Fuzzy Decision-Making Applications in Risk Analysis

Fuzzy decision-making offers a robust framework for assessing and managing risk when information is imprecise, incomplete or linguistically expressed. By representing uncertainty through membership functions rather than precise probabilities, fuzzy approaches capture the gradations inherent in real-world hazards. Applications span environmental risk modelling, where fuzzy sets characterise pollution thresholds; financial risk assessment, where fuzzy numbers handle market volatility; engineering safety analysis, where fuzzy rule bases evaluate structural reliability; and healthcare, where fuzzy multi-criteria methods support diagnostic and treatment choices under uncertain clinical data. Hybrid techniques combine fuzzy logic with grey systems, entropy measures or optimisation algorithms to refine decision support under ambiguity. The global significance is evident in disaster preparedness, portfolio management and critical infrastructure resilience, where decision-makers integrate expert judgement, statistical data and stakeholder preferences. Concrete examples include prioritising flood mitigation projects by fuzzy analytic hierarchy process, selecting investment portfolios with interval type-2 fuzzy sets and calibrating early-warning systems through fuzzy clustering. Across domains, interconnections emerge as methods evolve to balance interpretability and computational rigour, ensuring accessible yet authoritative guidance for complex risk scenarios.

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A foundational study on similarity measures for sequences of triangular fuzzy numbers established algebraic operations and centre-of-gravity calculations to quantify resemblance between fuzzy sequences. This work underpins subsequent fuzzy risk analysis by providing a systematic way to compare uncertain scenarios and supports the development of decision rules for risk prioritisation.

A novel group decision-making model under dual hesitant fuzzy information integrates decision-maker loss aversion into the evaluation process. By defining positive and negative ideal schemes as “clouts” and measuring distances via normalised Hamming metrics, the approach derives optimal attribute weights through nonlinear optimisation, yielding collective decisions that account for behavioural biases in uncertain environments.

An advanced grey target decision method based on Kullback-Leibler distance handles mixed attribute values in both indices and weights. It converts qualitative and quantitative criteria into binary connection numbers, derives two-tuple determinacy–uncertainty representations and applies a weight-conversion function to produce a comprehensive weighted divergence measure. Case studies demonstrate enhanced accuracy in ranking alternatives under ambiguous weight information.

Fuzzy Decision-Making Applications in Risk Analysis publication trend

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

Technical terms

Fuzzy set: A mathematical construct in which elements have graded membership between zero and one, modelling imprecise or vague concepts.

Fuzzy number: A special type of fuzzy set on the real line, typically triangular or trapezoidal, used to represent uncertain numerical values.

Interval type-2 fuzzy set: A higher-order fuzzy set with fuzzy membership functions themselves defined by intervals, capturing additional layers of uncertainty.

Grey target decision method: A multi-criteria technique that measures the closeness of alternatives to positive and negative ideal targets, often using grey systems theory to handle incomplete information.

Kullback-Leibler distance: A divergence metric from information theory quantifying the difference between two probability distributions or, in fuzzy contexts, between two uncertainty representations.

Hesitant fuzzy set: A fuzzy set where membership of an element may be represented by multiple possible values, reflecting hesitation or indecision among experts.

References

1. Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis. Advances in Mathematical Physics (2015).
2. A Grey Target Group Decision Method with Dual Hesitant Fuzzy Information considering Decision‐Maker’s Loss Aversion. Scientific Programming (2020).
3. Kullback-Leibler Distance Based Generalized Grey Target Decision Method With Index and Weight Both Containing Mixed Attribute Values. IEEE Access (2020).