Intuitionistic Fuzzy Decision-Making Models and Techniques
Summary
Intuitionistic fuzzy decision-making integrates the dual concepts of membership and non-membership degrees to capture both support and opposition alongside the residual hesitation or uncertainty. Building on Atanassov’s intuitionistic fuzzy sets, modern frameworks employ specialised number types—triangular, trapezoidal or interval-valued intuitionistic fuzzy numbers—to express imprecise preferences, incomplete weight information and expert opinions. Core methodologies encompass ranking procedures that balance value and ambiguity indices, aggregation operators such as ordered weighted averaging and geometric mean tailored for intuitionistic contexts, and similarity measures for comparing alternatives against ideal solutions. Recent advances extend these techniques to dynamic systems, reliability management and differential equations, illustrating broad applicability across engineering, environmental monitoring and strategic planning. Emphasis on algorithmic efficiency, such as semi-analytical decomposition methods, and on flexible group-decision structures has enhanced practical uptake, enabling decision support under deep uncertainty and conflicting criteria.
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A semi-analytical scheme based on a modified Adomian decomposition method was devised to solve systems of intuitionistic fuzzy differential equations with generalised trapezoidal fuzzy initial conditions. Applications to brine tank dynamics and coupled mass-spring models demonstrate high accuracy and computational efficiency compared with existing numerical approaches, with graphical analyses of solution intervals at varying uncertainty levels.
An intuitionistic fuzzy reliability model for wind-turbine systems employs a triangular flexibility ranking and aggregation operator to integrate expert judgements where data are scarce. This framework identifies critical failure modes—sensor tilts, accelerometers and actuators—while quantifying fault intensity and providing a comprehensive view of system behaviour under uncertainty.
A fundamental multi-criteria decision-making approach utilises intuitionistic trapezoidal fuzzy multi-numbers to capture repeated or varied preference information across criteria. The model defines operational laws via t-norms and t-conorms, introduces dedicated aggregation operators, and ranks alternatives by similarity to a positive ideal solution, illustrated through a numerical case that underlines both practicality and robustness.
Intuitionistic Fuzzy Decision-Making Models and Techniques publication trend
The graph below shows the total number of articles in intuitionistic fuzzy decision-making models and techniques across all publications each year (not limited to Nature Index journals).
Technical terms
Intuitionistic fuzzy set: A set characterised by membership, non-membership and hesitation degrees to model uncertainty.
Membership degree: A value in [0,1] indicating the extent to which an element belongs to a fuzzy set.
Non-membership degree: A value in [0,1] indicating the extent to which an element does not belong, complementary to membership.
Hesitation degree: The residual uncertainty, equal to one minus the sum of membership and non-membership degrees.
Triangular/trapezoidal intuitionistic fuzzy number: A parametrised membership and non-membership function defined by triangle or trapezoid shapes for decision variables.
Aggregation operator: A mathematical function that combines multiple fuzzy values into a single representative value under specified properties.
Adomian decomposition method: A semi-analytical technique for solving differential equations by decomposing nonlinear terms into series components.
References
- Semi-Analytical Scheme for Solving Intuitionistic Fuzzy System of Differential Equations. IEEE Access (2023).
- Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems. Complex & Intelligent Systems (2018).
- A Value and Ambiguity‐Based Ranking Method of Trapezoidal Intuitionistic Fuzzy Numbers and Application to Decision Making. The Scientific World JOURNAL (2014).
- A Generalized Triangular Intuitionistic Fuzzy Geometric Averaging Operator for Decision-Making in Engineering and Management. Information (2017).
- Intuitionistic Fuzzy Model for Reliability Management in Wind Turbine System. Applied Computing and Informatics (2020).
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