|تعداد مشاهده مقاله||9,734,115|
|تعداد دریافت فایل اصل مقاله||6,365,037|
Symmetric implicational algorithm derived from intuitionistic fuzzy entropy
|Iranian Journal of Fuzzy Systems|
|مقاله 4، دوره 19، شماره 4، مهر و آبان 2022، صفحه 27-44 اصل مقاله (245.98 K)|
|نوع مقاله: Research Paper|
|شناسه دیجیتال (DOI): 10.22111/ijfs.2022.7084|
|Y. M. Tang* 1؛ L. Zhang1؛ G. Q. Bao1؛ F. J. Ren2؛ W. Pedrycz3|
|1Key Laboratory of Knowledge Engineering with Big Data of Ministry of Education, School of Computer and Information, Hefei University of Technology, Hefei, 230601, P.R.China|
|2Institute of Technology and Science, the University of Tokushima, 770-8506, Japan|
|3Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia|
|On account of the idea of maximum fuzzy entropy and symmetric implicational mechanism under the environment of intuitionistic fuzzy sets, we come up with the intuitionistic fuzzy entropy derived symmetric implicational (IFESI) algorithm. Above all, novel symmetric implicational principles are presented, and the unified solutions of the IFESI algorithm are acquired for IFMP (intuitionistic fuzzy modus ponens) and IFMT (intuitionistic fuzzy modus ponens), which build upon in view of residual intuitionistic implications. Thereafter, the reductive properties and continuity of the IFESI algorithm are validated for IFMP and IFMT. In addition, the IFESI algorithm is extended to the $\alpha$-IFESI algorithm, and the unified solutions of the $\alpha$-IFESI algorithm are obtained for IFMP and IFMT. Finally, two examples of fuzzy classification for the $\alpha$-IFESI algorithm are presented to demonstrate the detailed computing process of the IFESI algorithm.|
|Fuzzy reasoning؛ intuitionistic fuzzy entropy؛ compositional rule of inference؛ symmetric implicational algorithm؛ reductive property؛ continuity|
 J. Andreu-Perez, F. Cao, H. Hagras, G. Z. Yang, A self-adaptive online brain-machine interface of a humanoid robot through a general type-2 fuzzy inference system, IEEE Transactions on Fuzzy Systems, 26 (2018), 101-116.
 K. K. Ang, Q. Chai, M. Pasquier, POPFNN-CRI(S): Pseudo outer product based fuzzy neural network using the compositional rule of inference and singleton fuzzifier, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 33 (2003), 838-849.
 K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
 K. Atanassov, Intuitionistic fuzzy sets: Theory and applications, Physica-Verlag, Heidelberg, Springer, 1999.
 M. Baczyński, B. Jayaram, On the characterizations of (S,N)-implications, Fuzzy Sets and Systems, 158 (2007), 1713-1727.
 P. Burillo, H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems, 78 (1996), 305-316.
 C. Cornelis, G. Deschrijver, E. E. Kerre, Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: Construction, classification, application, International Journal of Approximate Reasoning, 35 (2004), 55-95.
 S. S. Dai, Logical foundation of symmetric implicational methods for fuzzy reasoning, Journal of Intelligent and Fuzzy Systems, 39 (2020), 1089-1095.
 G. Deschrijver, C. Cornelis, E. E. Kerre, Class of intuitionistic fuzzy t-norms satisfying the residuation principle, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 11 (2003), 691-709.
 G. Deschrijver, C. Cornelis, E. E. Kerre, On the representation of intuitionistic fuzzy t-norms and t-conorms, IEEE Transactions on Fuzzy Systems, 12 (2004), 45-61.
 J. Fodor, M. Roubens, Fuzzy preference modeling and multicriteria decision support, Kluwer Academic Publishers, Dordrecht, 1994.
 D. H. Hong, S. Y. Hwang, A note on the value similarity of fuzzy systems variable, Fuzzy Set and Systems, 66 (1994), 383-386.
