Hybrid multicriteria decision-making with a novel 3D similarity measure in an intuitionistic fuzzy environment: application in medical diagnosis

Decision-making in medical diagnosis involves interpreting patient symptoms under uncertainty to identify potential conditions. Intuitionistic fuzzy sets (IFSs) extend fuzzy sets to handle uncertainties in complex information. Similarity measures (SMs) have become essential in comparing objects within the IFS framework. However, many existing SMs yield counterintuitive results, face zero divisor issues, and fail to meet the properties outlined in the axiomatic definition of SMs. This paper introduces a novel 3D similarity measure for IFSs, addressing these limitations. The measure is analyzed using 2D and 3D geometric representations, with numerical examples provided for clarity. A comparative analysis evaluates the proposed measure’s reliability against existing SMs. The paper also presents a hybrid decision-making framework combining the method for removal effects of criteria (MEREC) for objective weights, stepwise weight assessment ratio analysis (SWARA) for subjective weights, and the technique for order preference by similarity to the ideal solution (TOPSIS) for ranking alternatives. This IF-MEREC-SWARA-TOPSIS model is applied to diagnosing mental health conditions. The practical effectiveness of the hybrid approach is demonstrated through sensitivity analysis and comparisons with other techniques. Finally, the paper outlines future research directions, discusses limitations of the proposed similarity measure, and highlights potential challenges in implementing the hybrid approach.