Synergistic Effects of Water, Fertilizer and Oxygen Regulation Based on Fuzzy Evaluation in Custard Apple Cultivation

Abstract

To explore the mechanisms by which water, fertilizers, and dissolved oxygen affect the physiological growth and yield quality of custard apple, this study aims to optimize water–fertilizer–oxygen coupling regulation schemes for custard apple in dry hot valley regions through a multi-level fuzzy evaluation method, thereby addressing issues such as soil compaction and reduced aeration caused by long-term water and fertilizer drip irrigation. The experiment was conducted on custard apple in a dry, hot valley area, employing orthogonal and quadratic regression-orthogonal designs. Three factors were set at multiple levels: irrigation amount (60–100% ETc), fertilization rate (1500–1900 kg·ha⁻¹), and dissolved oxygen concentration (6–10 mg·L⁻¹). Custard apple development, production, and attributes were assessed. The two-year trial from 2023 to 2024 demonstrated that the new shoots, leaf area, and net photosynthetic rate of plants treated with W3F2O1 (100% ETc, 1700 kg·ha⁻¹ fertilization rate, and high oxygen 6 mg·L⁻¹) and W3F3O2 (100% ETC, 1500 kg·ha⁻¹ fertilization rate, and high oxygen 8 mg·L⁻¹) were significantly superior to those of W1F1O1 (60% ETc, 1900 kg·ha⁻¹ fertilization rate, and high oxygen 6 mg·L⁻¹), with a single-plant yield of 10.31 kg, and increases in diameter and length of 31.6% and 27.6%, respectively (p < 0.05); quality indicators were also optimal under W3F3O2 (100% ETC, 1500 kg·ha⁻¹ fertilization rate, and high oxygen 8 mg·L⁻¹) treatment, with soluble sugar and vitamin C levels increasing by 17.3% and 29.9%, respectively, compared to the control. Using a multi-level fuzzy evaluation to comprehensively evaluate the water–fertilizer–oxygen coupling, the comprehensive productivity of custard apples was significantly improved by optimizing the root zone microenvironment. It is recommended that dry hot valleys adopt an optimized range of 82.5–100% ETc irrigation, 1650–1847.86 kg·ha⁻¹ fertilization, and 7.4–9.25 mg·L⁻¹ dissolved oxygen, providing a theoretical basis for precise irrigation and sustainable cultivation of tropical fruit trees.

1. Introduction

In recent years, extensive research domestically and internationally has demonstrated the efficacy of integrated water and fertilizer irrigation in promoting crop water conservation and yield increases [1,2], and it has been popularized and applied in farmland with good results [3]. However, long-term comprehensive drip irrigation systems can be prone to issues like soil compacting, acidifying, and resultant salinity spikes [4], which consequently reduce soil aeration and moisture flow, and cause soil nutrient imbalance. Therefore, apart from monitoring crop hydration and nutrient needs, soil aeration must also be taken into account.

Adequate soil aeration fundamentally ensures healthy plant growth. Enhancing the oxygen flow through the soil greatly boosts the oxygen permeability in a crop’s root zone. This, in turn, enhances the soil’s microclimate and the enzymatic activity within the root area, ensuring the vitality of soil microorganisms [5], and then can coordinate well with the relationship between the three factors of soil water, fertilizer, and oxygen. Research indicates that using aerated irrigation significantly enhances the oxygen-rich environment around plant roots, leading to an expansion in the fine root network and heightened root activity. This not only bolsters the plant’s physiological processes but also improves water utilization, ultimately driving plant growth and boosting yields [6]. Given the coupled effects of crop demand for water, nutrients, and oxygen, regulating any single factor alone is no longer sufficient to simultaneously achieve water conservation, nitrogen reduction, and high yields. The integration of ‘aerobic drip irrigation’ with ‘water–fertilizer integrated drip irrigation’, combined with micro-nano bubble technology to simultaneously oxygenate the root zone and precisely supply fertilizers as needed, can significantly reduce irrigation water and fertilizer application rates while enhancing crop productivity. This approach has emerged as a cutting-edge research direction in the field of water-saving irrigation.

The custard apple is one of the five most famous tropical fruits in the world, along with mangosteen, mango, lychee, and pineapple [7]. It thrives predominantly in tropical and subtropical zones. The custard apple is a relatively emerging high-end fruit in China, with high nutritional value and economic benefits [8]. It is grown in many areas of Yunnan. Among them, the planting area in Yuanjiang County has increased from 53.33 ha in 2002 to more than 400 ha in 2022, successfully making custard apples a local characteristic industry in Yuanjiang. However, seasonal drought is prominent in dry and hot valley areas, and the drip irrigation mode of film-mulching planting is often used, which can easily cause hypoxia in the root system of the crops. In addition, there are unreasonable irrigation and fertilization problems in the process of planting custard apples, resulting in the unguaranteed economic benefits of custard apples. It is worth noting that this phenomenon is not unique to custard apple; similar water and fertilizer management challenges are also common in the cultivation of other tropical crops such as mangoes and lychees. For example, mangoes are sensitive to water during the fruiting period, and excessive irrigation can lead to fruit cracking and root diseases, while insufficient irrigation can result in poor fruit development [9]; lychees, with their shallow root systems, are prone to flower and fruit drop when water and fertilizer supply is unbalanced [10]. Additionally, traditional flood irrigation methods not only waste water resources but also make it difficult to precisely regulate nutrient absorption efficiency. These common issues not only constrain the yield and quality of individual crops but also act as bottlenecks hindering the efficient production and sustainable development of the tropical crop industry as a whole. Therefore, exploring optimal combinations of water, fertilizer, and air in drip irrigation is not only a prerequisite for ensuring efficient production of custard apple in arid and hot regions but also provides a referenceable research direction for addressing common cultivation challenges in tropical crops such as mangoes and lychees.

