Fuzzy logic in the simultaneous selection of quantitative and qualitative descriptors for kale

Fernandes, Ana Clara Gonçalves; Azevedo, Alcinei Mistico; Andrade Júnior, Valter Carvalho; Silva, Derly Jose Henriques da; Brito, Orlando Gonçalves; Valadares, Nermy Ribeiro

doi:10.4025/actasciagron.v48i1.73211

Simultaneous selection in genetic improvement presents difficulties in selecting qualitative traits as well as the desired commercial ranges for quantitative traits. Thus, fuzzy logic has become an alternative, enabling the computational modelling of the researcher’s experience. This study aimed to assess the efficiency of fuzzy logic in simultaneous selection considering both qualitative and quantitative descriptors. The developed methodology was applied to data from two experiments with kale half-sibs. The first experiment was carried out in Viçosa in randomised blocks, with 24 families of kale half-sibs, 4 replications, and 5 plants per plot. The second experiment was carried out in Montes Claros in randomised blocks, with 36 kale genotypes, 33 families of half-sibs, and 3 commercial cultivars, with 4 replications and 6 plants per plot. Quantitative and qualitative traits were evaluated, and individual genetic values were obtained using REML/BLUP. Genetic gains were evaluated based on the Mulamba-Mock index and the developed fuzzy systems. The selection gains were similar for quantitative traits, but fuzzy logic also selected qualitative traits, and thus stands out as a potential tool for kale genetic improvement. The selection of individuals by the fuzzy methodology enables estimated selection gains in a favourable direction for qualitative and quantitative traits, enabling the automation of more accurate and standardised decision-making.

Keywords:
selection indices; Mulamba-Mock; computational intelligence; genetical improvement; Brassica oleracea L. var. acephala DC.

[TFN1] NS, number of shoots; PH, plant height; PL, petiole length; SD, stem diameter; NL, number of leaves; FLM, fresh leaf matter; LL, leaf length; LW, leaf width; LS, leaf shape; LM, leaf margin; VC, vein colour; PC, petiole colour.

Input ECP
NS	PH (cm)	PL (cm)	SD (mm)
Excellent: a=0, b= 0, c=30, d= 45	Low: a=0, b=0, c=20, d=35	Little: a=0, b=0, c=3, d=4	Thin: a=0, b=0, c=2, d=3
Medium: a=30, b=45, c=75, d=90	Excellent: a=20, b=40, c=65, d=80	Excellent: a=3, b=4, c=6, d=7	Excellent: a=2, b=3, c=4, d=5
Bad: a=75, b=90, c=125, d= 125	Bad: a=70, b=90, c=175, d= 175	Long: a=6, b=8, c=35, d=35	Thick: a=4, b=5, c=8, d=8
Input PDF
NL	FLM (g)	LL (cm)	LW (cm)
Bad: a=0, b= 0, c=60, d= 80	Bad: a=0, b= 0, c=2, d=4	Bad 1: a=0, b=0, c=10, d=13	Bad 1: a=0, b=0, c=3, d=10
Medium: a=75, b=85, c=100, d=115	Medium: a=2, b=4, c=6, d=8	Medium: a=10, b=15, c=25, d=30	Medium: a=7, b=12, c=22, d=27
Excellent: a=110, b=120, c=155, d= 155	Excellent: a=6, b=7, c=10 d= 10	Bad 2: a=28, b=31, c=53, d=53	Bad 2: a=26, b=29, c=47, d=47
Input QDF
LS	LM	VC	PC
n1: a=0, b=1, c=2	n1: a=0, b=1, c=2	n1: a=0, b=1, c=2	n1: a=0, b=1, c=2
n2: a=1, b=2, c=3	n2: a=1, b=2, c=3	n2: a=1, b=2, c=3	n2: a=1, b=2, c=3
n3: a=2, b=3, c=4	n3: a=2, b=3, c=4	n3: a=2, b=3, c=4	n3: a=2, b=3, c=4
n4: a=3, b=4, c=5	n4: a=3, b=4, c=5	n4: a=3, b=4, c=5	n4: a=3, b=4, c=5
n5: a=4, b=5, c=6	n5: a=4, b=5, c=6	n5: a=4, b=5, c=6	n5: a=4, b=5, c=6
n6: a=5, b=6, c=7	-	-	-
n7: a=6, b=7, c=8	-	-	-
Outputs ECP, LFP e LFQ/Input FIM
ECP	LFP	LFQ
To bad: a=0, b=1, c=2	To bad: a=0, b=1, c=2	To bad: a=0, b=1, c=2
Bad: a=1, b=2, c=3	Bad: a=1, b=2, c=3	Bad: a=1, b=2, c=3
Medium: a=2, b=3, c=4	Medium: a=2, b=3, c=4	Medium: a=2, b=3, c=4
Good: a=3, b=4, c=5	Good: a=3, b=4, c=5	Good: a=3, b=4, c=5
Very good: a=4, b=5, c=6	Very good: a=4, b=5, c=6	Very good: a=4, b=5, c=6

