Document Type : Research Paper

Authors

1 VNU University of Science, Vietnam National University, Hanoi, Vietnam.

2 UPV Universitat Politècnica de València, Spain.

3 Universidad de Valladolid, Spain.

4 VNU Information Technology Institute, Vietnam National University, Hanoi, Vietnam.

5 University of New Mexico, Gallup Campus, USA.

Abstract

In order to solve the complex decision-making problems, there are many approaches and systems based on the fuzzy theory were proposed. In 1998, Smarandache introduced the concept of single-valued neutrosophic set as a complete development of fuzzy theory. In this paper, we research on the distance measure between single-valued neutrosophic sets based on the H-max measure of Ngan et al. [8]. The proposed measure is also a distance measure between picture fuzzy sets which was introduced by Cuong in 2013 [15]. Based on the proposed measure, an Adaptive Neuro Picture Fuzzy Inference System (ANPFIS) is built and applied to the decision making for the link states in interconnection networks. In experimental evaluation on the real datasets taken from the UPV (Universitat Politècnica de València) university, the performance of the proposed model is better than that of the related fuzzy methods.

Keywords

Main Subjects

  1. Zadeh, L. A. (1965). Fuzzy sets. Information and control8(3), 338-353.
  2. Khorshidi, H. A., & Nikfalazar, S. (2017). An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysis. Applied soft computing52, 478-486.
  3. Liang, D., & Xu, Z. (2017). The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Applied soft computing60, 167-179.
  4. Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences8(3), 199-249.
  5. Coupland, S., & John, R. (2008). New geometric inference techniques for type-2 fuzzy sets. International journal of approximate reasoning49(1), 198-211.
  6. Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets Syst., 20(1), 87–96.
  7. Chen, S. M., Cheng, S. H., & Lan, T. C. (2016). A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Information sciences343-344, 15-40. DOI: 1016/j.ins.2016.01.040
  8. Ngan, R. T., Cuong, B. C., & Ali, M. (2018). H-max distance measure of intuitionistic fuzzy sets in decision making. Applied soft computing69, 393-425.
  9. Chen, S. M., & Li, T. S. (2013). Evaluating students’ answerscripts based on interval-valued intuitionistic fuzzy sets. Information sciences235, 308-322. DOI: 1016/j.ins.2012.12.031
  10. Smarandache, F. (1999). A unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic, rehoboth. American Research Press, Rehoboth.
  11. Ali, M., & Smarandache, F. (2017). Complex neutrosophic set. Neural computing and applications28(7), 1817-1834.
  12. Dat, L. Q., Thong, N. T., Ali, M., Smarandache, F., Abdel-Basset, M., & Long, H. V. (2019). Linguistic approaches to interval complex neutrosophic sets in decision making. IEEE access7, 38902-38917.
  13. Smarandache, F. (2016). Degree of dependence and independence of the (sub) components of fuzzy set and neutrosophic set. Infinite Study.
  14. Smarandache, F. (2019). Neutrosophic set is a generalization of intuitionistic fuzzy set, inconsistent intuitionistic fuzzy set (picture fuzzy set, ternary fuzzy set), pythagorean fuzzy set (atanassov’s intuitionistic fuzzy set of second type), q-rung orthopair fuzzy set, spherical fuzzy set, and n-hyperspherical fuzzy set, while neutrosophication is a generalization of regret theory, grey system theory, and three-ways decision (revisited). Infinite Study.
  15. Cuong, B. C., & Kreinovich, V. (2013, December). Picture fuzzy sets-a new concept for computational intelligence problems. 2013 third world congress on information and communication technologies (WICT 2013)(pp. 1-6). IEEE.
  16. Thong, P. H. (2015). A new approach to multi-variable fuzzy forecasting using picture fuzzy clustering and picture fuzzy rule interpolation method. InKnowledge and systems engineering (pp. 679-690). Springer, Cham. 
  17. Wei, G., & Gao, H. (2018). The generalized Dice similarity measures for picture fuzzy sets and their applications. Informatica29(1), 107-124.
  18. Cong, C. B., Ngan, R. T., & Long, L. B. (2017). Some new de morgan picture operator triples in picture fuzzy logic. Journal of computer sscience and cybernetics33(2), 143-164.
  19. Cuong, B. C., Kreinovitch, V., & Ngan, R. T. (2016, October). A classification of representable t-norm operators for picture fuzzy sets. Eighth international conference on knowledge and systems engineering (KSE)(pp. 19-24). IEEE.
  20. Khalil, A. M., Li, S. G., Garg, H., Li, H., & Ma, S. (2019). New operations on interval-valued picture fuzzy set, interval-valued picture fuzzy soft set and their applications. IEEE access7, 51236-51253.
  21. Hung, K. C. (2012). Medical pattern recognition: applying an improved intuitionistic fuzzy cross-entropy approach. Advances in fuzzy systems, 863549. 1-6. DOI: 1155/2012/863549
  22. Mao, J., Yao, D., & Wang, C. (2013). A novel cross-entropy and entropy measures of IFSs and their applications. Knowledge-based systems48, 37-45.
  23. Maheshwari, S., & Srivastava, A. (2016). Study on divergence measures for intuitionistic fuzzy sets and its application in medical diagnosis. Journal of applied analysis and computation6(3), 772-789.
  24. Ngan, R. T., Cuong, B. C., & Tuan, T. M. (2018, August). Medical diagnosis from images with intuitionistic fuzzy distance measures. International joint conference on rough sets(pp. 479-490). Springer, Cham.
  25. Alonso, M., Coll, S., Martínez, J. M., Santonja, V., López, P., & Duato, J. (2010). Power saving in regular interconnection networks. Parallel computing36(12), 696-712.
  26. Alonso, M., Coll, S., Martínez, J. M., Santonja, V., & López, P. (2015). Power consumption management in fat-tree interconnection networks. Parallel computing48, 59-80.
  27. Phan, H. P., Tran, X. T., & Yoneda, T. (2017, May). Power consumption estimation using VNOC2. 0 simulator for a fuzzy-logic based low power Network-on-Chip. 2017 IEEE international conference on IC design and technology (ICICDT)(pp. 1-4). IEEE.
  28. Çaydaş, U., Hasçalık, A., & Ekici, S. (2009). An adaptive neuro-fuzzy inference system (ANFIS) model for wire-EDM. Expert systems with applications36(3), 6135-6139.
  29. Ali, M., Deo, R. C., Downs, N. J., & Maraseni, T. (2018). An ensemble-ANFIS based uncertainty assessment model for forecasting multi-scalar standardized precipitation index. Atmospheric research207, 155-180.
  30. Karaboga, D., & Kaya, E. (2019). Adaptive network based fuzzy inference system (ANFIS) training approaches: a comprehensive survey. Artificial intelligence review52(4), 2263-2293.
  31. Ali, M., Deo, R. C., Downs, N. J., & Maraseni, T. (2018). An ensemble-ANFIS based uncertainty assessment model for forecasting multi-scalar standardized precipitation index. Atmospheric research207, 155-180.
  32. Wang, W., & Xin, X. (2005). Distance measure between intuitionistic fuzzy sets. Pattern recognition letters26(13), 2063-2069.