Diffuse system simulating wheat productivity by nitrogen and temperature in the use of biopolymers

Sistema difuso simulando a produtividade do trigo pelo nitrogênio e temperatura no uso de biopolímeros

ABSTRACT

Fuzzy logic can simulate wheat yield by nitrogen and temperature nonlinearity, validating the use of hydrogel biopolymer. The objective of this study is to adapt the fuzzy logic model to the simulation of nitrogen biomass and wheat grain yield and non-linearity of the maximum air temperature, under the conditions of use of the hydrogel biopolymer, in high and low N-residual release systems. The study was conducted in 2014 and 2015, in Augusto Pestana, RS, Brazil (28 ° 26 ‘30’ latitude S and 54 ° 0 ‘58’ longitude W). The experimental design was a randomized block design with four replications in 5 x 5 factorial, for hydrogel doses (0, 30, 60, 90 and 120 kg ha^-1), added in the furrow next to the seed, and N-fertilizer doses. (0, 30, 60, 90 and 120 kg ha^-1), applied at the phenological stage V₃ (third expanded leaf) as top-dressing, respectively. The pertinence functions together with the quantitative and linguistic values ​​for the input and output variables are suitable for the use of fuzzy logic in the wheat yield simulation. The fuzzy model made it possible to estimate the values ​​of biomass and wheat grain yield by nitrogen and non-linearity of the maximum air temperature under the conditions of use of the hydrogel biopolymer in high and low N-residual release systems.

Key words:
Triticum aestivum; water stress; hydrogel; fuzzy logic

RESUMO

A lógica fuzzy pode simular a produtividade do trigo pelo nitrogênio e não linearidade da temperatura, validando o uso do biopolímero hidrogel. O objetivo com o estudo é adequar o modelo de lógica fuzzy à simulação da produtividade de biomassa e grãos de trigo pelo nitrogênio e não linearidade da temperatura máxima do ar, nas condições de uso do biopolímero hidrogel, em sistemas de alta e reduzida liberação de N-residual. O estudo foi conduzido nos anos de 2014 e 2015, em Augusto Pestana, RS, Brasil (28° 26’ 30’’ latitude S e 54° 0’ 58’’ longitude W).O delineamento experimental foi o de blocos casualizados com quatro repetições em fatorial 5 x 5, para doses de hidrogel (0, 30, 60, 90 e 120 kg ha^-1), adicionado no sulco junto à semente, e doses de N-fertilizante (0, 30, 60, 90 e 120 kg ha^-1), aplicado em cobertura no estádio fenológico V₃(de terceira folha expandida), respectivamente. As funções de pertinências junto aos valores quantitativos e linguísticos para as variáveis de entrada e de saída, se mostram adequados para o uso da lógica fuzzy na simulação da produtividade do trigo. O modelo fuzzy possibilitou estimar os valores de produtividade de biomassa e grãos de trigo pelo nitrogênio e não linearidade da temperatura máxima do ar, nas condições de uso do biopolímero hidrogel em sistemas de alta e reduzida liberação de N-residual.

Palavras-chave:
Triticum aestivum; estresse hídrico; hidrogel; lógica fuzzy

Introduction

Among the meteorological elements, photoperiod, rainfall and air temperature are the most related to wheat productivity (Bischoff et al., 2015; Santi et al., 2018). High temperature rapidly reduces soil moisture, implying an increased ratio of plant respiration rate and decreased photosynthesis efficiency. In addition, it intensifies N-fertilizer losses by volatilization (Scremin et al., 2017; Trautmann et al., 2017). It is noteworthy that nitrogen is the main nutrient absorbed by plants, by acting on different metabolic routes linked to the development of productivity components. Therefore, the need for alternatives to improve its use by plants with reduced environmental impacts (Camponogara et al., 2016; Costa et al., 2018). One possibility of minimizing problems related to higher nitrogen efficiency is the use of biopolymers to maintain soil moisture (Fernandes et al., 2015; Scremin et al., 2017). Hydrogel biopolymers are biodegradable three-dimensional polymer networks, capable of retaining water in their gel-forming structure, able to hydrate and release water over a long period (Kaewpirom & Boonsang, 2006; Venturoli & Venturoli, 2011).

From the perspective of understanding processes, modeling enables the simulation, optimization and validation of technologies, describing productivity behavior using controlled and uncontrolled variables (Barioni et al., 2011; Marolli et al., 2018). Fuzzy models are techniques that enable this description of complex systems (Silva et al., 2014; Wei et al., 2017), belonging to the smart controls class in the representation of uncertainties (Li et al., 2015; Mendel, 2017).

The aim of this study was to adapt the fuzzy logic model to the simulation of nitrogen biomass, wheat grain yield and non-linearity of the maximum air temperature, under the conditions of use of the hydropolymer in high succession and low N-residual release systems.