Varying irrigation, nutrient, and oxygen input connections impact plant development, harvest size, and produce grade. Even under the same water, fertilizer, and oxygen conditions, the effects on these indicators are also quite different. The traditional evaluation method mainly adopts the comprehensive analysis method; that is, it evaluates and analyzes through the comparison of individual indicators and the causal relationship or correlation between indicators [11,12]. Due to the subjectivity of researchers, the evaluation results have a certain degree of uncertainty [13]. Therefore, a sound assessment framework, incorporating diverse metrics, is key to defining peak irrigation, fertilization, and aeration strategies. The multi-level fuzzy comprehensive assessment is a subset of fuzzy algorithms. It is a methodology integrating both qualitative and quantitative aspects, distinguishing between precision and imprecision. Through the fuzzy evaluation of indicators at all levels, a more comprehensive and accurate evaluation value is finally obtained. Because of its superiority in dealing with complex system problems, multi-level fuzzy comprehensive evaluation has achieved good application results in the optimization of crop irrigation and fertilization and the analysis of forestry industrial structure and economic benefits [14,15].

The objective of this study is to develop a scientific assessment framework for growth, photosynthesis, yield, quality, and other indicators of custard apples through the analysis of multiple indicators. Specifically, under the conditions of multi-level fuzzy evaluation of water–fertilizer–oxygen coupling in custard apple, we made two assumptions: (1) The response of soursop growth, yield, and quality to the ‘water–fertilizer–oxygen’ combination follows a parabolic relationship that first increases and then decreases; (2) There is a significant synergistic effect between irrigation volume, fertilizer application rate, and dissolved oxygen. The optimal water–fertilizer–oxygen combination (W3F3O2) derived from the multi-level fuzzy comprehensive evaluation model is beneficial for the comprehensive growth of custard apple. In order to offer a theoretical foundation for attaining efficient watering and fertilization, substantial production, and premium custard apple produce, simulation optimization was used to determine the optimal blend of water, fertilizer, and oxygen suitable for the dry hot valley region.

2. Materials and Methods

2.1. Overview of the Test Area

The experiment took place in a custard apple orchard aged four years between March 2023 and October 2024, located in Nansha Village, Lijiang Subdistrict, Yuanjiang Hani, Yi, and Dai Autonomous County, Yuxi City, Yunnan Province (102°5′51″ E, 23°30′22″ N), at an altitude of 550 m. This region is characterized by extensive year-round solar exposure, averaging 2291.7 h annually, and experiences a mean temperature of 23.8°C, and it belongs to a typical dry hot river valley climate. The annual average rainfall is 780 mm. The orchard soil type is primarily reddish-brown sandy loam. Prior to the experiment, the orchard had a bulk density of 1.36 g·cm³ and a slightly acidic pH of 6.4. Total soil nitrogen measured 1.16 g·kg⁻¹; available phosphorus, 29.85 mg·kg⁻¹; readily available potassium, 125.11mg·kg⁻¹; and organic matter, 12.35 g·kg⁻¹. In March 2023, four-year-old custard apple trees were selected as the study subjects, with a spacing of 3 m × 4 m between rows and plants.

2.2. Design of Experiment

The custard apple’s maturation spans four distinct phases: (1) bud differentiation (mid-March to early May); (2) bloom and fruit formation (early May to mid-June); (3) fruit growth (mid-June to mid-August); (4) ripening stages (mid-August to early October). To investigate the effects of irrigation, fertilizer, and dissolved oxygen on growth and yield, we employed an orthogonal design combined with a quadratic regression-orthogonal rotation approach. Specifically, the orthogonal design assigned three levels to each factor and adopted an L9(3⁴) orthogonal array. We employed three distinct irrigation strategies: a severely limited water supply (W1, at 60% of ETc), a slightly limited water supply (W2, at 80% of ETc), and a fully irrigated control group (W3, at 100% of ETc), ETc represents crop evapotranspiration, where ETc represents crop evapotranspiration. The irrigation method adopts drip irrigation. Before the implementation of the program, two strips of drip irrigation were installed across each area, with a distance of 10 cm from the custard apple tree, and each tree was surrounded by four drippers. The drip tape measures 16 mm in diameter, the distance between the drippers is 40 cm, and the flow rate of the drippers is 3 L·h⁻¹. Based on the water requirements of different growth stages of custard apple [16], watering was carried out 8 times during the flower bud differentiation period, 6 times during the flowering and fruit setting period, 10 times during the fruit enlargement period, and 7 times during the ripening period. In 2023, the irrigation volume at 60% ETc was 289.76 mm, at 68.1% ETc was 321.55 mm, and at 80% ETc was 381.11 mm. The 91.9% ETc irrigation volume was 432.65 mm, and 100% ETc irrigation volume was 475.67 mm; in 2024, the irrigation volume at 60% ETc was 334.52 mm, at 68.1% ETc was 369.53 mm, at 80% ETc was 410.92 mm, 91.9% ETc irrigation volume is 476.01 mm, and 100% ETc irrigation volume is 503.21 mm.

According to the water balance equation:

$$M={ET}_{ci}-P_0$$

(1)

$${ET}_C={ET}_0·K_c$$

(2)

Among these, M represents the irrigation volume within the t time period. ETci denotes the crop water requirement within the t time period, ET₀ is the annual average evapotranspiration rate of the reference crop in the Yuanjiang region, which is 3.8 mm·d⁻¹, P₀ is the effective precipitation retained within the planned moist layer of the soil, and Kc is the comprehensive crop coefficient. In this experiment, Kc was set to 0.5 during the flower bud differentiation stage, 0.9 during the flowering and fruit set stage, 1.2 during the fruit enlargement stage, and 0.8 during the maturity stage.

The fertilization treatments included high (1900 kg·ha⁻¹), medium (1700 kg·ha⁻¹), and low (1500 kg·ha⁻¹) application rates. The three dissolved oxygen levels were high oxygen (10 mg·L⁻¹), medium oxygen (8 mg·L⁻¹), and hypoxic (6 mg·L⁻¹). The middle level of fertilization amount was determined according to relevant literature and local fertilization amount [17]. The test fertilizer is a special compound fertilizer for fruit trees that is easily soluble in water (the mass ratio of N, P₂O₅, and K₂O is 15:15:15, Xuelvfeng, Saigute Biotechnology Co., Ltd., Wuhan, China), of which total nutrients were ≥45%, and no additional macronutrients (Ca, Mg, S) or micronutrients were applied during the experiment to maintain nutrient uniformity and isolate the effects of water–fertilizer–oxygen coupling treatments. Using micro-nano bubble technology, dissolved oxygen levels in irrigation water were measured in real time using a JPB-607A portable dissolved oxygen meter (Hangzhou Qiwei Instrument Co., Ltd., Hangzhou, China), with micro-nano bubbles generated by an NGB-50 micro-nano bubble generator (Shanghai Baoheng Environmental Protection Technology Co., Ltd., Shanghai, China) and an ACO-008 aeration pump (Zhejiang Sensen Co., Ltd., Wenzhou, China).

