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

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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.