Document Type : Research Article
Authors
Department of Mathematics, Akal University, Talwandi Sabo (151302), Punjab, India
10.30473/coam.2026.74974.1318
Abstract
Multi-criteria decision-making (MCDM) often involves situations characterized by uncertainty, ambiguity, and vagueness. To address such complexities, MCDM techniques play a crucial role. This paper presents a comparative analysis of two widely used methods—Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR)—within a hesitant fuzzy environment. Hesitant fuzzy sets allow decision-makers to express hesitation by assigning multiple possible membership values to an element rather than a single value. In this framework, the TOPSIS ranks alternatives based on their closeness to the positive and negative ideal solutions, while the VIKOR identifies a compromise solution by balancing individual and collective regret measures. The effectiveness of the comparison is demonstrated through illustrative numerical examples. Moreover, some real life applications of these methods are discussed.
Highlights
- A systematic and quantitative comparison of TOPSIS and VIKOR is conducted within a Hesitant Fuzzy Sets framework.
- The analysis moves beyond descriptive evaluation by employing measurable indicators, including rank-difference metrics and Kendall’s Tau, across multiple independent numerical examples.
- Results show that TOPSIS consistently generates strict and stable rankings, exhibiting lower sensitivity to local deviations in hesitant fuzzy assessments.
- VIKOR demonstrates higher sensitivity to criterion conflict through its regret-based aggregation, frequently identifying compromise solutions under unstable advantage conditions.
- Ranking divergence between the two methods increases with greater hesitation dispersion and stronger inter-criterion conflict, with Kendall’s τ decreasing from 1.00 to 0.67 in complex scenarios.
- The study establishes that method suitability depends on decision-maker priorities: TOPSIS supports decisiveness and clear prioritization, whereas VIKOR facilitates negotiation-oriented and compromise-driven decisions.
- Practical implications are discussed for applications such as supplier selection, sustainability assessment, policy evaluation, and performance analysis under uncertainty.
- The findings provide quantitative guidance for selecting appropriate hesitant fuzzy MCDM techniques and lay the groundwork for future hybrid and robustness-oriented extensions.
Keywords
- Multi-criteria decision-making
- Fuzzy
- Hesitant fuzzy set
- TOPSIS
- VIKOR
- Kendall’s rank correlation
- Decision uncertainty
Main Subjects
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