Hamming Distance-Based Intuitionistic Fuzzy Artificial Neural Network with Novel Back Propagation Method †
Abstract
1. Introduction
2. The Backpropagation Method for Artificial Neural Networks
3. The Hamming–Intuitionistic Fuzzy Power Generalized Weighted Averaging (H-IFPGWA) Operator
- (1)
- Suppose .
- (2)
- Suppose then .
- (3)
- Suppose , then
4. The Back-Propagated IFS-ANN with the H-IFPGWA Operator
Pseudo-code for ANN with H-IFPGWA: Cn: n Matrix itemset of size k × m Input {An, Collection of n Intuitionistic Fuzzy Decision Matrices of size k } W = np.array([w1,w2,w3,w4,w5]) #weights Initialization //* Aggregation Phase*// Compute {Hamming-IFPGWA aggregator with the Initial Weight Vector} For (n = 1; An ∅; n++) do begin Generate {Individual Preference Intuitionistic Fuzzy Decision Matrices, Xn} //* Xn is the collection of Individual Preference IF-Decision Matrices *// Generate {Intuitionistic Fuzzy Attribute Weight Vector} //* The same H-IFPGWA is also used to derive the attribute weight vector *// While do {Defuzzify the IF column matrix into Fuzzy Column matrix} Generate {Collective Overall Preference Intuitionistic Fuzzy Decision Matrices the new Weight Vector, WT} //*Improvise the input vector by different Defuzzification functions , , , *// Input vector //* Back Propagation: Start*// Forward Pass: Calculate net input to each hidden layer: Learning Rate = 0.5 Error Calculation: Error = Target Output − Network output Backward Pass: (weights updating) ; Continue the Forward Pass with updated weights from Backward pass: Calculate net input to each hidden layer: Continue the weight updation until the error is minimized to a desired level //*Choosing the MAGDM best alternative*// Find {The Weighted Arithmetic Averaging (WAA) values between the alternatives} Find {The distance between WAA values and Net output} While Distance values Threshold do Generate {The best alternative} Output {Best Alternative(s) to be chosen} End. |
5. Numerical Illustration for Backpropagated IFS-ANN withH-IFPGWA Operator
6. Discussion
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Atanassov, K.; Sotirov, S.; Pencheva, T. Intuitionistic Fuzzy Deep Neural Network. Mathematics 2023, 11, 716. [Google Scholar] [CrossRef]
- Hájek, P.; Olej, V. Intuitionistic Fuzzy Neural Network: The Case of Credit Scoring Using Text Information. In Engineering Applications of Neural Networks: EANN 2015, Rhodes, Greece, 25–28 September 2015; Iliadis, L., Jayne, C., Eds.; Communications in Computer and Information Science; Springer: Cham, Switzerland, 2015; Volume 517. [Google Scholar] [CrossRef]
- Jekova, I.; Christov, I.; Krasteva, V. Atrioventricular synchronization for detection of atrial fibrillation and flutter in one to twelve ECG leads using a dense neural network classifier. Sensors 2022, 22, 6071. [Google Scholar] [CrossRef] [PubMed]
- Krasteva, V.; Christov, I.; Naydenov, S.; Stoyanov, T.; Jekova, I. Application of dense neural networks for detection of atrial fibrillation and ranking of augmented ECG feature set. Sensors 2021, 21, 6848. [Google Scholar] [CrossRef] [PubMed]
- Leonishiya, A.; Robinson, P.J. A Fully Linguistic Intuitionistic Fuzzy Artificial Neural Network Model for Decision Support Systems. Indian J. Sci. Technol. 2023, 16, 29–36. [Google Scholar] [CrossRef]
- Petkov, T.; Bureva, V.; Popov, S. Intuitionistic fuzzy evaluation of artificial neural network model. Notes Intuitionistic Fuzzy Sets 2021, 27, 71–77. [Google Scholar] [CrossRef]
- Robinson, P.J.; Leonishiya, M. Application of Varieties of Learning Rules in Intuitionistic Fuzzy Artificial Neural Network. In Machine Intelligence for Research & Innovations; Verma, O.P., Wang, L., Kumar, R., Yadav, A., Eds.; Lecture Notes in Networks & Systems; Springer: Singapore, 2024; Volume 832, pp. 35–45. [Google Scholar] [CrossRef]
- Sotirov, S.; Atanassov, K. Intuitionistic fuzzy feed forward neural network. Cybern. Inf. Technol. 2009, 9, 62–68. Available online: https://cit.iict.bas.bg/CIT_09/v9-2/62-68.pdf (accessed on 24 July 2024).
