Advancing group decision-making with an interval-valued intuitionistic fuzzy game model and a novel score function: application to sustainable AC system ranking

Sandeep Kumar; Reshu Tyagi; Saiful R Mondal; Sandeep Kumar; Reshu Tyagi; Saiful R Mondal

doi:10.3934/math.20261367

AIMS Mathematics

2026, Volume 11, Issue 10: 35156-35199. doi: 10.3934/math.20261367

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Research article

Advancing group decision-making with an interval-valued intuitionistic fuzzy game model and a novel score function: application to sustainable AC system ranking

1.
Department of Mathematics, Ch. Charan Singh University, Meerut-250004, Uttar Pradesh, India
2.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia

Received: 27 March 2026 Revised: 07 October 2026 Accepted: 13 October 2026 Published: 27 October 2026
MSC : 03E72, 90B50, 91A80, 91B06

This paper develops a game-theoretic framework for multiple-attribute group decision-making (MAGDM) under an interval-valued intuitionistic fuzzy (IVIF) environment. First, a generalized score function (GSF) is proposed for intuitionistic fuzzy numbers (IFNs) and extended to interval-valued intuitionistic fuzzy numbers (IVIFNs). By incorporating indeterminacy through two flexible parameters, the GSF improves the discrimination and sensitivity of alternative evaluations under uncertain information. Its effectiveness is validated through seven benchmark cases in which the existing score and accuracy functions fail to distinguish the considered IFNs and IVIFNs. In all cases, the GSF yields distinct rankings, resolving the ambiguities. An IVIF MAGDM algorithm is then developed for problems with unknown attribute weights. The aggregated IVIF decision matrix is formulated as the payoff matrix of a two-player zero-sum matrix game (TMG), enabling determination of the attribute weights from assessments of multiple decision-makers. The game models are defined for membership intervals excluding 1 and nonmembership intervals excluding 0, while these boundary cases lie outside the admissible domain of the formulation. An IVIF expected score function is introduced to evaluate the overall performance of alternatives, followed by the GSF to obtain their final ranking. The framework preserves the IVIF structure throughout the decision-making process, with scalarization restricted to the final ranking stage, thereby retaining the inherent uncertainty and hesitation of the original decision assessments. The applicability of the approach is demonstrated through a sustainable air-conditioning system selection problem. Comparative analysis with four existing approaches shows exact agreement with one method and slight differences from the others. Sensitivity analysis with respect to the preference parameter $ \omega $ confirms that the obtained ranking remains unchanged for $ \omega = 0.2 $, $ 0.5 $, and $ 0.8 $, indicating 100% ranking stability. These findings demonstrate the discrimination capability of the GSF and the robustness and reliability of the IVIF MAGDM framework.
- MAGDM problems,
- generalized score function,
- IVIFN,
- IVIF TMG model
Citation: Sandeep Kumar, Reshu Tyagi, Saiful R Mondal. Advancing group decision-making with an interval-valued intuitionistic fuzzy game model and a novel score function: application to sustainable AC system ranking[J]. AIMS Mathematics, 2026, 11(10): 35156-35199. doi: 10.3934/math.20261367

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Abstract

This paper develops a game-theoretic framework for multiple-attribute group decision-making (MAGDM) under an interval-valued intuitionistic fuzzy (IVIF) environment. First, a generalized score function (GSF) is proposed for intuitionistic fuzzy numbers (IFNs) and extended to interval-valued intuitionistic fuzzy numbers (IVIFNs). By incorporating indeterminacy through two flexible parameters, the GSF improves the discrimination and sensitivity of alternative evaluations under uncertain information. Its effectiveness is validated through seven benchmark cases in which the existing score and accuracy functions fail to distinguish the considered IFNs and IVIFNs. In all cases, the GSF yields distinct rankings, resolving the ambiguities. An IVIF MAGDM algorithm is then developed for problems with unknown attribute weights. The aggregated IVIF decision matrix is formulated as the payoff matrix of a two-player zero-sum matrix game (TMG), enabling determination of the attribute weights from assessments of multiple decision-makers. The game models are defined for membership intervals excluding 1 and nonmembership intervals excluding 0, while these boundary cases lie outside the admissible domain of the formulation. An IVIF expected score function is introduced to evaluate the overall performance of alternatives, followed by the GSF to obtain their final ranking. The framework preserves the IVIF structure throughout the decision-making process, with scalarization restricted to the final ranking stage, thereby retaining the inherent uncertainty and hesitation of the original decision assessments. The applicability of the approach is demonstrated through a sustainable air-conditioning system selection problem. Comparative analysis with four existing approaches shows exact agreement with one method and slight differences from the others. Sensitivity analysis with respect to the preference parameter $ \omega $ confirms that the obtained ranking remains unchanged for $ \omega = 0.2 $, $ 0.5 $, and $ 0.8 $, indicating 100% ranking stability. These findings demonstrate the discrimination capability of the GSF and the robustness and reliability of the IVIF MAGDM framework.

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