| Title of paper:
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Intuitionistic fuzzy modal operators in an entropy-weighted TOPSIS framework
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| Author(s):
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 3, pages 280–295
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| DOI:
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https://doi.org/10.7546/nifs.2026.32.3.280-295
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| Download:
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 PDF (1320 Kb, File info)
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| Abstract:
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Parametric intuitionistic fuzzy modal operators redistribute the degree of uncertainty in intuitionistic fuzzy evaluations by transforming their membership and non-membership degrees. This paper examines the effect of applying the E_(α,β) and Z_(α,β)^ω operators to the decision matrix in the entropy-weighted heuristic fuzzy TOPSIS method, where the criterion weights are derived from the Ye, Wang, Wu–Zhang, and Guo entropy measures. Since both operators are affine transformations with a common contraction coefficient of αβ, we show that their direct application to the evaluations in the Euclidean-based TOPSIS method does not alter the proximity coefficients; thus, the effect of these operators manifests solely through the recalculation of entropy weights and the nonlinear weighting step. A numerical example with four alternatives and six criteria, in which all details are defined, shows that in 38 of the 44 operator-entropy combinations considered, the transformations altered the ranking and, in each case, replaced the preferred alternative with a different option; the primary source of these changes is the recalculation of the weights. Analyses examining the parameters individually reveal how the values of α, β, and ω trigger these changes. The results suggest that modal operators should be considered more as a sensitivity analysis tool for the entropy-weighted TOPSIS method rather than as tools that improve the method in a way that preserves the ranking.
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| Keywords:
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Intuitionistic fuzzy sets, Intuitionistic fuzzy modal operators, Intuitionistic fuzzy entropy, TOPSIS, Multi-criteria decision-making, Sensitivity analysis.
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| AMS Classification:
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03E72, 90B50.
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| References:
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