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.

We define the Interval Neutrosophic Hesitant Fuzzy Choquet Integral (INHFCI) operator as a useful tool for multicriteria decision making (MCDM). The INHFCI operator generalizes both the interval neutrosophic hesitant fuzzy ordered weighted averaging operator and the interval neutrosophic hesitant fuzzy weighted averaging operator. A modified version of the score function to make comparison among Interval Neutrosophic Hesitant Fuzzy elements is proposed. We develop an approach for multicriteria decision making based on the interval neutrosophic hesitant fuzzy choquet integral operator that applies to our proposed score function. Finally the model is illustrated with the help of an example.

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.

We define intuitionistic fuzzy idempotent, prime, strongly irreducible and t-pure ideals on a semiring, and investigate some properties of such ideals. We show that all intuitionistic fuzzy ideals are idempotent in a fully idempotent semirings, and right weakly regular semirings. We establish that an intuitionistic fuzzy set of a semiring is an intuitionistic fuzzy ideal if and only if (α, β)-cut is an ideal. We prove that if all intuitionistic fuzzy ideals of a semiring are t-pure, then an intuitionistic fuzzy ideal is prime if and only if it is strongly irreducible. We also establish that for a fully idempotent semirings, an intuitionistic fuzzy ideal is prime if and only if it is strongly irreducible.

This paper deals with some theoretical aspects of hypergraphs related to hyperpaths and hypertrees. In ordinary graph theory, the intersecting or adjacent edges contain exactly one vertex; however, in the case of hypergraph theory, the adjacent or intersecting hyperedges may contain more than one vertex. This fact leads to the intuitive notion of knots, i.e., a collection of explicit vertices. The key idea of this manuscript lies in the introduction of the concept of the knot, which is a subset of the intersection of some intersecting hyperedges. We define knot-hyperpaths and equivalent knot-hyperpaths and study their relationships with the algebraic space continuity and the pseudo-open character of maps. Moreover, we establish a sufficient condition under which a hypergraph is a hypertree, without using the concept of the host graph.