- Xu, Z.S.; Yager, R.R. Some Geometric Aggregation Operators Based on Intuitionistic Fuzzy sets. Int. J. Gen. Syst. 2006, 35, 417–433. [Google Scholar] [CrossRef]
- Leonishiya, A.; Robinson, P.J. Varieties of Linguistic Intuitionistic Fuzzy Distance Measures for Linguistic Intuitionistic Fuzzy TOPSIS Method. Indian J. Sci. Technol. 2023, 16, 2653–2662. [Google Scholar] [CrossRef]
- Yager, R.R.; Filev, D.P. Induced Ordered Weighted Averaging Operators. IEEE Trans. Syst. Man Cybern.-Part B 1999, 29, 141–150. [Google Scholar] [CrossRef] [PubMed]
- Yager, R.R. The Power average operator. IEEE Trans. Fuzzy Syst. Man Cybern.-Part A Syst. Hum. 2001, 31, 724–731. [Google Scholar] [CrossRef]
- Kumar, A.; Sharma, T.K.; Verma, O.P. Detection of Heart Failure by Using Machine Learning. In Machine Intelligence for Research & Innovations; Verma, O.P., Wang, L., Kumar, R., Yadav, A., Eds.; Lecture Notes in Networks & Systems; Springer: Singapore, 2024; Volume 832, pp. 195–203. [Google Scholar]
- Sharma, R.; Verma, O.P.; Kumari, P. Application of Dragonfly Algorithm-Based Interval Type-2 Fuzzy Logic Closed-Loop Control System to Regulate the Mean Arterial Blood Pressure. In Machine Intelligence for Research & Innovations; Verma, O.P., Wang, L., Kumar, R., Yadav, A., Eds.; Lecture Notes in Networks & Systems; Springer: Singapore, 2024; Volume 832, pp. 183–194. [Google Scholar]
Sl. No.: | Transforming Vague Values to Fuzzy Values | Input Vector-1 | Input Vector-2 | Input Vector-3 | Ranking of Alternatives |
---|---|---|---|---|---|
1 | A2 < A5 < A4 < A3 < A1 | ||||
2 | A2 < A3 < A4 < A1 < A5 | ||||
3 | (u) + | A1 < A3 < A2 < A4 < A5 |
Sl. No.: | Learning Rule | Hidden Layer | Threshold P-IFWG | Threshold P-IFWA | Threshold IFWG | Threshold IFWA | Ranking |
---|---|---|---|---|---|---|---|
1 | Delta | No | 0.17875 | 0.19861 | 0.17885 | 0.18195 | A1, A2 |
0.19772 | 0.21238 | 0.20166 | 0.22589 | A1, A2 | |||
2 | Yes | 0.13971 | 0.13971 | 0.14204 | 0.14204 | A2, A4 | |
0.13656 | 0.13656 | 0.13641 | 0.13641 | A2, A3, A4 | |||
3 | Perceptron | No | 0.12992 | 0.13326 | 0.13017 | 0.2005896 | A1, A2, A3 |
0.17017 | 0.17175 | 0.17094 | 0.197562 | A1, A2, A3 | |||
4 | Yes | 0.05797 | 0.05797 | 0.05774 | 0.05774 | A4, A5 | |
0.05775 | 0.05775 | 0.057716 | 0.057696 | A2, A3, A4 | |||
5 | Hebb | No | 0.85408 | 0.81353 | 0.84579 | 1.39 | A4, A5 |
6 | Yes | 2.33259 | 2.33259 | 2.33647 | 2.33647 | A1, A3, A5 |
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Peter Dawson, J.R.; Selvaraj, W.A.P. Hamming Distance-Based Intuitionistic Fuzzy Artificial Neural Network with Novel Back Propagation Method. Eng. Proc. 2025, 95, 9. https://doi.org/10.3390/engproc2025095009
Peter Dawson JR, Selvaraj WAP. Hamming Distance-Based Intuitionistic Fuzzy Artificial Neural Network with Novel Back Propagation Method. Engineering Proceedings. 2025; 95(1):9. https://doi.org/10.3390/engproc2025095009
Chicago/Turabian StylePeter Dawson, John Robinson, and Wilson Arul Prakash Selvaraj. 2025. "Hamming Distance-Based Intuitionistic Fuzzy Artificial Neural Network with Novel Back Propagation Method" Engineering Proceedings 95, no. 1: 9. https://doi.org/10.3390/engproc2025095009
APA StylePeter Dawson, J. R., & Selvaraj, W. A. P. (2025). Hamming Distance-Based Intuitionistic Fuzzy Artificial Neural Network with Novel Back Propagation Method. Engineering Proceedings, 95(1), 9. https://doi.org/10.3390/engproc2025095009