 E. P. Klement, R. Mesiar, E. Pap, Triangular norms, Kluwer Academic Publishers, Dordrecht, 2000.
 H. W. Liu, New similarity measures between intuitionistic fuzzy sets and between elements, Mathematical and Computer Modelling, 42 (2005), 61-70.
 M. X. Luo, B. Liu, Robustness of interval-valued fuzzy inference triple I algorithms based on normalized Minkowski distance, Journal of Logical and Algebraic Methods, 86 (2017), 298-307.
 M. X. Luo, Y. J. Wang, Interval-valued fuzzy reasoning full implication algorithms based on the t-representable t-norm, International Journal of Approximate Reasoning, 122 (2020), 1-8.
 M. X. Luo, Y. J. Wang, R. R. Zhao, Interval-valued fuzzy reasoning method based on similarity measure, Journal of Logical and Algebraic Methods, 113 (2020), 100541.
 M. Mas, M. Monserrat, J. Torrens, E. Trillas, A survey on fuzzy implication functions, IEEE Transactions on Fuzzy Systems, 15 (2007), 1107-1121.
 P. Melo-Pinto, P. Couto, H. Bustince, et al., Image segmentation using Atanassov’s intuitionistic fuzzy sets, Expert Systems and Applications, 40 (2013), 15-26.
 D. W. Pei, Unified full implication algorithms of fuzzy reasoning, Information Sciences, 178 (2008), 520-530.
 D. W. Pei, Formalization of implication based fuzzy reasoning method, International Journal of Approximate Reasoning, 53 (2012), 837-846.
 E. Szmidt, J. Kacprzyk, Entropy for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 118 (2001), 467-477.
 Y. M. Tang, X. H. Hu, W. Pedrycz, X. C. Song, Possibilistic fuzzy clustering with high-density viewpoint, Neurocomputing, 329 (2019), 407-423.
 Y. M. Tang, W. Pedrycz, On the α(u,v)-symmetric implicational method for R- and (S, N)-implications, International Journal of Approximate Reasoning, 92 (2018), 212-231.
 Y. M. Tang, W. Pedrycz, Oscillation bound estimation of perturbations under Bandler-Kohout subproduct, IEEE Transactions on Cybernetics, (2021). DOI: 10.1109/TCYB.2020.3025793.
 Y. M. Tang, F. J. Ren, W. Pedrycz, Fuzzy c-means clustering through SSIM and patch for image segmentation, Applied Soft Computing, 87 (2020), 1-16.
 Y. M. Tang, X. Z. Yang, Symmetric implicational method of fuzzy reasoning, International Journal of Approximate Reasoning, 54 (2013), 1034-1048.
 M. Verma, K. K. Shukla, Fuzzy metric space induced by intuitionistic fuzzy points and its application to the orienteering problem, IEEE Transactions on Fuzzy Systems, 24 (2016), 483-488.
 G. J. Wang, On the logic foundation of fuzzy reasoning, Information Sciences, 117 (1999), 47-88.
 G. J. Wang, Formalized theory of general fuzzy reasoning, Information Sciences, 160 (2004), 251-266.
 G. J. Wang, J. Y. Duan, On robustness of the full implication triple I inference method with respect to finer measurements, International Journal of Approximate Reasoning, 55 (2014), 787-796.
 G. J. Wang, L. Fu, Unified forms of triple I method, Computers and Mathematics with Applications, 49 (2005), 923-932.
 X. Y. Yang, F. S. Yu, W. Pedrycz, Long-term forecasting of time series based on linear fuzzy information granules and fuzzy inference system, International Journal of Approximate Reasoning, 81 (2017), 1-27.
 L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems, Man, and Cybernetics, 3 (1973), 28-44.
 J. C. Zhang, X. Y. Yang, Some properties of fuzzy reasoning in propositional fuzzy logic systems, Information Sciences, 180 (2010), 4661-4671.
 M. C. Zheng, Z. K. Shi, Y. Liu, Triple I methods of approximate reasoning on Atanassov’s intuitionistic fuzzy sets, International Journal of Approximate Reasoning, 55 (2014), 1369-1382.
تعداد مشاهده مقاله: 23,874
تعداد دریافت فایل اصل مقاله: 8,545