During the last decade, researchers put a lot of effort into the development of the multicriteria decision methods (MCDM) capable of dealing with the uncertainty and vagueness of the initial information. MCDM approaches that work under the environment of the interval-valued neutrosophic sets (IVNS) demonstrate credibility for the analysis of different opinions as well as for the inconsistency of the criteria evaluation data. The novel multicriteria decision-making approach MULTIMOORA-IVNS (multi-objective optimisation by ratio analysis under interval-valued neutrosophic sets) is presented in this paper. A novel heuristic evaluation methodology HEBIN (heuristic evaluation based on interval numbers) that exploits MULTIMOORA-IVNS for the processing of the evaluation results is also presented in this research. HEBIN is able to increase the accuracy of the checklists-based heuristic evaluation and to diminish the impact of the inconsistencies caused by the evaluators. A comparison of six e-commerce websites is introduced to reveal the practicalities of the proposed multicriteria decision-making application.
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