Other daily field managements were kept the same. On the basis of the orthogonal experiment scheme, the study was honed down to a trio of variables and a quintet of levels, utilizing a quadratic regression orthogonal rotation combination design. This was performed to pinpoint the ideal irrigation dosage, fertilizer usage, and dissolved oxygen levels for the growth, photosynthesis, yield, and quality of custard apples. Quadratic regression orthogonal rotation design with five distinct irrigation levels includes (60%ETc, 68.1%ETc, 80%ETc, 91.9%ETc, 100%ETc), and 5 different fertilization amounts (1500 kg·ha⁻¹, 1581 kg·ha⁻¹, 1700 kg·ha⁻¹, 1819 kg·ha⁻¹, 1900 kg·ha⁻¹) and 5 different dissolved oxygen (6 mg·L⁻¹, 6.8 mg·L⁻¹, 8 mg·L⁻¹, 9.2 mg·L⁻¹, 10 mg·L⁻¹) 23 combinations, which refer to the article by He et al. [18]. The test program was implemented in March 2023. After the implementation of the test plan, the irrigation, fertilization, and aeration of custard apples in each growth period were carried out in strict accordance with the test plan. Other field management measures are consistent. Manual weeding is carried out around each tree within a 1-m diameter range every month. During the fruit enlargement period, the tree crown is pruned, and 3–4 main branches are retained. After thinning the fruit, insecticide and fungicide are sprayed, and the bags are put on after the solution has dried. See

Table 1. Experimental design.

Treament	Factors
	Irrigation Amount (W) mm	Fertilizer Amount (F) kg·hm−2	Dissolved Oxygen (O) mg·L−1
W1F1O1	60%ETc	1500	6
W1F2O2	60%ETc	1700	8
W1F3O3	60%ETc	1900	10
W2F1O2	80%ETc	1500	8
W2F2O3	80%ETc	1700	10
W2F3O1	80%ETc	1900	6
W3F1O3	100%ETc	1500	10
W3F2O1	100%ETc	1700	6
W3F3O2	100%ETc	1900	8

and

Table 2. Design of three factors and five levels of water, fertilizer and oxygen in orthogonal rotation combination test.

Level	Independent Variable
	Irrigation Amount X1	Fertilizer Amount X2 (kg·hm−2)	Dissolved Oxygen X3 (mg·L−1)
+1.682	100%ETc	1900	10
+1	91.9%ETc	1819	9.2
0	80%ETc	1700	8
−1	68.1%ETc	1581	6.8
−1.682	60%ETc	1500	6

for test factors and level coding and the test plan.

2.3. Measurement Method

2.3.1. Growth Indicators

For each experimental treatment, 3 fruit trees were randomly selected, the foliage atop the primary stem of every custard apple tree was indicated, and the leaves measured at each growth stage were all marked. Foliage dimensions (length, width) of custard apple were gauged via tape at each developmental phase. The leaf area is calculated according to the regression model of the leaf product of the custard apple, and the formula is as follows:

$$\mathrm{y}=\mathrm{a}·\mathrm{x}$$

(3)

In the formula, x represents the leaf area of custard apple, calculated by multiplying length by width (cm²), and a is the regression coefficient, a = 0.73; the shoot length is measured with a tape measure, and the measurement range is from the bottom of the shoot to the top of the shoot. The measurement interval was 15 days, and the measurement was stopped until the length of the shoots of the custard apple did not change much.

2.3.2. Net Photosynthesis Index

Outdoor measurements were conducted during the period from 08:00 a.m. to 05:00 p.m. on mornings with few clouds between 2023 and 2024, with one-hour intervals. Net photosynthetic rates were measured using a portable infrared gas analyzer (IRGA; LI-6400XT, LI-COR, Lincoln, NE, USA). For each treatment, three representative custard apple trees were selected, and five fully expanded healthy leaves were chosen from each tree. Three sampling points were selected on each leaf, avoiding the main leaf veins, with a 120-s steady-state period followed by data recording. The leaf chamber CO₂ concentration was set to 400 μmol mol⁻¹, and the photosynthetically active radiation was 1200 μmol m⁻² s⁻¹. Each treatment group yielded 45 measurement samples, and the average net photosynthetic rate for each treatment group was calculated.

2.3.3. Yield Index

On 19 September 2023 and 22 September 2024, during the custard apple ripening period, three fruit trees were measured in each treatment group, with 10 fruits marked on each tree, for a total of 30 marked fruits. Harvesting was conducted when the fruit reached technical maturity, characterized by the fruit peel turning from dark green to light green and beginning to show slight cracking. The longitudinal and transverse diameters were measured with vernier calipers; the fruit’s individual mass was assessed using a scale, accurate to 0.01 g, with a maximum measurable mass of 1000 g; the yield of a single plant was recorded by harvesting in stages to record the fruit weight of a production period.

2.3.4. Quality Indicators

After harvest, the custard apple fruits are stored at room temperature (25 ± 2 °C) until they soften. Subsequently, the quality parameters of each sample are repeatedly measured: (1) Soluble solids are measured using a digital handheld refractometer; (2) soluble sugar content was determined using the anthrone colorimetric method [19]; (3) vitamin C content was measured using the 2,6-dichlorophenol pyridine titration method; (4) organic acid content was determined by titrating with 0.1 mol/L NaOH using phenolphthalein indicator until pH 8.2 [20].

2.4. Data Analysis and Processing

Data analysis and graph creation were executed through Microsoft Excel 2016 and IBM SPSS Statistics 22 software, and Duncan’s method was used for multiple comparisons (α = 0.05). We used Origin 2024 to draw, and used Design-Expert version 13 software to analyze the data of the orthogonal rotation test. We used Matlab R2018a to analyze the optimal value of the multi-level fuzzy comprehensive evaluation index of custard apple. Yaahp, 12.3 was used to carry out a hierarchical analysis of the 3 categories of custard apple indicators; the model was analyzed, and related charts were drawn.