Material and Methods

The study was carried out in the field in 2014 and 2015, in the municipality of Augusto Pestana, RS, Brazil (28° 26’ 30’’ latitude S and 54° 0’ 58’’ longitude W). The soil of the experimental area is classified as Oxisol, and the climate of the region, according to Köppen classification, is the Cfa type, with hot summer without dry season. Ten days before sowing, soil analysis was performed and the following chemical characteristics were identified (Tedesco et al., 1995): i) soybean/wheat system (pH = 6.1, P = 49.1 mg dm^-3, K = 424 mg dm^-3, MO = 3.0%, Al = 0 cmol_c dm^-3, Ca = 6.3 cmol_c dm^-3 e Mg = 2.5 cmol_c dm^-3) and; ii) Corn/wheat system (pH = 6.5, P = 23.6 mg dm^-3, K = 295 mg dm^-3, MO = 2.9%, Al = 0 cmol_c dm^-3, Ca = 6.8 cmol_c dm^-3 and Mg = 3.1 cmol_c dm^-3). Regardless of the agricultural year, sowing was carried out in the third week of June, according to crop recommendation, in high and low C/N residual cover, corn/wheat and soybean/wheat systems, respectively. In sowing, a seeder-fertilizer was used in the composition of the plot with 5 rows of 5 m long and 0.20 m line spacing, forming the experimental unit of 5 m². The seeds were submitted to germination and vigor test in the laboratory to correct the desired density of 400 viable seeds m^-2, using the TEC 10 wheat cultivar, commercial class type "bread" of high productive potential. During the study, tebuconazole fungicide was applied at a dose of 0.75 L ha^-1. Weed control was carried out with metsulfuron-methyl herbicide at a dose of 4 g ha^-1 and additional weeding whenever necessary. In the experiments, 45 and 30 kg ha^-1 of P₂O₅ and K₂O were applied at sowing, based on soil phosphorus (P) and potassium (K) contents, for grain yield expectation of 3 t ha^-1, respectively, and 10 kg ha^-1 of nitrogen (N) in the base (except in the standard experimental unit), with the remainder in top-dressing at phenological stage V₃ (expanded third leaf). These fertilizations took into consideration the recommendations of fertilization for the state of Rio Grande do Sul. The application of different doses of biopolymer hydrogel was next to the wheat seed, being at the same depth and cultivation line in the soil, approximately at three centimeters.

In each cultivation system two experiments were conducted, one to quantify biomass yield (PB, kg ha^-1), and another to estimate grain yield (PG, kg ha^-1). Therefore, in the four experiments, the experimental design consisted of randomized blocks with four replications, following a 5 x 5 factorial scheme, in the sources of variation, hydrogel doses at levels 0, 30, 60, 90 and 120 kg ha^-1 and doses of N-fertilizer (source urea) at levels 0, 30, 60, 90 and 120 kg ha^-1. Grain yield was obtained by cutting three central lines (rows) in each plot at the harvest maturity stage, with grain moisture around 20%. The plants were tracked with a stationary harvester and directed to the laboratory to correct grain moisture to 13% and weighed to estimate PG (kg ha^-1). In experiments to quantify biomass productivity, the plant material was harvested close to the soil, from the collection of one linear meter of the three central lines of each plot, at 120 days after emergence. The biomass samples were directed to a forced air oven at 65 °C until reaching constant weight to the estimate productivity.

In the initial process of data analysis, the "data mining" technique was performed with the objective of forming association standards for the inferences of the rule base for the fuzzy model. From this knowledge, the rule base was elaborated in linguistic terms, with the help of an expert. The model input variables (independent variables) were the doses of N and the average maximum temperature (T_Max). The maximum temperature values during the cycle were obtained by the Total Automatic Station, installed 500 m from the experiment. The output variables (dependent variables) were PG and PB. For the independent variable T_Máx (ºC), the domain was considered in the range [21, 25], representing the ranges: < 22.5 ºC (Low Temperature) and > 22.5 ºC (High Temperature). For the independent variable N (kg ha^-1), the domain of the interval [0,120] was considered, representing the ranges: <15 = very low dose (MB); [15,45] = low dose (B); [45,75] = mean dose (M); [75, 105] = high dose (A) and [105, 120] = very high dose (MA). For the output variables, the image intervals were the maximum and minimum values of experimentally collected data on biomass and wheat grain yield, considering the cumulative effect of the years, in each condition of hydrogel use. Thus, 10 simulators were built, one for each condition of hydrogel use and cultivation system. The variable PG was divided into four equidistant intervals (Table 1): very low (MB), low (B), medium (M) and high (A). The variable PB was divided into five equidistant intervals (Table 2), four being used for the PG variable, plus the very high interval (MA).

Table 1
Fuzzy logic rule base for simulation of wheat grain yield in succession systems

N (kg ha-1)		Year	TMax (°C)			Output Linguistic variables
VL	VQ		VL	VQ		PGH0	PGH30	PGH60	PGH90	PGH120
Soybean/wheat system
MB	[0, 15[	2015	B	<22.5		MB	MB	B	B	B
		2014	A	>22.5		MB	MB	MB	MB	MB
B	[15, 45[	2015	B	<22.5		M	M	M	M	M
		2014	A	>22.5		B	B	B	B	B
M	[45, 75[	2015	B	<22.5		A	M	A	A	A
		2014	A	>22.5		B	M	B	B	B
A	[75, 105[	2015	B	<22.5		A	A	M	A	A
		2014	A	>22.5		M	M	M	B	B
MA	[105, 120]	2015	B	<22.5		A	A	A	A	A
		2014	A	>22.5		M	A	M	M	B
Real value (2014+2015)		Minimum				1214	1257	1265	1266	1151
		Maximum				3189	3395	3487	3222	3165
Corn/wheat system
MB	[0, 15[	2015	B	<22.5		MB	MB	B	B	B
		2014	A	>22.5		MB	MB	MB	MB	MB
B	[15, 45[	2015	B	<22.5		M	B	M	M	B
		2014	A	>22.5		MB	MB	B	MB	MB
M	[45, 75[	2015	B	<22.5		M	M	M	M	M
		2014	A	>22.5		B	B	B	MB	MB
A	[75, 105[	2015	B	<22.5		M	M	M	M	M
		2014	A	>22.5		B	M	M	B	B
MA	[105, 120]	2015	B	<22.5		A	A	A	M	M
		2014	A	>22.5		B	M	M	M	M
Real value (2014+2015)		Minimum				487	609	616	653	682
		Maximum				2678	2779	2657	2556	2450

