Intuitionistic Fuzzy Matrix Methods in Decision-Making
Summary
Intuitionistic fuzzy matrix methods extend classical fuzzy matrices by incorporating both membership and non-membership degrees for each element, together with a derived hesitation degree. This richer representation enables decision-making systems to account explicitly for uncertainty and incomplete information. In practice, decision makers assign weighted criteria values to alternatives, expressed in an intuitionistic fuzzy decision matrix, and then apply aggregation and ranking procedures to determine optimal solutions. Key techniques include similarity measures, divergence measures and spectral energies tailored to intuitionistic fuzzy matrices or associated graphs. These methods facilitate robust analysis in environments ranging from engineering design to environmental management, where expert judgments may conflict or lack full clarity. By preserving dual uncertainty parameters, intuitionistic fuzzy matrix approaches improve sensitivity to subtle distinctions among alternatives and enhance consensus modelling in group decision-making contexts. Recent advances have focused on developing novel distance and similarity metrics, improving algorithmic efficiency for large-scale problems and integrating network-based energies to capture relational structures among criteria or experts. The combination of theoretical developments with practical applications underscores the global significance of intuitionistic fuzzy matrix methods as a versatile toolkit for multi-criteria and multi-expert decision support.
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Intuitionistic Fuzzy Matrix Methods in Decision-Making publication trend
The graph below shows the total number of articles in intuitionistic fuzzy matrix methods in decision-making 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 for each element, capturing dual uncertainty.
Intuitionistic fuzzy matrix: A matrix whose entries are intuitionistic fuzzy numbers, used to represent evaluations in multi-criteria decision problems.
Membership degree: The extent to which an alternative belongs to a fuzzy set, expressed between 0 and 1.
Non-membership degree: The extent to which an alternative does not belong to a fuzzy set, also between 0 and 1.
Hesitation degree: The residual uncertainty in an intuitionistic fuzzy set, equal to one minus the sum of membership and non-membership degrees.
Cosine similarity measure: A metric that assesses the angle between two intuitionistic fuzzy vectors, indicating their directional closeness.
Divergence measure: A function quantifying the difference between two intuitionistic fuzzy matrices, reflecting both membership and non-membership discrepancies.
Seidel Laplacian energy: A spectral graph measure adapted to intuitionistic fuzzy graphs, capturing relational energy among nodes (e.g., experts or criteria).
Multi-criteria decision-making (MCDM): A process for evaluating and ranking alternatives based on multiple, often conflicting, criteria.
References
- Enhancing Expert Decision-Making for Wastewater Treatment Plants with Seidel Laplacian Energy and Cosine Similarity Measure in Intuitionistic Fuzzy Graphs. International Journal of Computational Intelligence Systems (2024).
- A New Divergence Measure for Intuitionistic Fuzzy Matrices. Informatica (2023).
- The Energy of rough neutrosophic matrix and its application to MCDM problem for selecting the best building construction site. Decision Making Applications in Management and Engineering (2022).
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