基于AFS理论的管理方法及其应用研究
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摘要
预测与决策是管理科学中两大重要的组成部分。近年来,国内外的众多学者都在致力于这两类问题的研究,所研究出来的方法已经成功地应用到工程、经济、市场分析等实际领域。本文主要针对具有代表性的预测方法—时间序列分析和最常用的决策方法—多属性决策方法,应用Axiomatic Fuzzy Set (AFS)模糊理论对其进行分析和改进,主要做了如下几个方面的工作：
(1)首先应用经典的ARIMA乘积季节模型对上海港的集装箱吞吐量进行预测。然后,提出了一个基于AFS理论的模糊时间序列预测方法,该方法主要是根据AFS隶属度的模糊变化趋势来预测模糊时间序列：①应用AFS模糊隶属函数计算出历史数据在每个模糊集上的隶属度；②根据隶属度来划分论域并应用AFS模糊逻辑将原始数据模糊化从而建立模糊关系；③根据隶属度的模糊变化趋势对历史数据进行预测。
(2)首先提出了一个基于AFS理论的综合多属性决策方法：①应用DEA方法从初始的数据集中选择出一个最佳的组合；②应用AFS模糊描述算法和AHP方法计算出属性的权重值；③应用TOPSIS方法将最佳组合中的候选单元做出一个最终的排序；其次,应用AFS理论延伸TOPSIS方法在模糊环境下的使用,主要是应用AFS模糊隶属函数将含有语义变量或模糊概念的候选单元转化成其在该模糊概念下的隶属度值,然后应用TOPSIS方法对其隶属度进行运算。另外,这两种方法都根据AFS模糊描述给出决策结果一个明确的语义解释。
(3)设计了一个基于DEA和AFS聚类算法的网上银行绩效评价方法。首先通过DEA方法从所有的网上银行中删减掉一部分效率较低的；接下来再应用AFS聚类算法将剩余的银行进行聚类,并且给出每一类的语义描述。
最后,论文总结了全部的研究工作,并简要展望了今后的研究方向。
Forecasting and decision-making are the two important parts of management science. In recent years, they have been studied by many scholars. The developed methods have been successfully applied to the actual field of engineering, economic, and market analysis. This paper analyzes and improves the representative prediction method-time series analysis and the most commonly used method of decision-making-multi-attribute decision making method, by the application of Axiomatic Fuzzy Set (AFS) fuzzy theory. The main contributions are the followings.
(1) Firstly, a multiplicative seasonal model was established for container throughput of Shanghai Port. Secondly, proposing a fuzzy time series forecasting method based on AFS theory, which predict the fuzzy time series according to the fuzzy trend of AFS membership:(ⅰ) the AFS fuzzy membership function is applied to calculate each fuzzy set membership on the historical data to divide the domain;(ⅱ) fuzzified the raw data according to AFS fuzzy logic so as to establish the fuzzy relations;(ⅲ) forecasting the historical data according to the trend of fuzzy membership.
(2) Firstly, presenting a Integrated multi-attribute decision making method based on AFS theory:(ⅰ) selecting a best combination from the initial data set by the application of data envelopment analysis (DEA);(ⅱ) calculating the weight values of attributes by combining the AFS fuzzy description algorithm and Analytic Hierarchy Process (AHP);(ⅲ) applying the technique for order preference by similarity to ideal solution(TOPSIS) to make a final sort in the best combination. Secondly, applying AFS theory to extend TOPSIS method in fuzzy environment, which mainly transform the candidate unit contained the semantic variable or the vague concept into its membership value in the fuzzy concept by AFS fuzzy membership function and then carrying out the steps of TOPSIS method on its membership degree. This fuzzy method can deal with various types of data including semantic variables, fuzzy concept and Boolean data so that the application range of TOPSIS method has been greatly expanded. In addition, a clear semantic interpretation of the decision-making result was given according to the AFS fuzzy description.