• N -Nitrogen; T_Máx -Maximum average temperature; V_L -Linguistic variables; V_Q- Quantitative variables; PG -Grain yield; MB -Very Low; B -Low; M -Medium; A-High; H - Hydrogel (kg ha^-1)

Table 2
Fuzzy logic rule base for simulating wheat biomass productivity in succession systems

N (kg ha-1)		Year	TMax (°C)			Output Linguistic variables
VL	VQ		VL	VQ		PBH0	PBH30	PBH60	PBH90	PBH120
Soybean/wheat system
MB	[0, 15[	2015	B	<22.5		B	B	B	B	B
		2014	A	>22.5		MB	MB	B	B	MB
B	[15, 45[	2015	B	<22.5		M	A	M	A	A
		2014	A	>22.5		B	M	B	M	B
M	[45, 75[	2015	B	<22.5		A	A	A	A	MA
		2014	A	>22.5		M	A	M	B	B
A	[75, 105[	2015	B	<22.5		A	MA	MA	A	MA
		2014	A	>22.5		A	MB	A	M	M
MA	[105, 120]	2015	B	<22.5		MA	MA	MA	MA	MA
		2014	A	>22.5		MA	MA	MA	A	A
Real value (2014+2015)		Minimum				6038	5255	6424	6396	5755
		Maximum				11212	11782	11796	12238	13021
Corn/wheat system
MB	[0, 15[	2015	B	<22.5		MB	MB	B	B	B
		2014	A	>22.5		MB	MB	MB	MB	MB
B	[15, 45[	2015	B	<22.5		B	B	A	M	B
		2014	A	>22.5		MB	MB	MB	MB	MB
M	[45, 75[	2015	B	<22.5		M	M	A	A	MA
		2014	A	>22.5		MB	MB	MB	MB	MB
A	[75, 105[	2015	B	<22.5		MA	MA	MA	MA	MA
		2014	A	>22.5		B	B	B	B	B
MA	[105, 120]	2015	B	<22.5		MA	MA	MA	MA	MA
		2014	A	>22.5		B	M	M	M	M
Real value (2014+2015)		Minimum				4400	4763	4453	4466	4287
		Maximum				11671	12451	12786	12168	11789

• N -Nitrogen; T_Máx -Maximum average temperature; V_L -Linguistic variables; V_Q -Quantitative variables; PB -Biomass productivity; MB -Very low; B -Low; M -Medium; A-High; MA -Very High; H -Hydrogel (kg ha^-1)

Tables 1 and 2 present the fuzzy logic rule base, considering the variables of nitrogen input and maximum temperature to the simulation of biomass and wheat grain yield, respectively.

In the development of fuzzy logic programming, the FuzzyLogic Toolbox module from MATLAB® software was used. In forecasting applications the fuzzy Mamdani model was used, which includes interface modules for transforming input variables into fuzzy sets and later outputs into proportional numerical quantities (Cecconello et al., 2010). The fuzzification process took place by 4 successive modules. In module 1 (fuzzification), the input variable information was mathematically modeled using fuzzy sets. From the expert, each input variable was assigned linguistic terms representing the states of this variable and each linguistic term was associated with a fuzzy set by a pertinence function. In module 2 (rule base), the variables in their linguistic classifications were adjusted, where each rule base satisfied the following structure:

If A is in A_i, then B is in B_i

A_i and B_i being the fuzzy sets. The expression A is in A_i means that μ_Ai (a) ? [0, 1]. Both the A_i and B_i sets are the Cartesian product of fuzzy sets, that is, A_i = A_i1 × A_i2 × ... × A_im and B_i = B_i1 × B_i2 × ... × B_in. In this case, each fuzzy set A_ij and B_ik represented a linguistic term for the jth input variable and kth output variable, and the expression A is in A_i which means:

$${\mu }_{A_i}\left(a\right)=\min \left\{{\mu }_{A_{i1\left(a\right)}},{\mu }_{A_{i2\left(a\right)}},\dots ,{\mu }_{A_{im\left(a\right)}}\right\}\in \left[\mathrm{0,}1\right]$$ (1)

In module 3 (inference), the logical connectives used to establish the fuzzy relationship were defined for rule base modeling. The relationship between linguistic variables was characterized by the fuzzy system operator (MIN). In each rule, a fuzzy R_i relationship with degree of relevance for each pair (a,b) was considered:

$${\mu }_{R_i}\left(a,b\right)=\min \{{\mu }_{A_i}\left(a\right),{\mu }_{B_i}\left.\left(b\right)\right\}$$ (2)

The relationship between each rule is characterized by the operator (MAX), of the fuzzy R relationship that represents the model determined by a rule base obtained by the MAX union of each individual rule, so that for each pair (a,b) it is obtained:

$${\mu }_R\left(a,b\right)=\underset{1\le i\le n}{\max }\left\{{\mu }_{A_i}\left(a\right)^{\mu }_{B_i}\left(b\right)\right\}$$ (3)

where ^ represents the MIN operator.

