Multiattribute Decision Making with Intuitionistic Fuzzy Sets

Multiattribute decision making under uncertainty often requires representation of imprecise, ambiguous and incomplete information. Intuitionistic fuzzy sets extend classical fuzzy sets by assigning to each element both a membership degree and a non-membership degree, with the remaining hesitation degree capturing residual uncertainty. This extra dimension facilitates richer modelling of expert judgments and risk attitudes when evaluating alternatives across multiple criteria. Common frameworks integrate intuitionistic representations into multi-criteria decision-making (MCDM) techniques such as TOPSIS, VIKOR and weighted averaging operators. Criteria weights and decision-maker preferences are incorporated to reflect relative importance, while aggregation operators summarise intuitionistic assessments into composite scores or rankings. Extensions to interval-valued and generalised intuitionistic fuzzy sets further refine uncertainty quantification by allowing degrees to range over intervals or parametric functions. Practical applications span supply-chain configuration, financial portfolio selection, engineering risk management and innovation assessment. By capturing both positive and negative evidence alongside the degree of hesitancy, intuitionistic fuzzy MCDM supports more robust, transparent and adaptable decisions in contexts where ambiguity cannot be ignored.

Research from Nature Portfolio

Recent studies have advanced intuitionistic fuzzy theory by generalising classical constructs and introducing novel aggregation operators tailored to decision preferences. These operators adhere to mathematical properties such as idempotency, boundedness, monotonicity and commutativity, ensuring aggregated values faithfully represent group sentiments. Demonstrated in a multi-criteria evaluation of startup success in the technology sector, generalised intuitionistic fuzzy operators provided finer differentiation among alternative ventures and aligned closely with expert strategic priorities.

Research from all publishers

Researchers have developed an interval-valued intuitionistic fuzzy rough set system to handle conflicts in socio-economic decision contexts. By combining rough set boundary approximations with interval-valued intuitionistic measures and a novel conflict distance metric, this approach sharpens the analysis of competing attributes and yields more decisive conflict resolutions in group negotiations and policy studies.

Another strand of work has introduced decision-maker mentality parameters into interval-valued intuitionistic fuzzy MCDM, reflecting individual risk attitudes in membership, non-membership and hesitation assignments. A new score function incorporating these dual risk parameters enhances the sensitivity of outcomes to personal risk profiles, enabling more tailored and adaptive decision support in areas such as infrastructure planning and environmental management.

Advances have also been made in defining order and ranking functions for interval-valued intuitionistic fuzzy numbers. By establishing an appropriate ordering mechanism, researchers have designed hybrid geometric and ordered weighted averaging operators that yield computationally efficient and easy-to-implement procedures for multiple attribute group decision making, demonstrated across manufacturing and service-sector case studies.

Multiattribute Decision Making with Intuitionistic Fuzzy Sets publication trend

The graph below shows the total number of articles in multiattribute decision making with intuitionistic fuzzy sets across all publications each year (not limited to Nature Index journals).

Technical terms

Intuitionistic fuzzy set: A set characterised by both a membership degree and a non-membership degree for each element, with the difference to unity representing hesitation.

Hesitation degree: The residual uncertainty, calculated as one minus the sum of membership and non-membership degrees.

Aggregation operator: A mathematical function that combines multiple intuitionistic fuzzy values into a single composite value, respecting properties such as monotonicity and boundedness.

Interval-valued intuitionistic fuzzy number: An intuitionistic fuzzy value whose membership and non-membership degrees are expressed as intervals, accommodating greater uncertainty.

Score function: A mapping that converts (interval-valued) intuitionistic fuzzy values into scalar scores for ranking or comparison, potentially embedding decision-maker preferences or risk parameters.

References

1. Optimizing decision-making with aggregation operators for generalized intuitionistic fuzzy sets and their applications in the tech industry. Scientific Reports (2024).
2. Interval-valued intuitionistic fuzzy rough set system over a novel conflict distance measure with application to decision-making. MethodsX (2023).
3. Multi-criteria decision-making method with double risk parameters in interval-valued intuitionistic fuzzy environments. Complex & Intelligent Systems (2020).
4. A New Order Function for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Group Decision Making. Fuzzy Information and Engineering (2021).