Multiple Attribute Decision Making in Fuzzy Environments

Over the past decades, decision problems characterised by multiple, often conflicting attributes have become ubiquitous in fields such as supply chain management, environmental policy, healthcare and engineering design. Traditional multiple attribute decision making approaches rely on precise numeric information but frequently fall short when data are vague, imprecise or linguistically expressed. Fuzzy set theory and its extensions offer a powerful framework to capture and manage such uncertainty. In a fuzzy environment, attributes are represented by membership functions rather than crisp values, enabling the accommodation of expert hesitation, interval uncertainty and linguistic assessments. This has given rise to a plethora of aggregation operators and weighting schemes, including entropy-based objective weights, correlation-driven weights and hybrid subjective–objective techniques. Concurrently, ranking approaches such as evaluation based on distance from average solution, technique for order preference by similarity to ideal solution, complex proportional assessment and prospect-theory-driven methods have been adapted to fuzzy contexts. Modern studies seek to enhance the interpretability of results, improve computational efficiency and ensure the robustness of rankings under data perturbation. Applications range from green supplier selection and infrastructure risk assessment to performance evaluation of intangible assets and renewable energy project prioritisation. The global significance of these methods lies in their ability to support informed, transparent decisions in uncertain environments, enabling organisations to balance economic, environmental and social objectives.

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Research from all publishers

Recent advances have extended multiple attribute group decision making under fuzzy conditions in several directions. A novel probabilistic dual hesitant fuzzy EDAS approach has been introduced to incorporate both decision-maker hesitation and probability information, coupled with a hybrid entropy–CRITIC weighting scheme; its efficacy was demonstrated in supplier selection scenarios. In another development, the Logarithmic TODIM and TOPSIS framework was integrated within an interval-valued intuitionistic fuzzy environment to evaluate intangible assets management performance in commercial sporting events, leveraging an objective weight derivation model and comparative analyses to validate robustness. Furthermore, the COPRAS method was generalised to picture fuzzy sets to tackle green supplier selection, employing a correlation-driven criteria weight assessment and utility degree calculations, thereby enhancing decision support in sustainable supply chain management.

Multiple Attribute Decision Making in Fuzzy Environments publication trend

The graph below shows the total number of articles in multiple attribute decision making in fuzzy environments across all publications each year (not limited to Nature Index journals).

Technical terms

Fuzzy set: A collection with elements assigned degrees of membership between zero and one, modelling vagueness.

Hesitant fuzzy set: An extension of fuzzy sets allowing multiple possible membership degrees to capture hesitation.

Interval-valued intuitionistic fuzzy set: A generalisation providing interval ranges for both membership and non-membership degrees.

Probabilistic dual hesitant fuzzy set: A framework combining dual hesitation regarding membership and non-membership with associated probabilities.

EDAS (Evaluation based on Distance from Average Solution): A distance-based ranking method measuring divergence of each alternative from the average solution.

TOPSIS (Technique for Order Preference by Similarity to Ideal Solution): Ranks alternatives by proximity to an ideal point and distance from a nadir point.

COPRAS (Complex Proportional Assessment): Evaluates alternatives using proportional relations of weighted criteria to calculate utility degrees.

TODIM: A decision method grounded in prospect theory accounting for decision-makers’ gain/loss perceptions and risk behaviour.

References

1. EDAS method for multiple attribute group decision making with probabilistic dual hesitant fuzzy information and its application to suppliers selection. Technological and Economic Development of Economy (2023).
2. Enhanced LogTODIM-TOPSIS framework for interval-valued intuitionistic fuzzy MAGDM and applications to intangible assets operational management performance evaluation of commercial sporting events. Heliyon (2024).
3. COPRAS method for multiple attribute group decision making under picture fuzzy environment and their application to green supplier selection. Technological and Economic Development of Economy (2021).