By Mamdani's method, the pertinence function of B is given by:

$${\mu }_B\left(b\right)=\underset{1\le i\le n}{\max }\left\{\underset{a}{\max }\{{\mu }_A\left(a\right)^{\mu }_{Ai}\left(a\right)\right\}^{\mu }_{Bi}\left(b\right)\}$$ (4)

If the input is a classic unitary set, then μ_A (a) = 1 and μ_A (a) ≤ 1. Therefore, the above expression results in:

$${\mu }_B\left(b\right)=\underset{1\le i\le n}{\max }\left\{{\mu }_{Ai}\left(a\right)^{\mu }_{Bi}\left(b\right)\right\}$$ (5)

Therefore, the fuzzy set B represents the action for each input A.

In module 4 (defuzzification), the state of the fuzzy output variable gives the numeric value. One of the main defuzzification methods is the center of mass for continuous variables, given by the expression:

$$m\left(B\right)=\frac{\int b_{\mu B}\left(b\right)db}{\int {\mu }_B\left(b\right)db}$$ (6)

and discrete variables by the expression:

$$m\left(B\right)=\frac{{{\displaystyle \sum }}_b{b}_{\mu B}\left(b\right)db}{{{\displaystyle \sum }}_b{b}_{\mu B}\left(b\right)b}$$ (7)

The fuzzy controller is described as a function f: Rⁿ → R^m, since given an input value, there is a single corresponding output value.

To validate the rule base and simulated values of biomass and grain yield by fuzzy logic, the behavior and parameters of polynomial regression were considered. These were obtained from the real value of the variables in the different doses of N use and the lower and upper limits, from the confidence interval of the real values of the mean of two agricultural harvests, at a level of 0,05 probability of error. For confidence intervals and regression models we used the computer program Genes.

Results and Discussion

In Figure 1, during the wheat crop cycle, accumulated rainfall of 952 mm in 2014 (Figure 1A) and 817 mm in 2015 (Figure 1B) were observed. The observed values are similar to the historical average of the last 20 years, which is 900 mm, but with different distribution of rainfall between years during cultivation (Figure 1). In 2014, there were shorter periods of rain at the beginning of the cycle, with higher maximum temperatures. A condition that favors nitrogen loss through volatilization during fertilization.

Figure 1
Rainfall and maximum temperature in the wheat cycle. (A) agricultural year 2014 and (B) agricultural year 2015

The highest rainfall in 2014 occurred between the half of the wheat cycle until near maturity (Figure 1A), which favored periods of lower insolation, indicating a reduction in photosynthesis efficiency. In addition, excess rainfall was observed near grain maturation. In 2015, the highest rainfall was recorded between emergence until around 36 days of wheat development and with maximum temperatures lower than those recorded in 2014. Precipitation was regular, with lower intensity and better distribution from the beginning of the reproductive phase to maturity (Figure 1B), facts report the higher productivity obtained in 2015 compared to 2014.

In cereals such as wheat, a favorable year for cultivation meets the minimum rainfall requirement for the crop, with adequate distribution of milder temperatures (Arenhardt et al., 2015). Water deficit corroborates N-fertilizer volatilization, increasing nutrient losses to the environment and increasing production costs, not to mention lower productivity by reducing photosynthesis efficiency (Minuzzi & Lopes, 2015). On the other hand, high rainfall causes nitrogen loss by leaching, favoring the incidence of leaf and root diseases (Souza et al., 2013). Thermal conditions influence the most diverse vital processes of plants, from germination to phenological development (Minuzzi & Lopes, 2015). In addition, temperature is decisive for productivity, acting as a catalyst for biological processes, which is why plants require a minimum and maximum temperature for normal physiological activities (Tonin et al., 2014).

Figures 2 and 3 show the behavior and parameters of the equation (y = a + bx) regarding the biological interpretation of nitrogen utilization for grain and biomass yield, respectively, considering the starting point of performance, given by the linear coefficient (a) and slope of the line by the angular coefficient (b), in the comparison between the real data and those simulated by fuzzy logic. Parameter “a” of the linear equation provides the agronomic efficiency, indicating the relationship between the yield obtained per unit of nitrogen supplied.

