A Multi-Criteria Decision-Making Framework for Analysing River Water Pollution Using Generalised L-R Intuitionistic Fuzzy VIKOR

Abstract

Effective decision-making under uncertainty is a critical challenge in multi-criteria decision-making problems, particularly when dealing with ambiguity, vagueness, inconsistency, and imprecise data. This study proposes a novel mathematical framework based on generalised trapezoidal L-R intuitionistic fuzzy numbers (GTrLRIFNs) integrated with the VIKOR method to address uncertainty in decision-making. The proposed generalised trapezoidal L-R intuitionistic fuzzy VIKOR (GTrLRIF VIKOR) method extends traditional intuitionistic fuzzy numbers by incorporating non-linear left and right membership and non-membership functions, as well as confidence levels, to better capture human judgment in the evaluation of VIKOR method. A generalised aggregation operator, generalised trapezoidal L-R intuitionistic fuzzy weighted average (GTrLRIF-WA), is developed to facilitate the combination of uncertain criteria values, enhancing the model’s capability to process complex linguistic and numerical data. The proposed method of GTrLRIF VIKOR is applied to classify alternatives in a real-world case involving water quality assessment for five rivers in Johor, Malaysia, based on six evaluation parameters. The results demonstrate that GTrLRIF VIKOR produces consistent rankings with traditional methods which are Water Quality Index (WQI) method and Fuzzy Complex Index (FCI) method while offering a more robust representation of uncertainty. The proposed GTrLRIF VIKOR method addresses uncertainty by incorporating degrees of confidence, making it a more suitable, flexible, and realistic approach as it captures greater uncertainty compared to the traditional WQI method and FCI method.