Yager’s classes of fuzzy implications: some properties and intersections

Michał Baczyński; Balasubramaniam Jayaram

Kybernetika (2007)

  • Volume: 43, Issue: 2, page 157-182
  • ISSN: 0023-5954

Abstract

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Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager2004] has introduced two new classes of fuzzy implications called the f -generated and g -generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the h -generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships amongst themselves and with the well established ( S , N ) -implications and R -implications. In the cases where they intersect the precise sub-families have been determined.

How to cite

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Baczyński, Michał, and Jayaram, Balasubramaniam. "Yager’s classes of fuzzy implications: some properties and intersections." Kybernetika 43.2 (2007): 157-182. <http://eudml.org/doc/33849>.

@article{Baczyński2007,
abstract = {Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager2004] has introduced two new classes of fuzzy implications called the $f$-generated and $g$-generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the $h$-generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships amongst themselves and with the well established $(S,N)$-implications and $R$-implications. In the cases where they intersect the precise sub-families have been determined.},
author = {Baczyński, Michał, Jayaram, Balasubramaniam},
journal = {Kybernetika},
keywords = {fuzzy implication; $f$-generated implication; $g$-generated implication; $h$-generated implication; $(S;N)$-implication; $S$-implication; $R$-implication; fuzzy implications},
language = {eng},
number = {2},
pages = {157-182},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Yager’s classes of fuzzy implications: some properties and intersections},
url = {http://eudml.org/doc/33849},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Baczyński, Michał
AU - Jayaram, Balasubramaniam
TI - Yager’s classes of fuzzy implications: some properties and intersections
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 2
SP - 157
EP - 182
AB - Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager2004] has introduced two new classes of fuzzy implications called the $f$-generated and $g$-generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the $h$-generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships amongst themselves and with the well established $(S,N)$-implications and $R$-implications. In the cases where they intersect the precise sub-families have been determined.
LA - eng
KW - fuzzy implication; $f$-generated implication; $g$-generated implication; $h$-generated implication; $(S;N)$-implication; $S$-implication; $R$-implication; fuzzy implications
UR - http://eudml.org/doc/33849
ER -

References

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  2. Balasubramaniam J., Contrapositive symmetrization of fuzzy implications – Revisited, Fuzzy Sets and Systems 157 (2006), 2291–2310 MR2251837
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  8. Klir G. J., Yuan, Bo, Fuzzy Sets and Fuzzy Logic, Theory and Applications. Prentice Hall, Englewood Cliffs, N.J. 1995 Zbl0915.03001MR1329731
  9. Pei D., R 0 implication: characteristics and applications, Fuzzy Sets and Systems 131 (2002), 297-302 Zbl1015.03034MR1939842
  10. Trillas E., Valverde L., On some functionally expressable implications for fuzzy set theory, In: Proc. 3rd Internat. Seminar on Fuzzy Set Theory (E. P. Klement, ed.), Johannes Kepler Universität, Linz 1981, pp. 173–190 (1981) Zbl0498.03015MR0646807
  11. Türksen I. B., Kreinovich, V., Yager R. R., A new class of fuzzy implications – Axioms of fuzzy implication revisited, Fuzzy Sets and Systems 100 (1998), 267–272 (1998) Zbl0939.03030MR1663741
  12. Yager R. R., On some new classes of implication operators and their role in approximate reasoning, Inform. Sci. 167 (2004), 193–216 Zbl1095.68119MR2103181

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