Figure 2
Behavior of grain yield observed and simulated by fuzzy logic. (A) Soybean/wheat system and (B) Corn/wheat system - 0 kg ha^-1 of hydrogel; (C) Soybean/wheat system and (D) Corn/wheat system - 30 kg ha^-1 of hydrogel; (E) Soybean/wheat system and (F) Corn/wheat system - 60 kg ha^-1 of hydrogel; (G) Soybean/wheat system and (H) Corn/wheat system - 90 kg ha^-1 of hydrogel; (I) Soybean/wheat system and (J) Corn/wheat system - 120 kg ha^-1 of hydrogel

Figure 3
Behavior of biomass productivity observed and simulated by fuzzy logic. (A) Soybean/wheat system and (B) Corn/wheat system - 0 kg ha^-1 hydrogel; (C) Soybean/wheat system and (D) Corn/wheat system - 30 kg ha^-1 hydrogel; (E) Soybean/wheat system and (F) Corn/wheat system - 60 kg ha^-1 hydrogel; (G) Soybean/wheat system and (H) Corn/wheat system - 90 kg ha^-1 hydrogel; (I) Soybean/wheat system and (J) Corn/wheat system - 120 kg ha^-1 hydrogel

In Figure 2, regardless of the cultivation system (soybean/wheat and corn/wheat), the behavior and values of the linear coefficients of observed and simulated grain yield were similar. The trend and slope values in estimating agronomic efficiency were also approximate. For the validation of fuzzy logic in the simulation of grain yield, Figure 2C stands out, showing that for every 1 kg of nitrogen supplied per hectare there is an increase of 11 kg of grain yield in the real cultivation condition. In the regression obtained by the simulation points, each 1 kg of nitrogen supplied per hectare increases the grain yield by 10 kg. Therefore, the equations show the same behavior and approximate coefficients between the real and simulated values.

In Figure 3, regardless of the succession system, the linear and angular behavior and coefficients of observed and simulated biomass yield were similar. This fact reports the validation of fuzzy logic in the simulation of biomass productivity. In view of this, we highlight in Figure 3E, that for every 1 kg of nitrogen supplied per hectare there is an increase of 30 kg of biomass productivity in the real cultivation condition. In the regression obtained by the simulation points, each 1 kg of nitrogen supplied per hectare increases the biomass productivity by 31 kg.

Figures 2 and 3 indicate that the simulation of wheat grain yield by fuzzy logic is qualified in each hydrogel use condition when compared to the real results obtained by bioexperimentation. Other researchers have also reported the potential of using nebulous logic in simulation studies involving the linear and nonlinear effects of environmental conditions, such as Castro et al. (2019) who used fuzzy to estimate feed consumption by Japanese quails. Ramos et al. (2015), using fuzzy logic, classified lambs for slaughter. Campos et al. (2013) used fuzzy logic to predict the occupancy rate of stalls in dairy cattle facilities under a free-stall system.

In Tables 3 and 4 of the soybean/wheat and corn/wheat system, respectively, the increase of nitrogen doses under real cultivation conditions showed an increase in grain yield, usually between 90 and 120 kg ha^-1 of nitrogen. On the other hand, in biomass productivity the increase of nitrogen doses showed an increase until the point of maximum use of nutrient. This same behavior was also recognized by the fuzzification process. In the simulation of grain yield and biomass (Tables 3 and 4) by fuzzy logic, it was observed that the results obtained were close to the observed mean, regardless of the conditions of nitrogen and hydrogel use, confirming the appropriate established rule base and the possibility of using nebulous logic in predicting wheat yield.

Table 3
Fuzzy logic in simulation of wheat productivity by nitrogen and maximum air temperature in hydrogel use, in soybean/wheat system

N (kg ha-1)	PG (kg ha-1)				PB (kg ha-1)				Simulation/Fuzzy (kg ha-1)			Absolute Error (kg ha-1)
	Li	X	Ls		Li	X	Ls		PG	PB		PG	PB
Joint analysis (2014 + 2015)
Hydrogel 0 (kg ha-1)
0	1286	1382	1463		6096	6552	6944		1460	6430		78	122
30	1815	2168	2470		7473	7811	8101		2200	7590		32	221
60	2116	2507	2843		8344	8659	8929		2230	8630		277	29
90	2627	2756	2886		9138	9725	9799		2610	9140		146	585
120	2360	2728	3045		10328	10697	10928		2610	10400		118	297
Mean	2041	2308	2541		8276	8689	8940		2222	8438		86	251
Hydrogel 30 (kg ha-1)
0	1364	1518	1649		5882	7034	8022		1530	6390		12	644
30	1966	2334	2651		8241	8613	8932		2330	8520		4	93
60	2305	2522	2707		8777	9128	9428		2680	9170		158	42
90	2400	2709	2975		5580	9580	11153		2770	9090		61	510
120	2522	2908	3239		10460	10961	11391		2880	10800		28	161
Mean	2111	2398	2644		7788	8863	9785		2438	8794		40	69
Hydrogel 60 (kg ha-1)
0	1351	1680	1963		6831	7481	8038		1910	7500		230	19
30	1770	2173	2518		8037	8290	8507		2380	8040		207	250
60	2167	2540	2859		8802	9183	9509		2410	9110		130	73
90	2284	2690	3038		9681	10109	10476		2730	10300		40	191
120	2445	2876	3246		10413	11073	11639		2840	11000		36	73
Mean	2003	2392	2725		8753	9227	9634		2454	9190		62	37
Hydrogel 90 (kg ha-1)
0	1336	1614	1853		6565	7211	7764		1840	7560		226	349
30	1720	2220	2648		7330	8224	8990		2240	8730		20	506
60	2103	2515	2868		8170	9071	9843		2270	9320		245	249
90	2151	2576	2940		8938	9806	10651		2270	10600		306	794
120	2273	2691	3049		9795	10912	11870		2650	11000		41	88
Mean	1917	2323	2672		8160	9045	9824		2254	9442		69	397
Hydrogel 120 (kg ha-1)
0	1274	1616	1909		6071	7137	8050		1740	7020		124	117
30	1616	2213	2725		6607	8094	9369		2160	8660		53	566
60	2011	2503	2924		7597	9001	10206		2290	9520		313	519
90	2013	2485	2891		8370	9962	11327		2290	10300		295	338
120	2103	2544	2923		9126	10820	12273		2290	11000		354	180
Mean	1803	2272	2674		7554	9003	10245		2154	9300		118	297

