Ordered Weighted Averaging Techniques in Multicriteria Decision Making

Ordered Weighted Averaging (OWA) techniques constitute a versatile family of aggregation operators that rank and weight individual criteria outputs to synthesise a single decision index. Introduced as a means to interpolate between extreme evaluative behaviours, OWA operators allow decision makers to calibrate the degree of compensation among criteria via a weight vector. Low-order weights emphasise poorer performances (andness), resembling conjunctive logic, whereas high-order weights accentuate superior performances (orness), akin to disjunctive logic. Over the past decade, advances have extended the theoretical foundations of OWA by integrating non-additive fuzzy measures, adaptive data-driven weight generation and axiomatically defined quantifiers. Novel indices permit finer control of orness and andness, while hybrid models combine OWA with Choquet and Sugeno integrals for nuanced interaction modelling. In parallel, practical applications span environmental sustainability assessments, risk analysis, recommender systems and group decision making under uncertainty. Emerging research has explored kernel-density-based weight estimation, extreme-value reduction quantifiers and linguistic quantifier design, each enriching the expressiveness and robustness of multicriteria synthesis. The global significance of OWA lies in its capacity to reconcile competing objectives, accommodate stakeholder preferences and support transparent decision frameworks across engineering, economics and public policy domains.

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Technical terms

Ordered Weighted Averaging (OWA) operator: An aggregation function that orders inputs and applies a predefined weight vector to produce a single value, allowing control over compensatory behaviour.

Fuzzy measure (capacity): A monotonic set function assigning weights to all subsets of criteria, enabling interaction modelling beyond additive weights.

Orness: A scalar index ranging from 0 to 1 that quantifies the degree to which an OWA operator behaves like a logical disjunction.

Andness: A complementary index to orness, measuring the degree to which an operator behaves like a logical conjunction.

Fuzzy linguistic quantifier: A mapping that translates qualitative expressions such as “most” or “few” into numerical weights for OWA operators.

Extreme Value Reduction (EVR): A class of fuzzy quantifiers designed to diminish the influence of extreme input values when generating weight vectors.

References

1. $\Upsilon$-Values: Power Indices La Orness for Nonadditive Measures. IEEE Transactions on Fuzzy Systems (2024).
2. Human-Centric Aggregation via Ordered Weighted Aggregation for Ranked Recommendation in Recommender Systems. Applied System Innovation (2023).
3. Symmetric weights for OWA operators prioritizing intermediate values. The EVR-OWA operator. Information Sciences (2022).
4. Determine OWA operator weights using kernel density estimation. Economic Research-Ekonomska Istraživanja (2020).
5. Discrete Integrals and Axiomatically Defined Functionals. Axioms (2012).