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

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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

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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 -

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