Fuzzy Multi-Criteria Decision-Making Techniques

Fuzzy multi-criteria decision-making (MCDM) techniques extend classical decision frameworks by incorporating fuzzy set theory to handle ambiguity and imprecision inherent in real-world choices. By representing criteria and expert judgements through membership functions rather than crisp values, these methods capture human reasoning more faithfully when priorities, preferences or outcomes cannot be expressed exactly. Common approaches combine fuzzy extensions of Analytic Hierarchy Process (AHP) to derive criteria weights with fuzzy ranking procedures such as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) or TODIM to order alternatives. Aggregation operators synthesise fuzzy evaluations into a single score, enabling prioritisation under uncertainty. Recent advances have focused on hybridising multiple fuzzy MCDM tools, developing new fuzzy set types with enhanced expressive power, and refining group decision frameworks to balance consensus and diversity among experts. Applications span supply-chain selection, sustainable resource allocation, healthcare planning and software testing parameter prioritisation, demonstrating the global relevance and versatility of fuzzy MCDM in engineering, management and policy contexts.

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Industry practitioners have adopted a hybrid fuzzy AHP-TOPSIS framework to prioritise parameter-influencing factors in software testing. Triangular fuzzy numbers are used to translate linguistic expert judgements into membership intervals. Fuzzy AHP determines criteria weights, while fuzzy TOPSIS ranks testing parameters such as automated testing and verification protocols, yielding an efficient, transparent prioritisation process in complex development environments. A novel group decision-making extension of AHP employs geometric standard deviation and interval group pairwise comparisons to control uncertainty and maximise group satisfaction. By aggregating individual judgements into interval preferences, the method adjusts the width of uncertainty intervals via a tuning parameter, ensuring a desired consensus level while deriving group weights through fuzzy preference programming. Validation through illustrative examples highlights its robustness for collaborative multi-expert decisions. In parallel, linear Diophantine fuzzy aggregation operators have been introduced to broaden the modelling capacity of fuzzy MCDM. Through reference parameters associated with membership and non-membership grades, new weighted average and weighted geometric operators accommodate higher flexibility when representing vague evaluations. A clear numerical example demonstrates how these operators guide choice under linear Diophantine fuzzy contexts, offering enhanced control over uncertainty and superior discrimination among alternatives in decision problems ranging from supply chain engineering to medical network design.

Fuzzy Multi-Criteria Decision-Making Techniques publication trend

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

Technical terms

Fuzzy set: A mathematical set in which each element has a degree of membership ranging between 0 and 1, representing partial truth or uncertainty.

Analytic Hierarchy Process (AHP): A structured technique for organising and analysing complex decisions by decomposing them into a hierarchy of criteria and alternatives and deriving weights via pairwise comparisons.

TOPSIS: A ranking method that identifies alternatives closest to an ideal solution and furthest from a nadir solution, extended to fuzzy data by replacing crisp distances with fuzzy distances.

Triangular fuzzy number: A simple fuzzy number represented by a triplet (l, m, u), where l and u are the lower and upper bounds of support and m is the modal value.

Aggregation operator: A mathematical function that combines multiple fuzzy inputs into a single output, preserving desired properties such as monotonicity and boundedness.

Linear Diophantine fuzzy set: A generalised fuzzy set characterised by membership and non-membership grades linked via integer reference parameters, enabling more flexible uncertainty modelling.

References

1. A hybrid novel fuzzy AHP-TOPSIS technique for selecting parameter-influencing testing in software development. Decision Analytics Journal (2023).
2. Group AHP framework based on geometric standard deviation and interval group pairwise comparisons. Information Sciences (2023).
3. Linear Diophantine Fuzzy Aggregation Operators with Multi-Criteria Decision-Making. Journal of Computational and Cognitive Engineering (2023).