Mathematics and Computational Sciences

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

Document Type : Original Article

Authors

Anandarajan Harishree
John Robinson. P

Department of Mathematics, Bishop Heber College (Autonomous), Bharathidasan University, Tiruchirappalli, India.

https://doi.org/10.30511/mcs.2025.2075187.1529
Abstract
Abstract
Objectives: 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.

Keywords

Keywords: Com-LinIFWAA Operator
Decision Support System
MAGDM
ANN
Com-LIFS

Subjects

[1] Bustince, H., Kacprzyk, J., & Mohedano, V. (2000). Intuitionistic fuzzy generators application to intuitionistic fuzzy complementation. Fuzzy Sets and Systems, 114(3), 485–504. 
[2] da Costa, C. G., Bedregal, B. C., & Neto, A. D. D. (2011). Relating De Morgan triples with Atanassovs intuitionistic DeMorgan triples via automorphisms. International Journal of Approximate Reasoning, 52(4), 473–487. 
[3] Higashi, M., & Klir, G. J. (1982). On measures of fuzziness and fuzzy complements. International Journal of General Systems, 8(3), 169–180. 
[4] Huang, S., Yue, Q., & Tao, Y. (2024). Linguistic intuitionistic fuzzy multi-attribute bilateral matching considering satisfaction and fairness degree. Heliyon, 10(5), 1–20.
[5] Hung, W. L., & Yang, M. S. (2008). On similarity measures between intuitionistic fuzzy sets. International Journal of Intelligent Systems, 23(3), 364–383. 
[6] Leonishvay, A., & Robinson, J. (2023). Varieties of linguistic intuitionistic fuzzy distance measures for linguistic intuitionistic fuzzy TOPSIS. Indian Journal of Science and Technology, 16(33), 2653–2662. 
[7] Leonishvay, A., & Robinson, J. P. (2023). A Fully Linguistic Intuitionistic Fuzzy Artificial Neural Network Model for Decision Support Systems. Indian Journal of Science and Technology, 16(SP4), 29–36. 
[8] Liu, C., & Peng, Y. (2023). Improved hesitant intuitionistic fuzzy linguistic term sets and their application in group decision making. Symmetry, 15(9), 1645. 
[9] Lowen, R. (1978). On fuzzy complements. Information Sciences, 14(2), 107–135. 
[10] Malik, R., Bhardwaj, R., & Kumar, K. (2024). Multiattribute group decision making based on AczelAlsina linguistic intuitionistic fuzzy weighted averaging operator of linguistic intuitionistic fuzzy environment. Granular Computing, 9(1), 10.
[11] Neog, T. J., & Sut, D. K. (2011). Complement of an extended fuzzy set. International Journal of Computer Applications, 29.
[12] Peter Dawson, J. R., & Selvaraj, L. A. (2025). Linguistic Intuitionistic Fuzzy VIKOR Method with the Application of Artificial Neural Network. Engineering Proceedings, 95(1), 7.
[13] Rahim, N., Yusoff, B., Abdullah, L., & Merigó, J. M. (2025). A Bibliometric Analysis of Linguistic Variables Based on Intuitionistic Fuzzy Set. Journal of Computational and Cognitive Engineering, 4(2), 121–131. 
[14] Ralescu, D. (1995). Cardinality, quantifiers, and the aggregation of fuzzy criteria. Fuzzy sets and systems, 69(3), 355–365. 
[15] Robinson, P. J. R. (2023). A Novel Learning Rule in Intuitionistic Fuzzy Artificial Neural Network and its Applications to MAGDM Support System. Research square. 
[16] Yager, R. R. (2015). Multicriteria decision making with ordinal/linguistic intuitionistic fuzzy sets for mobile apps. IEEE Transactions on Fuzzy Systems, 24(3), 590–599.
Mathematics and Computational Sciences
Volume 6, Issue 4
Autumn 2025
Pages 50-63

  • Receive Date 20 October 2025
  • Revise Date 25 November 2025
  • Accept Date 26 November 2025

Home

Submit Manuscript

Reviewers

Contact Us