• N-nitrogen; L_i and L_s - Lower and upper limit of confidence interval at 0,05 probability of error; X -Mean; PG -Grain Productivity; PB - Biomass Productivity

Table 4
Fuzzy logic in the simulation of wheat yield by nitrogen and maximum air temperature involving hydrogel use in the corn/wheat system

N (kg ha-1)	PG (kg ha-1)				PB (kg ha-1)				Simulation/Fuzzy (kg ha-1)			Absolute error (kg ha-1)
	Li	X	Ls		Li	X	Ls		PG	PB		PG	PB
Joint analysis (2014 + 2015)
Hydrogel 0 (kg ha-1)
0	554	880	1160		4557	5027	5429		1100	5090		115	63
30	1184	1468	1712		5582	6600	7473		1550	5980		82	620
60	1385	1751	2065		5770	7247	8514		1580	7040		171	207
90	1485	1888	2233		6634	8894	10831		1680	7770		308	1124
120	1589	2048	2440		7499	9276	10800		1920	7770		428	1506
Mean	1239	1607	1922		6008	7409	8609		1419	6730		188	679
Hydrogel 30 (kg ha-1)
0	669	996	1276		5060	5733	6309		885	5490		111	243
30	1195	1436	1643		5533	6469	7272		1240	6440		196	29
60	1345	1692	1990		5514	7173	8595		1690	7550		2	377
90	1690	2008	2280		7280	8889	10269		2060	8320		52	569
120	1972	2324	2626		8441	10302	11897		2150	9620		174	682
Mean	1374	1691	1963		6366	7713	8868		1605	7484		86	229
Hydrogel 60 (kg ha-1)
0	657	1043	1374		4907	6566	7989		1210	6270		167	296
30	1213	1584	1903		5088	7434	9446		1640	8850		56	1416
60	1236	1714	2125		5723	7689	9376		1640	8850		74	1161
90	1601	1965	2278		7417	9252	10825		1980	9310		15	58
120	1840	2151	2417		8827	10437	11818		2060	9710		91	727
Mean	1309	1691	2019		6392	8276	9891		1706	8598		15	322
Hydrogel 90 (kg ha-1)
0	689	1036	1333		4735	6275	7596		1210	6140		174	135
30	1104	1404	1661		5406	6750	7904		1570	6140		166	610
60	1225	1694	2096		5672	7838	9696		1570	8520		124	682
90	1503	1866	2178		7148	8845	10301		1600	8030		266	815
120	1727	2057	2340		8307	9950	11358		1920	9330		137	620
Mean	1250	1611	1922		6253	7932	9371		1574	7632		37	300
Hydrogel 120 (kg ha-1)
0	702	1044	1337		4548	6274	7755		1000	5920		156	354
30	1022	1306	1505		5512	6480	7311		1200	5920		106	560
60	1187	1685	2112		5678	8080	10140		1540	7940		145	140
90	1401	1781	2108		6959	8631	10066		1570	7760		211	871
120	1593	1944	2245		7965	9619	11037		1860	9020		84	599
Mean	1181	1552	1861		6132	7817	9262		1434	7312		118	505

• N-nitrogen; L_i and L_s-Lower and upper confidence interval limit at 0,05 probability of error; X -Mean; PG-Grain Productivity; PB - Biomass Productivity

Fuzzy logic has been used in many areas of knowledge to assign linear and nonlinear effects of processes to the observer's acquired experience (Marques et al., 2016). He & Dong (2018) using fuzzy and neural networks obtained good predictive performance in the interaction between robot and environment. Schiassi et al. (2015) simulated the productivity of chicken meat with greater efficiency in feed consumption from the nebulous logic. Silva et al. (2014), developed a neuro-fuzzy hybrid model that made it possible to estimate wheat yield values as a function of nitrogen doses. In studies with hydrogel in oat cultivation, Scremin et al. (2017) showed increased efficiency of nitrogen utilization, especially under conditions of 30 and 60 kg ha^-1 of the biopolymer, but the beneficial effect was dependent on the succession system and weather conditions. Studies involving hydrogel and nitrogen with possibility of simulation considering biological and environmental indicators were not found in the world literature. This highlights the innovative character of this research.

Conclusions

1. The pertinence functions together with the quantitative and linguistic values for the input and output variables are suitable for the use of fuzzy logic in wheat yield simulation.

2. The fuzzy model makes it possible to estimate the yield values of biomass and wheat grain by nitrogen and non-linearity of maximum air temperature under conditions of use of hydrogel biopolymer in high and low N-residual release systems.

