	15	7.49
V₁₂	12	361.2^hiHI	3	6.43	10	1.75	12	5.39
V₁₃	6	396.9^deDE	14	19.97	20	7.71	4	1.43
V₁₄	13	352.4^ijIJ	11	18.33	2	0.59	14	7.38
V₁₅	3	415.3^bBC	16	21.93	3	0.69	3	1.33
V₁₆	4	411.7^bcC	9	15.71	14	2.59	7	2.41
V₁₇	5	404.2^cdCD	6	12.68	6	1.22	2	0.57
V₁₈	14	346.8^jkJK	19	24.17	11	1.84	17	8.82
V₁₉	2	426.4^aAB	13	19.91	15	2.61	6	2.26
V₂₀	16	337.5^klKLM	15	20.71	7	1.34	13	6.87

表8 不同分析方法结果比较

Tab.8 Comparisons of results from different analysis methods

品种编号 Varieties number	产量 Yield		DTOPSIS法 DTOPSIS methods		灰色关联分析 Grey correlation analysis
品种编号 Varieties number	排序 Rank	显著性 Significance	排序 Rank	C_i差异值 Difference value of C_i(%)	排序 Rank	r_i差异值 Difference value of r_i(%)	排序 Rank	$r_{i}^{'}$ 差异值 Difference value of $r_{i}^{'}$ (%)
V₁	20	318.9^nN	18	23.81	19	4.38	20	11.85
V₂	19	324.1^mnMN	10	15.71	17	4.27	19	9.79
V₃	17	331.9^lmLMN	8	13.04	16	2.82	16	8.80
V₄	8	382.8^fFG	2	2.34	4	0.76	1	0.00
V₅	9	372.6^gGH	4	7.46	1	0.00	8	2.99
V₆	10	372.0^gGH	17	22.46	5	1.04	9	3.36
V₇	7	387.5^efEF	1	0.00	13	2.58	11	4.86
V₈	18	328.7^lmnMN	12	19.33	12	2.26	18	8.90
V₉	1	432.0^aA	5	8.98	18	4.31	5	1.77
V₁₀	11	367.3^ghH	7	13.01	8	1.49	10	3.54
V₁₁	15	343.5^jkJKL	20	30.01	9	1.56	15	7.49
V₁₂	12	361.2^hiHI	3	6.43	10	1.75	12	5.39
V₁₃	6	396.9^deDE	14	19.97	20	7.71	4	1.43
V₁₄	13	352.4^ijIJ	11	18.33	2	0.59	14	7.38
V₁₅	3	415.3^bBC	16	21.93	3	0.69	3	1.33
V₁₆	4	411.7^bcC	9	15.71	14	2.59	7	2.41
V₁₇	5	404.2^cdCD	6	12.68	6	1.22	2	0.57
V₁₈	14	346.8^jkJK	19	24.17	11	1.84	17	8.82
V₁₉	2	426.4^aAB	13	19.91	15	2.61	6	2.26
V₂₀	16	337.5^klKLM	15	20.71	7	1.34	13	6.87

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基于熵权法和灰色关联度分析法综合评价谷子品种的农艺性状及产量与品质

Comprehensive evaluation of foxtail millet varieties based on entropy weight method and grey relational analysis

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