Application of Rough Set Theory to Determine Weights of Soil Fertility Factor

【Objective】Soil fertility is controlled by many basic soil characters. Assessing soil fertility scientifically, rationally and practicably is of importance for guidance of agricultural production, land use planning and administration. Evaluation of soil fertility is a multiattribute decision-making process without decision attribute. The premise of multiattribute decision-making process is to determine attribute weights. 【Method】The methods to determine attribute weights mainly include subjective weighting method(SWM) and objective weighting method(OWM). However, the SWM usually requires massive prior knowledge, which is somewhat subjective and do not consider the dependency between evaluation indexes. The OWM has not fully considered the difference of each index's influence on evaluation. Meanwhile, even if statistical data have well correlations, it does not necessarily mean that the two variables have causation relationship. By considering the advantages and disadvantages of SWM and OWM, the concepts of reduction of knowledge and relative positive region in rough set theory were adopted in this study to explore the method for determination of indexes weights by combining subjective method with objective method in soil fertility evaluation and by testifying the evaluation results using crop yield data. 【Result】The determination of weight using rough set theory for soil fertility evaluation involve several steps: data discretization, preliminary determination of soil fertility grade, attribute value reduction, equivalence partitioning, attribute significance calculation, and index weights calculation. Taking soil fertility evaluation of farmland samples in Daxing district in Beijing City, China as an example, the weights of soil organic matter, total N, available P and available K determined by Delphi method were 0.300, 0.250, 0.250, and 0.200, respectively. There was a significant linear correlation between soil integrated fertility index(IFI) and crop yield. The determination coefficient R2 was 0.77 and root mean square error(RMSE) was 1.25. Using rough set theory, the determined weights of soil organic matter, total N, available P, and available K were 0.455, 0.111, 0.111, and 0.333, respectively. Again, a significant linear correlation between IFI and crop yield was observed. The later method has higher accuracy, as indicated by higher values of R2(0.83) and lower value of RMSE(1.06). 【Conclusion】Results of this study indicates that it is feasible to adopt rough set theory for determining the index weights of soil fertility, which provides a useful choice for evaluation of soil fertility and other related fields.