Symmetric implicational restriction method of fuzzy inference

Yiming Tang; Wenbin Wu; Youcheng Zhang; Witold Pedrycz; Fuji Ren; Jun Liu

Kybernetika (2021)

  • Volume: 57, Issue: 4, page 688-713
  • ISSN: 0023-5954

Abstract

top
The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy implications. The conditions are obtained for the supremum to become the maximum (or the infimum to be the minimum). Lastly, four concrete examples are provided, and it is shown that the new method is better than the triple I restriction method, because the former is able to let the inference more compact, and lead to more and superior particular inference schemes.

How to cite

top

Tang, Yiming, et al. "Symmetric implicational restriction method of fuzzy inference." Kybernetika 57.4 (2021): 688-713. <http://eudml.org/doc/297737>.

@article{Tang2021,
abstract = {The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy implications. The conditions are obtained for the supremum to become the maximum (or the infimum to be the minimum). Lastly, four concrete examples are provided, and it is shown that the new method is better than the triple I restriction method, because the former is able to let the inference more compact, and lead to more and superior particular inference schemes.},
author = {Tang, Yiming, Wu, Wenbin, Zhang, Youcheng, Pedrycz, Witold, Ren, Fuji, Liu, Jun},
journal = {Kybernetika},
keywords = {fuzzy inference; fuzzy entropy; compositional rule of inference; continuity},
language = {eng},
number = {4},
pages = {688-713},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Symmetric implicational restriction method of fuzzy inference},
url = {http://eudml.org/doc/297737},
volume = {57},
year = {2021},
}

TY - JOUR
AU - Tang, Yiming
AU - Wu, Wenbin
AU - Zhang, Youcheng
AU - Pedrycz, Witold
AU - Ren, Fuji
AU - Liu, Jun
TI - Symmetric implicational restriction method of fuzzy inference
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 4
SP - 688
EP - 713
AB - The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy implications. The conditions are obtained for the supremum to become the maximum (or the infimum to be the minimum). Lastly, four concrete examples are provided, and it is shown that the new method is better than the triple I restriction method, because the former is able to let the inference more compact, and lead to more and superior particular inference schemes.
LA - eng
KW - fuzzy inference; fuzzy entropy; compositional rule of inference; continuity
UR - http://eudml.org/doc/297737
ER -

References

top
  1. Baczyński, M., Jayaram, B., , Fuzzy Sets Syst. 158 (2007), 1713-1727. DOI
  2. Dai, S. S., , J. Intell. Fuzzy Syst. 39 (2020), 1089-1095. DOI
  3. Dai, S. S., Pei, D. W., Guo, D. H., , Int. J. Approx. Reason. 54 (2013), 653-666. DOI
  4. Fodor, J., Roubens, M., Fuzzy Preference Modeling and Multicriteria Decision Support., Kluwer Academic Publishers, Dordrecht, 1994. 
  5. Hájek, P., Metamathematics of Fuzzy Logic., Kluwer Academic Publishers, Dordrecht, 1998. Zbl1007.03022
  6. Hou, J., You, F., Li, H. X., , Prog. Nat. Sci. 15 (2005), 29-37. DOI
  7. Li, H. X., , Sci. China Ser. F Inf. Sci. 49 (2006), 339-363. DOI
  8. Li, D. C., Li, Y. M., , Int. J. Approx. Reason. 53 (2012) 892-900. DOI
  9. Li, H. X., You, F., Peng, J. Y., , Prog. Nat. Sci. 14 (2004), 15-20. DOI
  10. Liu, H. W., Wang, G. J., , Inf. Sci. 177 (2007), 956-966. DOI
  11. Luo, M. X., Liu, B., , J. Log. Algebr. Methods 86 (2017), 298-307. DOI
  12. Luo, M. X., Yao, N., , Int. J. Approx. Reason. 54 (2013), 640-652. DOI
  13. Luo, M. X, Zhang, K., , Int. J. Approx. Reason. 62 (2015), 61-72. DOI
  14. Kaur, P., Goyal, M., Lu, J., , IEEE Trans. Fuzzy Syst. 25 (2017) 425-438. DOI
  15. Klement, E. P., Mesiar, R., Pap, E., Triangular Norms., Kluwer Academic Publishers, Dordrecht, 2000. Zbl1087.20041
  16. Mas, M., Monserrat, M., Torrens, J., Trillas, E., , IEEE Trans. Fuzzy Syst. 15 (2007), 1107-1121. DOI
  17. Novák, V., Perfilieva, I., Močkoř, J., Mathematical Principles of Fuzzy Logic., Kluwer Academic Publishes, Boston, Dordrecht, 1999. Zbl0940.03028
  18. Peng, J. Y., , Prog. Nat. Sci. 15 (2005), 539-546. DOI
  19. Song, S. J., Feng, C. B., Wu, C. X., Theory of restriction degree of triple I method with total inference rules of fuzzy reasoning., Prog. Nat. Sci. 11 (2001), 58-66. 
  20. Song, S. J., Wu, C., 10.1007/BF02714092, Sci. China, Ser. F, Inf. Sci. 45 (2002), 344-364. DOI10.1007/BF02714092
  21. Pei, D. W., , Fuzzy Set Syst. 131 (2002), 297-302. DOI
  22. Pei, D. W., , Soft Comput. 8 (2004), 539-545. DOI
  23. Pei, D. W., , Int. J. Approx. Reason. 53 (2012), 837-846. DOI
  24. Pedrycz, W., Granular Computing: Analysis and Design of Intelligent Systems., CRC Press/Francis and Taylor, Boca Raton 2013. 
  25. Pedrycz, W., , Fuzzy Set Syst. 274 (2015), 12-17. MR3355341DOI
  26. Pedrycz, W., Wang, X. M., , IEEE Trans. Fuzzy Syst. 24 (2016), 489-496. DOI
  27. Tang, Y. M., Yang, X. Z., , Int. J. Approx. Reason. 54 (2013), 1034-1048. DOI
  28. Tang, Y. M., Pedrycz, W., , Int. J. Approx. Reason. 92 (2018), 212-231. DOI
  29. Wang, L. X., A Course in Fuzzy Systems and Control., Prentice-Hall, Englewood Cliffs, NJ 1997. 
  30. Wang, G. J., , Inform. Sci. 117 (1999), 47-88. DOI
  31. Wang, G. J., Fu, L., , Comput. Math. Appl. 49 (2005), 923-932. DOI
  32. Wang, G. J., Zhou, H. J., Introduction to Mathematical Logic and Resolution Principle., Co-published by Science Press and Alpha International Science Ltd., 2009. 
  33. Zadeh, L. A., , IEEE Trans. Syst. Man Cyber. 3 (1973), 28-44. DOI

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.