Acknowledgement

To the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), to the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), to the Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS), to the Universidade Regional do Noroeste do Estado do Rio Grande do Sul (UNIJUÍ) and the Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) for the contribution of funds for the development of this study and the Scientific and Technological Initiation scholarships, Technical Support, Postgraduate and Research Productivity.

Literature Cited

• Arenhardt, E. G.; Silva, J. A. G.; Gewehr, E.; Oliveira, A. C.; Binelo, M. O.; Valdiero, A. C.; Silva, J. A. G. The nitrogen supply in wheat cultivation dependent on weather conditions and succession system in southern Brazil. African Journal of Agricultural Research, v.10, p.4322-4330, 2015. https://doi.org/10.5897/AJAR2015.10038
  » https://doi.org/10.5897/AJAR2015.10038
• Barioni, L. G.; Albertini, T. Z.; Medeiros, S. R. Modelagem matemática do balanço de gases do efeito estufa na pecuária de corte. Revista Brasileira de Zootecnia, v.40, p.201-212, 2011.
• Bischoff, T. Z.; Simonetti, A. P. M. M.; Nuernberg, P. H. Influencia de las diferentes temperaturas eneldesarrollo de semillas de trigo. Revista de Ciencia y Tecnología, v.17, p.12-15, 2015.
• Camponogara, A. da S.; Oliveira, G. A.; Georgin, J.; Rosa, A. L. D. da. Avaliação dos componentes de rendimento do trigo quando submetido a diferentes fontes de nitrogênio. Revista Eletrônica em Gestão, Educação e Tecnologia Ambiental, v.2, p.524-532, 2016.
• Campos, A. T.; Castro, J. D. O.; Schiassi, L.; Yanagi Junior, T.; Pires, M. D. F. Á.; Mattioli, C. C. Prediction of free-stall occupancy rate in dairycattle barns through fuzzy sets. Engenharia Agrícola, v.33, p.1079-1089, 2013. https://doi.org/10.1590/S0100-69162013000600001
  » https://doi.org/10.1590/S0100-69162013000600001
• Castro, J. D. O.; Yanagi, J.; Schiassi, L.; Fassani, E. J.; Ferraz, P. F. P. Fuzzy model to predict feed intake of Japanese quails. Journal of Animal Behaviour and Biometeorology, v.7, p.18-24, 2019.
• Cecconello, M. S.; Silva, J. de D. M. de; Bassanezi R. C. Sistemas dinâmicos fuzzy: Modelagens alternativas para sistemas biológicos. 50.ed. São Carlos: Sociedade Brasileira de Matemática Aplicada, 2010. 120p.
• Costa, J. S. P.; Mantai, R. D.; Silva, J. A. G. da; Scremin, O. B.; Arenhardt, E. G.; Lima, A. R. C. de. Single and split nitrogen dose in wheat yield indicators. Revista Brasileira de Engenharia Agrícola e Ambiental, v.22, p.16-21, 2018. https://doi.org/10.1590/1807-1929/agriambi.v22n1p16-21
  » https://doi.org/10.1590/1807-1929/agriambi.v22n1p16-21
• Fernandes, D. A.; Araujo, M. M. V.; Camili, E. C. Crescimento de plântulas de maracujazeiro-amarelo sob diferentes lâminas de irrigação e uso de hidrogel. Revista de Agricultura, v.90, p.229-236, 2015.
• He, W.; Dong, Y. Adaptive fuzzy neural network control for a constrained robot using impedance learning. IEEE Transactions on Neural Networks and Learning Systems, v.29, p.1174-1186, 2018. https://doi.org/10.1109/TNNLS.2017.2665581
  » https://doi.org/10.1109/TNNLS.2017.2665581
• Kaewpirom, S.; Boonsang, S. Electrical response characterisation of poly (ethylene glycol) macromer (PEGM)/chitosan hydrogels in NaCl solution. European Polymer Journal, v.42, p.1609-1616, 2006. https://doi.org/10.1016/j.eurpolymj.2006.01.010
  » https://doi.org/10.1016/j.eurpolymj.2006.01.010
• Li, Y.; Tong, S.; Li, T. Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control directions and unknown dead zones. IEEE Transactions on Fuzzy Systems, v.23, p.1228-1241, 2015. https://doi.org/10.1109/TFUZZ.2014.2348017
  » https://doi.org/10.1109/TFUZZ.2014.2348017
• Marques, J. I.; Lopes Neto, J. P.; Lopes, F. F. M.; Furtado, D. A.; Araújo, T. G. P. Fuzzy modeling in the prediction of climate indices and productive performance of quails kept in climate chamber. Engenharia Agrícola, v.36, p.604-612, 2016. https://doi.org/10.1590/1809-4430-Eng.Agric.v36n4p604-612/2016
  » https://doi.org/10.1590/1809-4430-Eng.Agric.v36n4p604-612/2016
• Marolli, A.; Silva, J. A. G.; Sawicki, S.; Binelo, M. O.; Scremin, A. H.; Reginatto, D. C.; Dornelles, E. F.; Lambrecht, D. M. A simulação da biomassa de aveia por elementos climáticos, nitrogênio e regulador de crescimento. Arquivo Brasileiro de Medicina Veterinária e Zootecnia, v.70, p.535-544, 2018. https://doi.org/10.1590/1678-4162-9504
