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

熵（一种不确定性的度量）的概念在管理科学、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标准决策模型的动机，这些模型具有从熵的度量中得到的客观权重。更广泛的熵测度类将与条件信息一起探讨。标准权重是一个不断调整的过程，决策者在决策分析中应同时考虑客观和主观权重。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。它不是指向一个单一的值，而是指向一组可能的值，每个值都有自己的成员值，范围在0到1之间。我将考虑这些库存模型中的各种参数是非线性模糊数。在应用程序方面，我计划在供应链管理中使用高阶可能性时刻。可能性矩生成函数（PMGF）为计算模糊数的高阶可能性矩提供了统一的方法。偏度和峰度可用于模型识别，并可作为供应链内模糊时间序列模型参数估计的输入。我也提出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未得到深入研究。在本研究项目中，基于所涉及的参数是模糊且不一定是线性的假设，将开发一个可能性辅助分数规划模型。利用可能性理论发展对偶理论，并将结果与其他研究人员已有的结果进行比较。在可能性设置模糊矩阵游戏也将探讨与应用在供应链管理。将得到的结果与现有的（清晰/模糊）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.