Parameters	NS	PH	PL	SD	NL	FLM	LL	LW
Experiment 1
Va	390.72	2.62	10.39	0.02	55.32	0.37	11.42	8.12
Vparc	4.43	41.18	0.17	0.01	2.49	0.07	1.14	1.41
Ve	195.69	323.61	9.27	0.2	262.24	1.66	18.4	17.46
Vf	590.84	367.41	19.83	0.24	320.06	2.1	30.96	26.98
h²a	0.66	0.01	0.52	0.1	0.17	0.18	0.37	0.3
CVgi%	33.55	1.85	21.1	4.82	10.87	12.02	10.26	9.79
CVe%	5.78	8.98	4.13	3.47	3.72	6.24	3.71	5.84
CVr	2.9	0.1	2.55	0.7	1.46	0.96	1.38	0.84
Experiment 2
Va	241.94	141.39	1.00	0.12	248.80	0.21	0.67	4.01
Vplot	51.59	22.72	1.21	0.02	0.00	0.06	7.20	1.37
Ve	195.86	118.36	5.61	0.31	48.93	0.42	20.40	8.66
Vp	489.39	282.47	7.82	0.45	297.73	0.69	28.27	14.04
h²a	0.49	0.50	0.13	0.26	0.84	0.30	0.02	0.29
CVgi%	38.42	17.82	11.60	9.92	24.48	19.98	2.63	9.74
CVe%	34.57	16.30	27.41	16.14	10.86	28.48	14.49	14.32
CVr	1.11	1.09	0.42	0.61	2.25	0.70	0.18	0.68

Variables	Experiment 1				Experiment 2
Variables	ECP	LFP	LFQ	FIM	ECP	LFP	LFQ	FIM
ECP	1.00**	0.26**	0.13*	0.68**	1.00**	-0.01	-0.10	0.45**
LFP	0.26**	1.00**	-0.01	0.59**	-0.01	1.00**	0.11	0.52**
LFQ	0.13*	-0.01	1.00**	0.58**	-0.10	0.11	1.00**	0.64**
FIM	0.68**	0.59**	0.58**	1.00**	0.45**	0.52**	0.64**	1.00**
NS	-0.78**	-0.06	-0.06	-0.51**	-0.73**	0.07	0.05	-0.30**
PH	-0.34**	-0.06	-0.06	-0.26**	-0.51**	-0.14*	0.13*	-0.20**
PL	-0.40**	-0.21**	-0.02	-0.37**	-0.32**	-0.29**	-0.08	-0.36**
SD	0.13*	0.08	0.12*	0.21**	-0.09	-0.18**	-0.05	-0.17**
NL	0.18**	0.72**	-0.29**	0.35**	-0.17**	0.41**	0.04	0.12*
FLM	0.19**	0.35**	-0.12*	0.25**	-0.15**	-0.05	-0.06	-0.14*
LL	-0.23**	-0.56**	0.04	-0.39**	-0.05	-0.65**	-0.22**	-0.46**
LW	-0.23**	-0.55**	0.13*	-0.35**	-0.01	-0.58**	-0.01	-0.27**

