A framework of Trapezoidal Fuzzy Best-Worst Method in Location Selection for Surface Water Treatment Plant

Document Type : Original Research Paper


1 Department of Mathematics, National Institute of Technology Agartala, Tripura-799046, India

2 Department of Textile Technology, Indian Institute of Technology Delhi, New Delhi, India


Decision-making under uncertainty refers to a dilemma when a decision-maker is aware of a variety of potential natural states but lacks adequate information to assign any probabilities of occurrence to them. The uncertainty related to the input parameters is one of the main issues in the majority of decision-making situations. Uncertainty may produce some irrational results, which could make the decision-making process even more challenging. To overcome this challenge, a fuzzy extension of Best-Worst Method (BWM) has been proposed, using trapezoidal fuzzy sets, to combine the advantages of a reduced number of pair-wise comparisons and easy handling of ambiguity. The criteria and alternatives have been evaluated by the proposed Trapezoidal Fuzzy Best-Worst Method (TrFBWM), where the weight of each element is represented by a Trapezoidal Fuzzy Number (TrFN). To verify the coherence of judgment, the consistency ratio is evaluated for TrFBWM. The proposed method is then applied to the location selection of a water treatment plant along the bank of the Brahmaputra river in Assam. The obtained results are compared to one previous work and found that the outcomes of the proposed method indicate a good agreement with that. The outcomes of the study provide useful insights for selecting a suitable location for a surface water treatment plant which can also be extended to other service facilities.


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