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The identification of phosphorus (P) fractions is essential for understanding the transformation and availability of P in paddy soils. To investigate the soil P fractions associated with soil properties under long-term fertilization, we selected three fertilization treatments, including no fertilization (CK), chemical fertilizers (NPK) and chemical fertilizers combined with manure (NPKM), from three long-term experiments located in Nanchang (NC), Jinxian (JX) and Ningxiang (NX). The results showed that chemical fertilizers combined with manure (NPKM) significantly ( P ≤ 0.05) increased the soil total phosphorus, Olsen P and soil organic matter (SOM) by 2, 3 and 1 times, respectively, compared with the NPK treatment, and by 4, 17 and 2 times, respectively, compared with the CK treatment. NPKM significantly increased the grain yield compared with CK and NPK at all sites. The apparent P balance with NPK was higher in NC and NX but lower in JX compared with NPKM. Hedley fractionation revealed the predominance of most of the organic and inorganic phosphorus (Po and Pi) fractions with long-term fertilization, especially with the NPKM treatment, at all sites. The nonlabile P pool decreased by 14% and 18% whereas the moderately labile P pool proportions increased by 3 and 6 times with the NPK and NPKM treatments, respectively, compared to the CK treatment. The labile P pool showed a significant positive relationship with the SOM, total P and Olsen P contents. The moderately labile P was positively correlated with the total P and Olsen P. A significant positive correlation was observed between soil pH and the nonlabile P pool. Redundancy analysis revealed that the moderately labile P fraction (HCl dil. Pi fraction) was remarkably increased by the NPKM treatment and significantly correlated with the soil pH and total P concentration. The labile P fraction (NaHCO 3 -Pi) showed a strong relationship with the Olsen P and total P. However, the residual P fraction was negatively correlated with the HCl. dil. Pi fraction. We concluded that NPKM application improved P availability by many folds compared to NPK, which could lead to environmental pollution; therefore, the rate of combined application of manure and chemical fertilizer should be reduced compared to chemical fertilizer inputs to minimize the wastage of resources and environmental P losses.

AbstractIn this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.