Response of tomato yield-quality evaluated by fuzzy Borda combined model to irrigation and fertilization supply

Abstract: The combination evaluation method is widely used in many fields, while rarely in agriculture, especially in the management of water and fertilizer supply in tomato plants. This study was to establish a combined evaluation model of tomato yield-quality and to explore its response to water and fertilizer supply. Tomato were grown in greenhouse from Sep. 2014 to Jul. 2015 in Yangling, Shaanxi, China (108.07 °E, 34.26 °N). The experiment was designed based on a 5-D quadratic rotation combination with factors including irrigation amount, nitrogen fertilizer rate, phosphorus fertilizer rate, potassium fertilizer rate and manure rate, resulting in 32 treatments. Tomato yield and quality parameters, i.e. the content of soluble solid, soluble sugar, titratable acid, lycopene, vitamin C in tomato fruit and ratio of sugar to acid were determined. Tomato yield and quality were comprehensively evaluated by principle component analysis (PCA), grain regression analysis (GRDA), membership function analysis (MFA) and technique for order performance by similarity to ideal solution model based on portfolio weighting (TOPSIS-CW). After then, Kendall-W concordance coefficient pre-test was conducted, and 4 combined evaluating models for tomato yield-quality was established using the methods of Broda, Copeland, fuzzy Borda and combined evaluation method based on overall difference, respectively. Spearman level correlation coefficient test method was used to test the above 4 combined evaluating methods for post-test. The result showed that the rank of the comprehensive value for the experiment treatments was inconsistent among 4 single evaluation methods, and the standard deviations of the ranking values varied from 0 to 6.85. However, the correlation coefficient between the evaluation value of each single model and the other 3 varied from 0.605 to 0.812, indicating a certain correlation between the results of single models existed. Additionally, pre-test was passed with high Kendall-W concordance coefficient (0.916) showing the 4 methods were of compatibility. Post-test indicated that ranking values of the 4 combined evaluating models were in good correlation with that of the 4 single evaluation methods (with correlation coefficients 0.920-0.952), especially for fuzzy Broda combined evaluating model. Furthermore, mathematical model between tomato yield-quality comprehensive index and amount of irrigation and fertilization supply was established. The main effect of each factor and coupling effect of 2 factors were analyzed. By calculating the amplitude of the function, the importance of each factor to the comprehensive value was well illustrated. The influence of nitrogen fertilizer (evaluation value 155.90) on the comprehensive value was top-drawer, followed by irrigation (evaluation value 154.36), manure fertilizer (133.79), phosphorus (evaluation value 92.95) and potassium fertilizer (evaluation value 0). The comprehensive value changed as downwards parabola with the increased rate of irrigation, nitrogen, phosphorus or manure fertilizer, while was not affected by potassium fertilizer rate. Additionally, negative interaction between irrigation and manure fertilizer (with interaction coefficient -30.29), and positive interaction between nitrogen and phosphorus fertilizer (with interaction coefficient 32.70) were observed, showing evaluation value increased then decreased by the increased rate of manure fertilizer irrespective of irrigation amount, indicating excessive amount of irrigation was not beneficial to the enhancement of tomato yield-quality comprehensive value, but reasonable application of manure fertilizer, nitrogen and phosphorus fertilizer could promote the comprehensive yield and quality. In this study, tomato yield and quality were expected to be superior when the amount of irrigation, manure fertilizer, nitrogen, phosphorus and potassium fertilizer were 488.3-508.7 mm,19.3-21.8 t/hm2,498.4-565.6 kg/hm2,399.7-447.1 kg/hm2 and 698.1-777.9 kg/hm2, respectively. It is still a scientific problem to be worthy further studied to establish a proper evaluation model to assess and guide the management of water and fertilizer application in tomato production by selecting appropriate evaluation indices. The results from the combined evaluation model in this study provide novel knowledge for integrated assessment of water and fertilizer effect in tomato production