Aggregation Techniques in Multi-Criteria Decision Making

Aggregation techniques form the backbone of multi-criteria decision making by transforming a collection of criteria evaluations into a single coherent value that supports ranking, selection and strategy development. Early methods relied on simple weighted sums, but these proved inadequate when criteria interact or when uncertainty is high. In response, a spectrum of sophisticated operators has emerged. The Choquet integral and Ordered Weighted Averaging operator enable explicit modelling of criterion interdependencies. Mean-based operators such as Bonferroni, Heronian and Maclaurin symmetric means capture pairwise and higher-order interactions in crisp and fuzzy environments. Recent decades have seen these operators extended into fuzzy frameworks, including intuitionistic, Pythagorean and q-rung orthopair fuzzy sets, to handle hesitation and indeterminacy. Partitioned and interaction-aware versions cluster related criteria, preserving local relationships while suppressing spurious links. Across domains as diverse as environmental management, medical diagnosis, supply-chain design and social policy, aggregation techniques are applied to integrate heterogeneous data, accommodate stakeholder preferences and deliver transparent, robust decisions.

Research from Nature Portfolio

Recent studies have advanced partitioned dual mean operators in fuzzy settings to address structured criterion interrelationships. A novel picture fuzzy partitioned Dual Maclaurin symmetric mean operator was developed, together with its weighted form, to manage multi-attribute decision problems represented by picture fuzzy numbers. Rigorous analysis of idempotency, boundedness and monotonicity underpins the operator’s soundness. Comparative case studies demonstrate that this method outperforms classical approaches by more effectively capturing both membership–non-membership–indeterminacy interactions and criterion clustering. Applications to real-world decision problems illustrate the technique’s flexibility and greater discrimination among alternatives.

Research from all publishers

Extensions of Maclaurin symmetric mean operators in spherical fuzzy settings have shown promise for decisions involving rich uncertainty representations. A spherical fuzzy Maclaurin symmetric mean and its weighted variant allow four-graded membership information to be aggregated while preserving inter-argument relations. Applied to a real multi-attribute decision problem, these operators yield clearer ranking stability and enhanced sensitivity to criterion weights compared with conventional means. Another strand of work has introduced picture fuzzy soft Bonferroni mean operators, both unweighted and weighted, to exploit the advantages of soft set theory in handling parameterised uncertainty. Fundamental properties such as reducibility and interaction modelling have been established. An algorithmic framework illustrates application to medical diagnosis, where the proposed operators improve differentiation among disease-scenario alternatives and support more reliable clinical decision support.

Aggregation Techniques in Multi-Criteria Decision Making publication trend

The graph below shows the total number of articles in aggregation techniques in multi-criteria decision making across all publications each year (not limited to Nature Index journals).

Technical terms

Aggregation operator: A mathematical function that fuses multiple criterion values into a single score.

Multi-criteria decision making (MCDM): A framework for evaluating and ranking alternatives based on several, often conflicting, criteria.

Fuzzy set: A generalisation of classical sets where elements have degrees of membership between zero and one.

Bonferroni mean operator: An aggregation operator capturing pairwise interrelationships among inputs.

Maclaurin symmetric mean operator: A higher-order mean that preserves symmetric interactions among multiple inputs.

Picture fuzzy set: An extension of fuzzy sets characterised by degrees of membership, non-membership and neutrality (indeterminacy).

References

1. Maclaurin Symmetric Mean Aggregation Operators Based on Spherical Fuzzy Information and Application to Decision-Making. Journal of Computational and Cognitive Engineering (2023).
2. Partitioned dual Maclaurin symmetric mean operators based on picture fuzzy sets and their applications in multi-attribute decision-making problems. Scientific Reports (2023).
3. Picture fuzzy soft Bonferroni mean aggregation operators and their applications. Heliyon (2023).