Yaahp, 12.3 was used to carry out a hierarchical analysis of the 3 categories of custard apple indicators, the model was analyzed and related charts were drawn. In the figure, u1, u2, and u3 are yield indicators, growth indicators and quality indicators, respectively, and these four types of indicators are defined as the first layer of indicators: u11, u12, u13, and u14 are vertical diameter, transverse diameter, fruit weight per plant, yield per plant, u21, u22 and u23 are net photosynthetic rate, leaf area, and shoot length respectively, u31, u32, u33, u34 are vitamin C levels, total dissolved sugars, soluble dry extract, and organic acids, these 11 sub-indices are defined as level 2 indicators.

Based on the above-mentioned hierarchical analysis, a complete assessment framework using hierarchy is constructed, and the factor sets of each index and its sub-indices are shown in Formulas (4) and (5).

$$U=\{u_1,u_2,u_3\}$$

(4)

$$\left\{\begin{array}{c}{u}_1=\left\{u_{11},u_{12},u_{13},\left.u_{14}\right\}\right.\\ u_2=\left\{u_{21},u_{22}\right.,\left.u_{23}\right\}\\ u_3=\left\{u_{31},u_{32},u_{33},\left.u_{34}\right\}\right.\end{array}\right.$$

(5)

Through establishing the comprehensive evaluation hierarchy model, the individual factors and their corresponding subsets of sub-factors are formulated. Each indicator and its sub-indicators have their corresponding evaluation value sets, which are generally represented by V and v_ij. Because the experiment has 23 treatments, each has 23 evaluation values, and evaluation sets are shown in Formulas (6) and (7).

$$V=\{V_1,V_2,V_{23}\}$$

(6)

$${\mathrm{v}}_{\mathrm{i}\mathrm{j}}=\left\{{\mathrm{v}}_1,{\mathrm{v}}_2,{\mathrm{v}}_{23}\right\}$$

(7)

3. Results

3.1. Changes in Custard Apple Growth Indicators Under Different Treatments

Figure 1a shows the changes in the length of new shoots of custard apple under water–fertilizer–oxygen coupling treatment in 2023 and 2024. Under the same irrigation conditions, irrigation volume and fertilizers elevated the leaf area of custard apples, the enhancement correlating with the rise in irrigation levels. Overall, the new shoots of custard apples in 2024 were longer than those in 2023. In 2023 and 2024, new shoots reached their peak length (63.28 cm and 67.56 cm) under W3F2O1 treatment, which was appreciably elevated beyond W1F1O1 treatment by 35.74% and 36.46%, respectively. As shown in Figure 1b, under orthogonal experimental conditions, the average leaf area of custard apples in 2023 and 2024 showed a consistent trend throughout the entire growing season, with an overall upward trend as the treatment intensity increased. In both years, the largest leaf area was observed under the W3F2O1 treatment, with values of 100.55 cm² and 101.09 cm², respectively. Among these, no notable variation was observed between the W3F2O1 and W3F3O3 treatments in 2023. Over the two years, the leaf area was smallest at the W1 irrigation regime, with the W1 level significantly lower than the W3 level (p < 0.05). The mean values of W1 in 2023 and 2024 were 18.51% and 18.39% lower than the mean values of W3, respectively.

3.2. Daily Net Photosynthetic Rate of Custard Apple Leaves Under Different Treatments

The daily variation in the net photosynthetic rate of each treatment group of custard apple in the orthogonal experiment is shown in Figure 2. In 2023 and 2024, the net photosynthetic rate of the lower leaves showed a double-peak change, with a trend of fluctuating initially upward, then downward, followed by another upward shift, and ultimately a second downward trend as the water–fertilizer–oxygen coupling method was carried out. Two peaks appeared at 11:00 and 15:00, while the ‘midday rest’ phenomenon occurred at around 14:00. The maximum daily variation in net photosynthetic rate for custard apples occurred around 11:00 a.m., with peak ranges of (9.23–11.17 μmol·m⁻²·s⁻¹) and (8.18–12.38 μmol·m⁻²·s⁻¹) in 2023 and 2024, respectively. Under two years of W3F3O2 treatment, maximum photosynthetic efficiency occurred at 11:00 a.m. throughout the day, with a value of 1.17 μmol·m⁻²·s⁻¹ in 2023, and 12.38 μmol·m⁻²·s⁻¹ in 2024. In contrast, W1F1O1-treated custard apple exhibited the minimal net photosynthetic rate, at 8.87 μmol·m⁻²·s⁻¹ in 2023 and 9.43 μmol·m⁻²·s⁻¹ in 2024, while the net photosynthetic rates under the W3F3O2 treatment were 29.99% and 24.50% higher than those under the W1F1O1 treatment in the two years, respectively. During daylight hours, the average hourly photosynthetic rate of custard apple leaves was highest under the W3F3O2 treatment. The net photosynthetic rates for different treatments were as follows: W3F3O2 > W3F2O1 > W3F3O1 > W1F2O2 > W2F1O2 > W2F3O1 > W1F3O3 > W2F2O3 > W1F1O1.

3.3. Yield Indicators for Custard Apples Under Water, Fertilizer and Oxygen Treatment

Figure 3 depicts the impact of water–fertilizer–oxygen integration on alterations in the transverse and longitudinal diameters of custard apple fruits across 2023 and 2024. The data in the figure shows that the trends in the horizontal and vertical diameters of two-year-old custard apple trees are roughly similar. In 2024, the mean values of the horizontal and vertical diameters exceeded those of 2023 by 1.68% and 2.41%, respectively. Custard apple dimensions (2-year-old fruit) exhibited marked increases in transverse and longitudinal axes under the W3 treatment, significantly exceeding those of W1 and W2 treatments (p < 0.05). Among these, the transverse diameter of custard apple in 2023 and 2024 displayed an initial rise followed by a subsequent decline, followed by another increase and decrease under water–fertilizer–oxygen coupling treatments, reaching maximum values of 90.30 mm and 92.34 mm, respectively, under the W3F2O1 treatment, and were significantly higher than those of the W1F1O1 treatment group (p < 0.05). The maximum longitudinal diameter of the fruit (113.13 mm and 116.99 mm) in the W3F2O1 treatment was 31.58% and 27.59% higher than that in the W1F1O1 treatment (85.98 mm and 91.69 mm), respectively. The changes in custard apples yield indicators under different treatments in 2023 and 2024 are shown in

Table 3. Custard apple production indicators for 2023 and 2024. different letters indicate significant differences at the level of p < 0.05.

