Application of possibility theory to supply chain management problems in fuzzy environments

熵的概念(不确定性的度量)在管理科学、供应链和市场营销中有着非常重要的应用。这给了我们作为研究人员考虑各种多准则决策模型的动机，这些决策模型的客观权重来自于熵的度量。我们将探索更广泛类别的熵度量以及条件信息。标准权重是不断调整过程的一部分，决策者在决策分析中应同时考虑客观权重和主观权重。我计划开发一些库存模型的模糊版本，其中模糊数是实数的扩展。它不是指一个单一的值，而是指一组相连的可能值，每个值都有自己的从属关系值在0到1之间。我将把这些库存模型中的各种参数视为非线性模糊数。在应用方面，我计划在供应链管理中使用更高阶的可能性时刻。可能性矩母函数(PMGF)为计算模糊数的高阶可能性矩提供了统一的方法。偏度和峰度在模型识别中是有用的，并且可以作为供应链模糊时间序列模型的参数估计的输入。我还建议推广模糊系数自回归模型的结果。这些模型可以用来研究供应链中的牛鞭效应。模糊加权系数自回归时间序列模型和广义自回归条件异方差模型在供应链管理中的应用尚不多见。在这个研究项目中，将开发一个可能性辅助分式规划模型，该模型基于所涉及的参数是模糊的且不一定是线性的假设。将利用可能性理论发展对偶性理论，并将结果与其他研究人员已有的结果进行比较。此外，还将探讨可能性设置下的模糊矩阵博弈及其在供应链管理中的应用。这样得到的结果将与已经存在的(CRISP/FUZZY)模型进行比较。

The concept of entropy (a measure of uncertainty) has had very important applications in management science, supply chain and marketing. This gives us as researchers the motivation to consider various multi-criteria decision making models with objective weights derived from measures of entropy. A wider class of entropy measures will be explored along with conditional information. Criteria weight is part of a continuously adjusting process and that decision makers should consider both objective and subjective weights in decision analysis. I plan to develop fuzzy versions of some inventory models, where a fuzzy number is an extension of a real number. It does not refer to one single value but rather to a connected set of possible values, each with its own membership value between 0 and 1. I will consider the various parameters in those inventory models to be non-linear fuzzy numbers. On the applications front, I plan to use higher order possibilistic moments in supply chain management. The possibilistic moment generating function (PMGF) provides a unified approach for computing higher order possibilistic moments of fuzzy numbers. Skewness and kurtosis can be useful in model identification and can serve as inputs for parameter estimation in fuzzy time series models within a supply chain. I also propose to extend results of the fuzzy coefficient autoregressive models. Those models can be used to study the bullwhip effect within a supply chain. The application of fuzzy weighted coefficient autoregressive time series models and generalized autoregressive conditional heteroskedasticity models in supply chain management is largely unexplored. In this research project, a possibility-assisted fractional programming model will be developed, based on the assumption that the parameters involved are fuzzy and not necessarily linear. Duality theory, using possibility theory, will be developed and the results will be compared with already existing results developed by other researchers. Fuzzy Matrix Games in a possibilistic setup will also be explored along with applications in supply chain management. A comparison of the results so obtained will be made with already existing (crisp/fuzzy) models.