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This thesis presents a detailed study about one of the Multiple Criteria Decision Making (MCDM) models, namely Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), based on fuzzy set theory (FST) by focusing on improving modelling uncertain information provided by a group of decision makers (DMs). An exploration of issues and limitations in current models of standard TOPSIS and fuzzy TOPSIS were made. Despite many variations of type-1 fuzzy TOPSIS (T1-TOPSIS) model, none of the studies explaining the details of the key stages of standard TOPSIS (non-fuzzy) and T1-TOPSIS are based on a step-wise procedure. A detailed study was conducted which involve the process of identifying the limitations of standard TOPSIS and T1-TOPSIS. Based on this, a novel contribution on the comparison between these two models in systematic stepwise procedure was given. This study successfully identified and discussed the limitations, issues and challenges which have not been investigated sufficiently in the context of T1-TOPSIS model. Based on this exploration, further investigation of multiple variants of the extension of the fuzzy TOPSIS model for solving the MCDM problem was made with the primary aim of detailing the steps involved. One challenge that has risen is that it is not straightforward to differentiate between the multiple variants of TOPSIS existing today. A systematic comparison was made between standard T1-TOPSIS model with the recently extended model to show the differences between both models and to provide context for their respective strengths and limitations both in the complexity of application and expressiveness of results. Based on the resulting comparison, the differences in the steps implemented by these two Fuzzy TOPSIS models were highlighted throughout the worked example. Furthermore, this task highlights the ability of both models to handle different levels of uncertainty. Following the exploration of issues and limitations of the current model, as well as a comparative study, a novel extension of type-2 fuzzy TOPSIS model is proposed in this thesis which suggests providing an interval-valued output to reflect the uncertainties and to model subjective information. The proposed model enables to uniquely captures input uncertainty (i.e., decision-makers' preferences) in the decision-making outputs and provide a direct mapping of uncertainty in the inputs to outputs. By keeping the output values in interval form, the proposed model reduces the loss of information and maximises the potential benefit of using Interval Type-2 Fuzzy Sets (IT2 FSs). To demonstrate the MCDM problems when a various level of uncertainty is introduced, a novel experimental method was proposed in this study. The primary aim is to explore the use of IT2 FSs in handling uncertainty based on the TOPSIS model. This experiment was conducted to show how the variation of uncertainty levels in the input affects the final outputs. An implementation of the proposed model to two different case studies was conducted to evaluate the proposed model. The proposed model for the first time generates an interval-valued output. As intervals can, for example, exhibit partial overlap, a novel extended measure is proposed to compare the resulting interval-valued output from various cases (i.e., overlapping and non-overlapping) of the interval with considering uncertainty. |
