Interval Type-2 Fuzzy Decision-Making Approaches

Interval type-2 fuzzy decision-making approaches extend conventional fuzzy set theory by allowing the membership of each element to be represented by an interval rather than a single value. This second-order uncertainty captures both fuzziness and variability in human judgments and sensor measurements. In multi-criteria contexts, interval type-2 fuzzy sets are embedded within established frameworks—such as Analytic Hierarchy Process, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), VIKOR, Weighted Aggregated Sum-Product Assessment (WASPAS), Simultaneous Evaluation of Criteria and Alternatives (SECA), and Data Envelopment Analysis—to enhance robustness under deep uncertainty. These methods have been successfully applied in a wide array of domains including strategic planning, facility location, sustainable manufacturing, healthcare logistics and environmental management. By quantifying the uncertainty of membership functions through upper and lower bounds, decision makers can derive more reliable rankings, sensitivity analyses and consensus measures, supporting global challenges from water security to disaster relief.

Research from Nature Portfolio

Recent studies have developed a multi-criteria decision-making framework for emergency medical facility location that integrates a systems-thinking guidance with interval type-2 fuzzy TOPSIS. Factors are categorised into physical, relational and human dimensions and weighted by a combination of entropy and best–worst methods. The resulting model produces stable location rankings even when criterion weights vary, and its application to real disaster scenarios has demonstrated both practical feasibility and resilience to uncertainty in stakeholder assessments.

Research from all publishers

An extended interval type-2 fuzzy VIKOR technique has been proposed for water security planning. By incorporating equitable linguistic scales and Z-Numbers, this method balances positive and negative memberships alongside reliability, using fuzzy entropy to determine objective criterion weights. Applications to Malaysian water supply projects reveal improved discrimination among competing strategies.

A novel interval type-2 trapezoidal fuzzy decision-making method combines a consistency-improving algorithm with Data Envelopment Analysis to derive priority weight vectors. Demonstrated on a fog-haze influence factor selection case, the approach retains decision-maker preferences while ensuring multiplicative consistency and reliable ranking of environmental indicators.

An integrated model based on WASPAS and SECA under interval type-2 fuzzy sets has been developed for sustainable manufacturing strategy evaluation. The hybrid method assesses eco-efficiency and other sustainability metrics, with sensitivity analysis confirming the stability of strategy rankings under varying uncertainty levels.

Interval Type-2 Fuzzy Decision-Making Approaches publication trend

The graph below shows the total number of articles in interval type-2 fuzzy decision-making approaches across all publications each year (not limited to Nature Index journals).

Technical terms

Interval type-2 fuzzy set: A fuzzy set whose membership function is defined by an interval at each point, modelling uncertainty in the degree of membership.

Membership function: A mapping that assigns to each element a degree of belonging to a fuzzy set, here expressed by lower and upper bounds.

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS): A ranking method that identifies solutions closest to the ideal and furthest from the nadir by means of distance calculations.

VIKOR: A compromise-based MCDM technique that focuses on ranking and selecting from alternatives by measuring closeness to a compromise solution.

Weighted Aggregated Sum-Product Assessment (WASPAS): A hybrid MCDM method combining additive and multiplicative aggregations to evaluate and rank alternatives.

Data Envelopment Analysis (DEA): A non-parametric efficiency measurement technique that evaluates the performance of decision-making units relative to an empirical frontier.

References

1. An integrated type-2 fuzzy decision model based on WASPAS and SECA for evaluation of sustainable manufacturing strategies. Journal of Environmental Engineering and Landscape Management (2019).
2. Interval Type-2 Trapezoidal Fuzzy Decision- Making Method With Consistency-Improving Algorithm and DEA Model. IEEE Access (2020).
3. An Extended Interval Type‐2 Fuzzy VIKOR Technique with Equitable Linguistic Scales and Z‐Numbers for Solving Water Security Problems in Malaysia. Advances in Fuzzy Systems (2023).
4. Research on the location decision-making method of emergency medical facilities based on WSR. Scientific Reports (2023).