Treatment	2023		2024
	Yield per Plant (kg)	Single Fruit Weight (g)	Yield per Plant (kg)	Single Fruit Weight (g)
W1F1O1	9.10 ± 0.23 f	298.04 ± 3.63 d	8.68 ± 0.13 f	306.64 ± 3.63 d
W1F2O2	8.92 ± 0.16 ef	315.22 ± 4.08 c	9.01 ± 0.14 e	317.78 ± 4.00 c
W1F3O3	9.41 ± 0.13 cd	323.42 ± 4.45 c	9.46 ± 0.16 d	332.82 ± 4.23 c
W2F1O2	9.41 ± 0.19 cd	323.18 ± 5.65 c	9.59 ± 0.14 bcd	312.86 ± 5.16 d
W2F2O3	9.87 ± 0.12 b	323.13 ± 5.09 c	9.85 ± 0.19 bc	336.23 ± 4.97 c
W2F3O1	9.33 ± 0.18 de	341.52 ± 5.63 b	9.53 ± 0.15 d	330.72 ± 5.33 c
W3F1O3	9.64 ± 0.13 bc	343.96 ± 4.18 b	9.71 ± 0.17 cd	349.21 ± 4.66 b
W3F2O1	10.21 ± 0.13 a	356.99 ± 4.79 a	10.31 ± 0.20 a	359.47 ± 5.09 a
W3F3O2	9.66 ± 0.18 bc	346.97 ± 5.12 b	9.90 ± 0.15 b	353.12 ± 4.25 ab

. The data from the two years indicate that the W3F2O1 treatment achieved the best yield per custard apple tree, with 10.21 kg and 10.31 kg, respectively, followed by the W2F2O3 treatment, which also yielded a high yield per custard apple tree. Remarkably, in the W1F1O1 treatment, the single-plant yield of custard apples in 2024 decreased by 4.84% compared to 2023. The effects of the W1F3O3 and W2F1O2 treatments on single-plant yield in 2023 were similar. Compared to other treatments under W2, the single-plant yield of custard apple in both years was lower under the W2F3O1 treatment. Overall, the fruit average weight was notably greater under the W3 regimen compared to the W1 and W2 treatments, and there was a clear pattern of growth followed by a decline as the fertilizer and oxygen supply increased. However, it remained higher than the W1 treatment, with increases of 11.88% and 10.92% in 2023 and 2024, respectively. Among these, under the W2F1O2 treatment, the average fruit weight in 2023 was 3.30% lower than in 2024.

3.4. Changes in the Quality of Custard Apples Under Various Treatments

Figure 4 presents alterations to custard apple quality metrics in 2023 and 2024, corresponding to varied water–fertilizer–oxygen treatments. Figure data reveal consistent custard apple quality indicators across two years. The vitamin C content, soluble solids content, and soluble sugar content all increased with the application of fertilizers and oxygen in the W1, W2, and W3 treatments. The W3F3O2 treatment exhibited the highest vitamin C levels after two years, reaching 29.90 mg·100 g⁻¹ and 30.24 mg·100 g⁻¹. The W2F3O1 treatment also showed relatively high values. The vitamin C content of the fruit did not change significantly between the W3F3O2 and W2F3O1 treatments after two years. W3F2O1 and W3F3O2 showed comparable impacts on custard apple fruit soluble sugar levels during the 2023–2024 period, with W3F3O2 significantly increasing the soluble sugar content by 17.25% and 16.90% relative to the W1F1O1 treatment (p < 0.05). The soluble solid content was optimal under W3F3O2 treatment for two years, showing a significant increase relative to other treatments (p < 0.05). The soluble solid content was lowest under W2F1O2 treatment, which was 24.52% and 24.11% lower than that under W3F3O2 treatment. It is worth noting that the organic acid content of custard apple fruits was highest under the W1F1O1 treatment in 2023 and 2024, and highest under the W3F3O2 treatment, at 0.17% and 0.16%, respectively.

3.5. Response of Comprehensive Growth of Custard Apple to Water, Fertilizer, and Oxygen Coupling Based on Fuzzy Evaluation

Quadratic regression’s orthogonal rotation combination examination, the comparison matrix of factor layer, yield index, growth index, and quality index sub-indices, was established by analytical hierarchy process (AHP). The AHP-calculated weights for each index were ascertained, and the single index of the custard apple was given a weight by the entropy weight method. Employing the AHP and entropy weight methods, considering the individual index weights, the M(·, ⊕) operator is used for fuzzy comprehensive calculation [21]. For the specific calculation method and steps, the final comprehensive growth evaluation results of custard apple are shown in

Table 4. Multi-level fuzzy evaluation index and ranking.

Process	Irrigation Amount X1	Fertilizer Amount X2	Dissolved Oxygen X3	2023 Judging Index	2023 Judging Index Ranking	2024 Judging Index	2024 Judging Index Ranking
T1	1	1	1	0.0448	2	0.0512	12
T2	1	1	−1	0.045	3	0.051	13
T3	1	−1	1	0.0446	15	0.0502	14
T4	1	−1	−1	0.0322	13	0.0382	18
T5	−1	1	1	0.0285	19	0.0355	19
T6	−1	1	−1	0.0293	16	0.0353	20
T7	−1	−1	1	0.0278	23	0.0338	22
T8	−1	−1	−1	0.0248	21	0.0307	23
T9	−1.682	0	0	0.0365	22	0.0425	17
T10	1.682	0	0	0.0548	1	0.0597	1
T11	0	−1.682	0	0.0279	20	0.0339	21
T12	0	1.682	0	0.0454	4	0.0514	11
T13	0	0	−1.682	0.0402	17	0.0462	16
T14	0	0	1.682	0.0403	18	0.0473	15
T15	0	0	0	0.0513	8	0.0543	9
T16	0	0	0	0.0504	6	0.055	8
T17	0	0	0	0.047	12	0.0572	3
T18	0	0	0	0.0483	10	0.0564	5
T19	0	0	0	0.051	7	0.053	10
T20	0	0	0	0.049	14	0.0553	6
T21	0	0	0	0.0493	9	0.056	7
T22	0	0	0	0.0522	5	0.057	4
T23	0	0	0	0.049	11	0.0573	2

.