Variables	NS	PH	PL	SD	NL	FLM	LL	LW
Experiment 1
NS	-47.87	-0.03	-11.44	0.91	3.41	3.89	-1.67	-2.91
PH	-1.46	-0.26	-2.24	-0.26	0.12	-2.07	-3.37	-2.35
PL	-15.59	-0.02	-23.07	0.08	0.67	-0.64	-3.79	-4.24
SD	-7.15	-0.04	-2.82	3.06	3.49	5.98	-1.52	-1.06
NL	-7.61	-0.02	-3.47	0.84	9.63	6.24	-4.34	-3.86
FLM	-15.9	0	1.57	1.51	6.25	8.7	-0.58	0.02
LL	2.74	-0.07	-9.2	-0.76	2.45	-1.59	-10.24	-6.79
LW	0.46	-0.05	-9.99	-0.63	3.42	-1.08	-7.02	-9.24
Experiment 2
NS	-41.46	-3.99	-0.17	-1.07	-0.21	0.04	0.08	-0.56
PH	-11.05	-19.05	-1.49	-3.36	-7.51	-9.21	-0.30	-3.12
PL	0.16	-3.85	-6.22	-0.51	5.34	-1.49	-0.35	-1.90
SD	5.76	0.06	0.44	8.36	14.02	11.54	0.26	3.95
NL	8.30	2.44	-0.22	3.50	38.45	11.53	-0.01	-1.42
FLM	0.56	2.73	2.36	5.45	20.59	18.06	0.41	3.45
LL	1.53	-7.19	-3.43	-3.58	-1.77	-8.12	-0.72	-6.04
LW	0.33	-2.04	-1.04	-3.19	1.86	-7.67	-0.40	-8.81

Variables	MM	SGecp	SGlfp	SGlfq	SGfim
Experiment 1
NS	-30.96	-41.54	-3.43	1.91	-29.11
PH	-0.06	-0.04	-0.01	-0.01	-0.05
PL	-13.33	-14.99	-8.79	-0.75	-13.59
SD	1.62	0.97	0.07	-0.5	0.63
NL	5.96	3.63	5.38	-2.5	5.26
FLM	5.81	3.72	1.73	-2.38	5.28
LL	-4.41	-3.14	-7.1	-0.88	-5.33
LW	-4.22	-2.63	-6.13	0.98	-5.04
Experiment 2
NS	-14.25	5.46	-27.77	7.64	-16.38
PH	-6.40	-3.03	-9.56	4.30	-6.62
PL	-3.86	-2.56	-2.43	0.58	-2.99
SD	1.61	-1.54	-2.06	-0.94	-2.56
NL	19.52	13.51	-5.24	-1.23	0.69
FLM	3.07	-0.41	-4.58	-0.60	-4.85
LL	-0.35	-0.48	-0.13	-0.17	-0.43
LW	-3.79	-4.85	-1.03	0.14	-3.22

Strategies	LS (1, 2, and 3)	LM (1 and 2)	VC (2 and 3)	PC (2 and 3)
Experiment 1
No selection	98.07	63.74	44.51	55.49
MM	100	89.09	47.27	49.09
ECP	96.74	77.17	54.35	60.87
LFP	98.7	71.43	41.55	48.05
LFQ	100	93.38	74.26	81.62
FIM	100	92.86	60.71	73.21
Experiment 2
No selection	91.4	68.7	68.7	77.3
MM	91.4	67.1	81.9	77.0
ECP	91.7	69.6	82.4	72.3
LFP	93.6	73.5	75.9	68.9
LFQ	95.3	79.2	94.7	92.6
FIM	96.8	74.3	96.3	91.6