A Neural Network-Based framework for complemented linguistic intuitionistic Fuzzy Aggregation in MAGDM problems

AbstractObjectives: To define a mathematical formulation for the complement of Linguistic Intuitionistic Fuzzy Set (LIFS) that ensures logical consistency and alignment with linguistic intuitionistic fuzzy theory and to design suitable aggregation operator that incorporate the complement of LIFS for more robust analysis in uncertain environments. To develop an innovative neural network-based framework for handling Multi-Attribute Group Decision-Making Problems (MAGDM), which builds on the fundamental work of Complement Linguistic Intuitionistic Fuzzy Arithmetic Aggregation operator for Linguistic Intuitionistic Fuzzy Sets (LIFS). Methods: The proposed model introduces an innovative integration of a Perceptron-driven Artificial Neural Network (ANN) with linguistic intuitionistic fuzzy inputs to handle uncertainty, vagueness and hesitation often encountered in complex decision-making environments. By dynamically adjusting the connection weights, the ANN continuously refines its decision-making process, leading to greater flexibility, improved robustness and higher precision in ranking the alternatives within Multiple Attribute Group Decision Making (MAGDM) problems. Findings: To improve the decision making problem, a novel Com-LinIFWAA (Complement Linguistic Intuitionistic Fuzzy Weighted Arithmetic Aggregation) operator and novel defuzzification functions are proposed for combining the linguistic data effectively. Finally, the ANN model employing the Perceptron learning rule, specifically designed for Linguistic Intuitionistic Fuzzy Sets are applied to process the inputs derived from solving the MAGDM problem. Novelty: The empirical results confirm that the model effectively balances scalability and interpretability, ensuring reliable performance in handling complex decision-making scenarios framed in linguistic terms.