粗糙集理论在土壤肥力评价指标权重确定中的应用

【目的】土壤肥力是土壤诸多基本特性的综合反映，科学、合理、实用地评价土地肥力将为指导农业生产、土地利用规划和管理提供理论依据。其评价过程是一个无决策属性的多属性决策过程，而解决多属性决策问题的重要前提是各属性权重分配问题。【方法】确定指标权重的方法主要有主观赋权法和客观赋权法，然而，主观赋权法往往需要大量的先验知识，评价结果有一定的主观随意性，而且较少考虑评价指标之间的依赖关系；客观赋权法没有充分考虑到各参评因素对评价的重要度不同，统计数据有相关性也并不意味着两个事件具有因果联系。综合考虑主、客观赋权法各自的优缺点，利用粗糙集理论中知识约简和相对正域理论在消除冗余信息和处理不确定性信息等方面的优势，探究土壤肥力评价过程中一种主观和客观相结合的权重确定方法，并利用作物产量对评价结果进行验证。【结果】粗糙集理论在土壤肥力评价中的具体赋权思路包括：数据的离散化、土壤肥力综合等级的初步确定、属性值约简、等价类划分、属性重要度的计算和指标权重计算等步骤。以北京大兴区农田土壤样点的肥力评价对上述赋权思路进行实例分析，对比传统特尔斐法和粗糙集理论赋权结果发现，特尔斐法确定的土壤有机质、全氮、有效磷和速效钾等指标的权重分别为0.300、0.250、0.250和0.200，利用其评价得到的土壤综合肥力指数（IFI）与产量显著线性相关，R2为0.77，均方根误差（RMSE）为1.25；而粗糙集理论确定的土壤有机质、全氮、有效磷和速效钾等指标的权重依次为0.455、0.111、0.111和0.333，利用其评价得到的IFI与产量也显著线性相关，R2达0.83，RMSE为1.09，精度均较特尔斐法有了提高，其中RMSE相对精度提高值达12.80%。【结论】粗糙集理论在土壤肥力评价中的具体赋权思路基本是可行的，且相对于特尔斐法其确定出各指标权重更为合理、准确，可为土壤肥力评价及相关领域的评价提供一个有益的思路。

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.