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的动机，考虑各种多标准决策模型的客观权重来自熵的措施。沿着条件信息将探讨更广泛的熵测度。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，其中模糊数是真实的数的扩展。它不是指一个单一的值，而是指一组连接的可能值，每个值都有自己的成员值，介于0和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。在应用方面，我计划在供应链管理中使用高阶可能性矩。可能性矩母函数（PMGF）提供了一种计算模糊数高阶可能性矩的统一方法。偏度和峰度可以在模型识别中是有用的，并且可以作为供应链内的模糊时间序列模型中的参数估计的输入。本文还推广了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在很大程度上是未知的。 在本研究项目中，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，不一定是线性的假设。对偶理论，使用可能性理论，将被开发，其结果将与其他研究人员开发的现有结果进行比较。模糊矩阵游戏在一个可能性的设置也将探讨沿着与供应链管理中的应用。这样得到的结果将与现有的（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.