The quadratic polynomial fitting is carried out on the multi-level fuzzy evaluation index of the custard apple, and after removing the insignificant items, the regression model is obtained as

$$\begin{gathered} Y_1=0.04984+0.00637X_1+0.00349X_2+0.00107X_3-0.00262X_1^2-0.00580X_2^2-0.00453X_3^2 \\ +0.00097X_1{X}_2+0.00125X_1{X}_3-0.00205X_2{X}_3, R^2={0.9058}^{\ast } \end{gathered}$$

(8)

$$\begin{gathered} Y_2=0.0557+0.0062X_1+0.0036X_2+0.0013X_3-0.0027X_1^2-0.0057X_2^2-0.0043X_3^2+0.0009X_1 \\ {X}_2+0.0011X_1{X}_3-0.0018X_2{X}_3, R^2={0.9088}^{\ast } \end{gathered}$$

(9)

To eliminate the impact of interannual differences on the applicability of the model, a generalized equation was constructed using the mean integration method based on the parameter characteristics of the two independent regression models. By taking the mean of the coefficients of the linear terms, quadratic terms, and interaction terms of each variable in the two-year model, the generalized equation is obtained as follows:

$$\begin{gathered} Y=0.0528+0.00629X_1+0.00355X_2+0.00119X_3-0.00266X_1^2-0.00575X_2^2-0.00442X_3^2+0.00094X_1{X}_2 \\ +0.00118X_1{X}_3-0.00193X_2{X}_3,R^2={0.9073}^{\ast } \end{gathered}$$

(10)

The independent models for 2023 and 2024 both showed high degrees of fit, with consistent trends in the indicators, and the equations provided a good explanation of the data for both years. In the formula, the indices in 2023 and 2024 are represented by Y1 and Y2, respectively. Y is the generalized equation evaluation index fitted for two years. * Means p < 0.05, indicating that the fitting effect is good.

3.5.1. Effect of a Single Factor on the Comprehensive Growth of Custard Apple

Dimension reduction and element elimination were performed on the two-year comprehensive generalized regression model, and each factor is defined within its coding range, and the rest of the elements are at an intermediate level, which can eliminate the influence of other elements on the analysis elements [22]. Figure 5 illustrates that as irrigation levels, fertilization levels, and dissolved oxygen levels rise, the images all present a downward parabola; that is, they exhibit an initial rise followed by a decline. Too high or too low will affect the comprehensive growth unfavorably. There is a reasonable range for the amount of irrigation water, fertilization, and dissolved oxygen, and they will become negative effects after reaching the optimum value.

3.5.2. The Influence of the Interaction of Two Factors on the Comprehensive Growth of Custard Apple

Dimensionality reduction and element elimination are performed on Formula (10), so that X3, X2, and X1 are at 0 levels, respectively. From Figure 6a, it can be seen that when X3 is at 0 levels, the judgment index of the custard apple increases as irrigation and fertilization levels escalate within a specified area. When the evaluation index is higher, the amount of irrigation needs a higher level, and the amount of fertilization needs a medium level, which shows that there is mutual inhibition between the two on the growth of custard apple. It can be seen from Figure 6b that when X2 is at the level of 0, within a certain range, the evaluation index of custard apple increases with escalating irrigation volumes, and depicts an upward followed by a downward trend as dissolved oxygen levels rise. When the judgment index is in the optimal range, the irrigation amount needs to be at a high level, while the dissolved oxygen amount needs to be at a medium level, so there is a negative interaction between the two within a certain range, and there is mutual inhibition. An observation of Figure 6c reveals that the multilevel fuzzy rating of the custard apple elevates in correspondence with ascending levels of fertilization, at the null setting for X1, and shows a pattern of initially rising and subsequently falling in correlation with the rise in dissolved oxygen levels. When the fuzzy judgment index is in the optimal range, the amount of fertilization needs to be at a high level, and the amount of dissolved oxygen needs to be at a medium level, indicating that there is also a negative interaction between the two within a certain range, and there is mutual inhibition.

3.5.3. Multi-Level Fuzzy Evaluation-Based Analysis of Optimal Water, Fertilizer, and Oxygen Factors for Custard Apples Growth

Matlab R2018a software was used to solve the optimal value of Formulas (6) and (7) in a fixed interval. When the multi-level fuzzy comprehensive evaluation index of custard apple in 2023 reaches a maximum of 0.0549, X1 is 1.3391, X2 is 0.3993, and X3 is 0.1605; that is, the amount of irrigation water is 96.64% ETc, the amount of fertilization is 1747.48 kg·ha⁻¹, and the dissolved oxygen level of 8.19 mg·L⁻¹. When the multi-level fuzzy comprehensive evaluation index of custard apple is 0.0604 at the maximum in 2024, X1 is 1.2634, and X2 is 0.3992, X3 is 0.1895; that is, the irrigation amount is 95.02% ETc, the fertilization amount is 1747.47 kg·ha⁻¹, and the dissolved oxygen amount is 8.23 mg·L⁻¹. The 2-year calculation of the comprehensive evaluation index is set to a confidence interval of more than 90% and coincides with the area. When the comprehensive evaluation index does not show a downward trend from the optimal combination corresponding to the best evaluation index model in Figure 6, it can be concluded that when given the peak value among hierarchical fuzzy assessment indicators, the corresponding optimal coding value intervals are as follows: water irrigation amount 0.21–1.682, fertilization amount 0.61–1.43, dissolved oxygen amount 0.94–0.66; that is, when the irrigation amount is 82.5–100%ETc, the fertilization rate is 1650.73 kg·ha⁻¹–1847.86 kg·ha⁻¹ and the dissolved oxygen is 7.4 mg·L⁻¹–9.25 mg·L⁻¹, the multi-level fuzzy evaluation index of custard apple has an optimal value interval, and this time is most conducive to the comprehensive growth of custard apple.