  » https://doi.org/10.1590/1678-4162-9504
• Mendel, J. M. Uncertainrule-basedfuzzy systems. 2.ed. Los Angeles: Springer, 2017. 675p.
• Minuzzi, R. B.; Lopes, F. Z. Desempenho agronômico do milho em diferentes cenários climáticos no Centro-Oeste do Brasil. Revista Brasileira de Engenharia Agrícola e Ambiental , v.19, p.734-740, 2015. https://doi.org/10.1590/1807-1929/agriambi.v19n8p734-740
  » https://doi.org/10.1590/1807-1929/agriambi.v19n8p734-740
• Ramos, F. S.; Souza, C. C.; Reis Neto, J. F.; Frainer, D. M. Practical tool in classification of animals for slaughter by fuzzy logic. African Journal of Agricultural Resarch, v.10, p.604-612, 2015. https://doi.org/10.5897/AJAR2014.9429
  » https://doi.org/10.5897/AJAR2014.9429
• Santi, A.; Vicari, M. B.; Pandolfo, C.; Dalmago, G. A.; Massignam, A. M.; Pasinato, A. Impacto de cenários futuros de clima no zoneamento agroclimático do trigo na região Sul do Brasil. Revista da Sociedade Brasileira de Agrometeorologia, v.25, p.303-311, 2018. https://doi.org/10.31062/agrom.v25i2.26167
  » https://doi.org/10.31062/agrom.v25i2.26167
• Schiassi, L.; Yanagi Júnior, T.; Reis, G. M.; Abreu, L. H.; Campos, A. T.; Castro, J. D. O. Modelagem Fuzzy aplicada na avaliação do desempenho de frangos de corte. Revista Brasileira de Engenharia Agrícola e Ambiental , v.19, p.140-146, 2015. https://doi.org/10.1590/1807-1929/agriambi.v19n2p140-146
  » https://doi.org/10.1590/1807-1929/agriambi.v19n2p140-146
• Scremin, O. B.; Silva, J. A. G.; Mamann, A. T. W.; Mantai, R. D.; Brezolin, A. P.; Marolli, A. Nitrogen efficiency in oat yield through the biopolymer hydrogel. Revista Brasileira de Engenharia Agrícola e Ambiental , v.21, p.379-385, 2017. https://doi.org/10.1590/1807-1929/agriambi.v21n6p379-385
  » https://doi.org/10.1590/1807-1929/agriambi.v21n6p379-385
• Silva, A. A.; Silva, I. A. F.; Teixeira Filho, M. C. M.; Buzetti, S.; Teixeira, M. C. M. Estimativa da produtividade de trigo em função da adubação nitrogenada utilizando modelagem neuro fuzzy. Revista Brasileira de Engenharia Agrícola e Ambiental , v.18, p.180-187, 2014. https://doi.org/10.1590/S1415-43662014000200008
  » https://doi.org/10.1590/S1415-43662014000200008
• Souza, J. L. M.; Gerstemberger, E.; Araujo, M. A. Calibração de modelos agrometeorológicos para estimar a produtividade da cultura do trigo, considerando sistemas de manejo do solo, em Ponta Grossa-PR. Revista Brasileira de Meteorologia, v.28, p.409-418, 2013. https://doi.org/10.1590/S0102-77862013000400007
  » https://doi.org/10.1590/S0102-77862013000400007
• Tedesco, M. J.; Gianello, C.; Bissani, C. A.; Bohnen, H.; Volkweiss, S. J. Análise de solo, plantas e outros materiais. 2.ed. Porto Alegre: UFRGS, 1995. 174p.
• Trautmann, A. P. B.; Silva, J. A. G.; Binelo, M. O.; Scremin, O. B.; Mamann, A. T. W.; Bandeira, L. M. Simulation of wheat biomass yield by thermal time, rainfall and nitrogen. Revista Brasileira de Engenharia Agrícola e Ambiental , v.21, p.763-768, 2017. https://doi.org/10.1590/1807-1929/agriambi.v21n11p763-768
  » https://doi.org/10.1590/1807-1929/agriambi.v21n11p763-768
• Tonin, R. F. B.; Lucca Filho, O. A.; Labbe, L. M. B.; Rossetto, M. Potencial fisiológico de sementes de milho híbrido tratadas com inseticidas e armazenadas em duas condições de ambiente. Scientia Agropecuaria, v.5, p.7-16, 2014. https://doi.org/10.17268/sci.agropecu.2014.01.01
  » https://doi.org/10.17268/sci.agropecu.2014.01.01
• Venturoli, F.; Venturoli, S. Recuperação florestal em uma área degradada pela exploração de areia no Distrito Federal. Ateliê Geográfico, v.5, p.183-195, 2011. https://doi.org/10.5216/ag.v5i1.13831
  » https://doi.org/10.5216/ag.v5i1.13831
• Wei, Y.; Qiu, J.; Karimi, H. R. Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults. IEEE Transactions on Circuits and Systems I: Regular Papers, v.64, p.170-181, 2017. https://doi.org/10.1109/TCSI.2016.2605685
  » https://doi.org/10.1109/TCSI.2016.2605685

Publication Dates

• Publication in this collection
  29 May 2020
• Date of issue
  May 2020

History

• Received
  18 Jan 2019
• Accepted
  04 Mar 2020
• Published
  30 Mar 2020