In today’s complex decision-making landscape, multi-criteria decision-making (MCDM) frameworks play a crucial role in managing conflicting criteria. Traditional MCDM methods often face challenges due to uncertainty and interdependencies among criteria. This paper presents a novel framework that combines the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) with random hypergraphs to enhance decision processes. In TOPSIS, asymmetry in criterion interactions is typically managed by assigning different weights, while for independent criteria, Euclidean distance introduces geometric symmetry, treating all dimensions (criteria) equally when calculating an alternative’s distance from ideal or negative-ideal solutions. Although assigning weights can partially address asymmetry caused by interdependencies and uncertainties among criteria, it cannot fully account for uncertainty in data and criteria interactions. Our approach integrates random hypergraphs to better capture these relationships, offering a more refined representation of decision problems and improving the robustness of the decision-making process. In this method, we first capture criteria interactions in a random hypergraph. Using properties of the graph and input data, the algorithm then generates weights for interacted groups of criteria. These weights, termed “dynamic weights”, adapt in response to changes in criteria interactions and data, forming the basis for a generalized TOPSIS algorithm. A comparative study with illustrative examples highlights the advantages of this enhanced TOPSIS framework, showing how random hypergraphs expand its analytical capabilities. This research advances the theoretical foundation of MCDM frameworks while offering practical insights for practitioners seeking robust solutions in complex and uncertain decision environments.

In today’s complex decision-making landscape, multi-criteria decision-making (MCDM) frameworks play a crucial role in addressing conflicting criteria. This paper introduces a novel framework that combines the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) with random hypergraphs to enhance decision processes. Traditional MCDM methods often face challenges due to uncertainty and interdependencies among criteria. Our approach leverages random hypergraphs to better capture the relationships between criteria, offering a refined representation of decision problems. We delve into the theoretical foundations of this framework, detailing its algorithmic implementation and methodologies for evaluating alternatives under uncertainty. Performance comparisons illustrate the advantages of the proposed TOPSIS framework, emphasizing how random hypergraphs enrich TOPSIS’s analytical capabilities. This research advances the theoretical understanding of MCDM frameworks while providing practical insights for practitioners seeking robust solutions in complex and uncertain decision-making environments.