4. Discussion

The dry and hot river valley region suffers from seasonal drought and water shortages. Irrigation and fertilization during the cultivation process are unreasonable, severely restricting the efficient production of custard apples in this region. The healthy growth of this crop requires not only suitable water and fertilizer conditions but also a balance between soil water, fertilizer, and oxygen conditions [23]. Leaf area and new shoot length can reflect the nutritional and growth status of custard apple plants. This research reveals that as irrigation water volume increases, the leaf area and new shoot length of custard apple plants show a gradual increasing trend. Combining research data with physiological mechanisms indicates that under W3F2O1 treatment (100% ETc irrigation, 1700 kg·ha⁻¹ fertilization, 6 mg·L⁻¹ dissolved oxygen), the leaf area and new shoot length of the custard apple tree reached their peak. Within the given soil irrigation range (60%Etc–100%ETc), increasing the irrigation amount increases the absorption rate of elements such as N and K by the root system of the custard apple, as well as the leaf area and new shoot length, which is consistent with the pattern reported by Bhattacharya [24] under water stress. However, excessive irrigation often leads to the leaching of more nutrients needed for plant growth. When the water content rises to saturation, all the pores in the soil are filled with water, which causes oxygen deficiency in crop roots, restricting water and nutrient uptake in agricultural crops, and ultimately inhibiting plant growth. In aerated irrigation, the persistent generation of micro- and nano-bubbles within the water supplies oxygen to the soil, sustaining an optimal oxygen-rich environment for the crop’s root zone [25]. Findings show considerable influence of aerated irrigation on plant development. Root hypoxia causes a surge in plant growth hormones, leading to the closure of stomata in crop leaves and a reduction in ATP. Micro- and nano-aeration promote aerobic respiration in the root system, increasing ATP production, which helps the root system of the custard apple absorb soil moisture and nutrients, providing energy for cell division and elongation, and promoting an increase in leaf area and new shoot growth [26]. In addition, in this study, as irrigation volume and oxygenation levels increased, the leaf area of the custard apple significantly expanded, enhancing light energy capture and thereby increasing the peak net photosynthetic rate. This provided more assimilates for dry matter accumulation, directly promoting fruit enlargement and new shoot growth [27]. The significant change in net photosynthetic rate with increasing water oxygen concentration can be used as a quantitative indicator of the sensitivity of custard apple to changes in the water oxygen environment. A higher rate indicates stronger light energy capture and utilization capabilities, a more rapid response to environmental improvements, and stronger adaptability. By improving soil moisture, fertilizer, and oxygen conditions, the photosynthetic capacity of crop leaves can be enhanced, thereby affecting crop yield and quality [28]. This study indicates that the diurnal variation in the net photosynthetic rate of custard apple leaves exhibits a bimodal pattern. Throughout the entire growth cycle, the net photosynthetic rate of custard apple exhibits an overall trend of initial increase, followed by a decrease, another increase, and finally a reduction. Under conditions of adequate irrigation, high fertilization, and moderate oxygen levels, the net photosynthetic rate of custard apple leaves is relatively high. Among these, the peak net photosynthetic rate of the W3F3O2 treatment is significantly higher than that of the W1F1O1 combination (p < 0.05). This is because under low irrigation conditions, crop leaves reduce water transpiration losses by closing their stomata, while also reducing their absorption of light energy, thereby inhibiting photosynthesis and thus suffering significant negative effects [29]; under high irrigation conditions, a moderate oxygen environment inhibits leaf photorespiration, reducing energy loss and providing sufficient energy for carbon assimilation [30].

Pursuing high yields and high quality is an important goal of agricultural production. Soil moisture, nutrient content, and aeration within the plant root zone collectively influence how effectively crops absorb and employ these elements, thereby significantly impacting yield and crop quality [31]. This study found that the transverse and longitudinal diameters of custard apples were inversely proportional to fertilization levels and dissolved oxygen levels under the same irrigation conditions. Under W3F2O1 treatment, the transverse and longitudinal diameters of the fruit reached their maximum values. This is because adequate irrigation maintains cell turgor pressure, promotes cell wall relaxation, and increases cell volume [24]; under low fertilization conditions, nitrogen limitation inhibits protein synthesis, while photosynthetic products are prioritized for transport to the fruit, thereby amplifying transverse and longitudinal elongation [32]; under adequate irrigation, although dissolved oxygen levels are relatively low, they can moderately inhibit root respiration, reducing energy and nutrient consumption by root growth and preventing fruit growth from being inhibited due to insufficient nutrient supply [33]. The yield indicators for custard apples were highest under the W3F2O1 treatment, and the diameter, length, single fruit weight, and single plant yield of custard apples were directly proportional to the amount of irrigation, highlighting the beneficial impact of irrigation on custard apple crop productivity. However, as the amount of fertilizer increases, custard apple yield indicators demonstrate an upward slope followed by a downward trend. This is because excessive fertilization promotes excessive nutrient growth in crops, reduces photosynthetic activity, hinders the redistribution of photosynthetic products in crops, and consequently results in a reduction in productivity [34]. Findings indicate that enhancing the dissolved oxygen levels in irrigation water elevates the production of custard apples. The main reason for this is that aeration treatment improves the aerobic environment in the crop root zone, which promotes crop root respiration and improves the uptake of water and nutrients by the plant roots [35]. In addition, the research also revealed that the levels of vitamin C, soluble sugars, and solutes in custard apple fruits are inversely proportional to the amount of fertilizer applied, increase initially and then decrease with irrigation, and decrease initially and then increase with dissolved oxygen concentration. Under W3F3O2 treatment, all quality indicators of custard apple showed the best results. Moderate drought stress can suppress crop transpiration, promote the transfer of photosynthetic products to soluble sugars, and increase the accumulation of soluble sugars in custard apples [36]. Excessive moisture, on the other hand, dilutes the nutrients in custard apple fruits, thereby reducing vitamin C content and fruit quality [37]. Of significance is that the organic acid composition found in custard apple drupes is low under low-fertility conditions, and decreases first and then increases with increasing irrigation gradients. Under appropriate deficit irrigation, cells swell, producing a dilution effect, while when N is limiting, photosynthates are channeled mainly into soluble sugars. Low fertilization reduces the supply of organic acids to the fruit, resulting in lower organic acid content in custard apples [38,39]. Crop yield and quality are often inversely related, with quality decreasing to varying degrees as yield increases [40], and this aligns with the findings of the current research. In this study, the F2 treatment with higher fertilization rates yielded higher yields, but the F3 treatment produced apples of higher quality. The indicators were higher than those of the F2 treatment. Therefore, moderate increases in fertilization rates can improve the quality of custard apples.