(3) Designing a online banking performance evaluation method based by on the DEA and AFS clustering algorithm. First of all, deleting part of the less efficient banks from all the online banking through the DEA method; next, applying AFS clustering algorithm to cluster the remaining banks, and giving the semantic description of each category.
Finally, the thesis draws the conclusion on the researches and discusses about the further study.
(1)首先应用经典的ARIMA乘积季节模型对上海港的集装箱吞吐量进行预测。然后,提出了一个基于AFS理论的模糊时间序列预测方法,该方法主要是根据AFS隶属度的模糊变化趋势来预测模糊时间序列：①应用AFS模糊隶属函数计算出历史数据在每个模糊集上的隶属度；②根据隶属度来划分论域并应用AFS模糊逻辑将原始数据模糊化从而建立模糊关系；③根据隶属度的模糊变化趋势对历史数据进行预测。
(2)首先提出了一个基于AFS理论的综合多属性决策方法：①应用DEA方法从初始的数据集中选择出一个最佳的组合；②应用AFS模糊描述算法和AHP方法计算出属性的权重值；③应用TOPSIS方法将最佳组合中的候选单元做出一个最终的排序；其次,应用AFS理论延伸TOPSIS方法在模糊环境下的使用,主要是应用AFS模糊隶属函数将含有语义变量或模糊概念的候选单元转化成其在该模糊概念下的隶属度值,然后应用TOPSIS方法对其隶属度进行运算。另外,这两种方法都根据AFS模糊描述给出决策结果一个明确的语义解释。
(3)设计了一个基于DEA和AFS聚类算法的网上银行绩效评价方法。首先通过DEA方法从所有的网上银行中删减掉一部分效率较低的；接下来再应用AFS聚类算法将剩余的银行进行聚类,并且给出每一类的语义描述。
最后,论文总结了全部的研究工作,并简要展望了今后的研究方向。
Forecasting and decision-making are the two important parts of management science. In recent years, they have been studied by many scholars. The developed methods have been successfully applied to the actual field of engineering, economic, and market analysis. This paper analyzes and improves the representative prediction method-time series analysis and the most commonly used method of decision-making-multi-attribute decision making method, by the application of Axiomatic Fuzzy Set (AFS) fuzzy theory. The main contributions are the followings.
(1) Firstly, a multiplicative seasonal model was established for container throughput of Shanghai Port. Secondly, proposing a fuzzy time series forecasting method based on AFS theory, which predict the fuzzy time series according to the fuzzy trend of AFS membership:(ⅰ) the AFS fuzzy membership function is applied to calculate each fuzzy set membership on the historical data to divide the domain;(ⅱ) fuzzified the raw data according to AFS fuzzy logic so as to establish the fuzzy relations;(ⅲ) forecasting the historical data according to the trend of fuzzy membership.
(2) Firstly, presenting a Integrated multi-attribute decision making method based on AFS theory:(ⅰ) selecting a best combination from the initial data set by the application of data envelopment analysis (DEA);(ⅱ) calculating the weight values of attributes by combining the AFS fuzzy description algorithm and Analytic Hierarchy Process (AHP);(ⅲ) applying the technique for order preference by similarity to ideal solution(TOPSIS) to make a final sort in the best combination. Secondly, applying AFS theory to extend TOPSIS method in fuzzy environment, which mainly transform the candidate unit contained the semantic variable or the vague concept into its membership value in the fuzzy concept by AFS fuzzy membership function and then carrying out the steps of TOPSIS method on its membership degree. This fuzzy method can deal with various types of data including semantic variables, fuzzy concept and Boolean data so that the application range of TOPSIS method has been greatly expanded. In addition, a clear semantic interpretation of the decision-making result was given according to the AFS fuzzy description.
(3) Designing a online banking performance evaluation method based by on the DEA and AFS clustering algorithm. First of all, deleting part of the less efficient banks from all the online banking through the DEA method; next, applying AFS clustering algorithm to cluster the remaining banks, and giving the semantic description of each category.
Finally, the thesis draws the conclusion on the researches and discusses about the further study.
引文
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