The comprehensive adjustment measures of soil water, fertilizer, and oxygen adopted in this paper have positive effects on cultivation, photosynthetic activity, output, and attributes of custard apple. The main reason is that the three factors of water, fertilizer, and oxygen promote and influence each other. The trifecta of water, fertilizer, and oxygen works to align water and nutrients in an organic fashion. This synergy boosts the efficiency of water and nutrient uptake by the crops, while simultaneously improving soil aeration and enriching the oxygen levels in the root zone of custard apples [41]. It promotes root respiration and regulates the activity of crop roots, so that it can coordinate with the relationship between the three factors of water, fertilizer and oxygen, ensure standard crop growth, enhance productivity, and boost quality [42]. The organic whole of synergy should be paid attention to in future research. It is worth noting that this integrated regulatory approach also has high applicability for other tropical fruit crops, such as mangoes and lychees. From a biological perspective, mango roots are fleshy, fibrous roots that are highly sensitive to soil aeration. If they are exposed to waterlogged or oxygen-deprived conditions for extended periods, root rot may occur. The synergistic regulation of water, fertilizer, and air can precisely control irrigation volume and frequency, combined with an aerated fertilization strategy, to prevent root oxygen deprivation while enhancing nutrient absorption efficiency, thereby aligning well with mango’s concentrated demand for water and potassium during the fruit enlargement stage [43,44]. Lychees, on the other hand, exhibit strong responses to water stress during the flowering and fruiting stages. Traditional irrigation methods often cause flower and fruit drop due to sudden fluctuations in water supply [10]. The proposed regulatory measures can dynamically balance soil moisture and aeration to create a stable root zone environment for lychees with shallow root systems. Combined with a demand-based fertilization model, this approach can mitigate quality degradation issues caused by nutrient imbalances in lychees. Additionally, both mangoes and lychees are tropical evergreen fruit trees, and their requirements for water, nutrients, and air exhibit phased changes throughout their annual growth cycle. This common characteristic aligns closely with the dynamic regulation logic established in this study, providing a theoretical foundation and practical potential for the cross-crop application of this method.

At present, most evaluation methods use subjective evaluation, objective evaluation, or subjective and objective comprehensive evaluation methods to evaluate a certain class of crop indicators, and few use multiple methods to comprehensively evaluate the coupling scheme of water, fertilizer and oxygen of crops from multiple perspectives. In order to comprehensively analyze all kinds of indices, the study employs a multi-tiered fuzzy assessment technique for an integrated appraisal of the 11 sub-indices related to the three main indices of custard apple. The fuzzy evaluation is stratified, and the AHP and entropy-based techniques are amalgamated for the modeling and computation of diverse indices. Utilizing the multi-level fuzzy evaluation approach, it was observed that the comprehensive assessment index experienced a rise followed by a decline as the amount of fertilizer was augmented, aligning with the findings of Cai [45]. In custard apples, results suggested a symbiotic benefit to plant development from proxygene water, fertilizer, and oxygen application within the oxygen range optimized for abundant hydration and nutrition. The amount of irrigation water, fertilization, and dissolved oxygen obtained through comprehensive evaluation are respective; that is, when the amount of irrigation water is 82.5–100%ETc, the amount of fertilizer is 1650.73 kg·ha⁻¹–1847.86 kg·ha⁻¹. When the amount of dissolved oxygen is 7.4 mg·L⁻¹–9.25 mg·L⁻¹, the multi-level fuzzy evaluation index of custard apple has an optimal value range; that is, the growth index, photosynthetic index, yield index and quality index of custard apple can reach the optimum.

The comprehensive growth of custard apples is affected by different combinations of water, fertilizer, and oxygen factors. Different water, fertilizer, and oxygen couplings will affect different indicators in the comprehensive growth, and then affect the final multi-level fuzzy evaluation index, which is obtained in the simulation optimization of the final evaluation model. The conclusion is not the same as that of predecessors. One possible explanation is that these predecessors have seldom conducted comprehensive research on multiple indicators. On the other hand, it may also be related to the influence of external factors, such as cultivation facilities and climate. Therefore, further research is needed in the evaluation of various indices in the future. However, this study has certain limitations in data collection. The experimental data are solely derived from observations conducted over the 2023–2024 period in a single orchard located in the dry hot river valley region of Yuanjiang, Yunnan Province. The soil type is red-brown sandy loam, with an annual average temperature of 23.8 °C and annual precipitation of 780 mm, which may limit the general applicability of the conclusions. Furthermore, while measurements of shoot length and leaf area were taken on a 15-day cycle, covering the main growth period, this approach may not adequately capture the immediate effects of short-term extreme weather conditions on crop growth. Therefore, further research is needed to evaluate various indicators, particularly by expanding the experimental area, optimizing data collection frequency, and refining detection methods to enhance the reliability and generalizability of research conclusions. In the future, we will expand the trial to diverse soil and climate zones, shorten the indicator measurement cycle to capture the impact of extreme weather, and use high-precision detection technology to optimize data. We will explore low-cost micro-nano aeration equipment to address the energy consumption issues associated with current dissolved oxygen regulation, thereby supporting the sustainable development of custard apple cultivation.

5. Conclusions

The three factors of water, fertilizer and oxygen have significant differences in the growth, yield and quality indicators of custard apples. Using the multi-tier fuzzy assessment technique, a regulatory framework for the intertwined influence of water, nutrient, and oxygen factors on the holistic advancement of custard apple has been formulated. It was found that under the single factor analysis, the comprehensive growth of custard apple and the amount of fertilizer, fertilizer amount, and dissolved oxygen showed a parabolic relationship with an opening downward trend. There was an inhibitory effect between irrigation amount and fertilization amount, irrigation amount and dissolved oxygen amount, and fertilization amount and dissolved oxygen amount. For different multi-factor combination models, X1, X2, and X3 are 1.3391, 0.3993, and 0.1605, which are more conducive to the comprehensive growth of custard apple; the optimal interval is as follows: irrigation amount is 82.5–100% ETc, fertilizer amount is 1650.73 kg·ha⁻¹–1847.86 kg·ha⁻¹, and dissolved oxygen is 7.4 mg·L⁻¹–9.25 mg·L⁻¹, providing a sustainable strategy for tropical fruit cultivation in arid regions. Guiding the precise water and fertilizer management of custard apple and promoting the efficient and sustainable development of the tropical crop industry after adjusting parameters for mangoes and lychees is of great significance.