Skip to main content Accessibility help


  • D. PEI (a1) and Y. ZHU (a1)


A new generalized class of fuzzy implications, called ( $h,f,g$ )-implications, is introduced and discussed in this paper. The results show that the new fuzzy implications possess some good properties, such as the left neutrality property and the exchange principle.


Corresponding author


Hide All
[1] Baczyński, M. and Jayaram, B., “Yager’s classes of fuzzy implications: some properties and intersections”, Kybernetika 43 (2007) 157182;
[2] Baczyński, M. and Jayaram, B., Fuzzy implications (Springer, Berlin, 2008); doi:10.1007/978-3-540-69082-5.
[3] Dubois, D. and Prade, H., “Fuzzy sets in approximate reasoning (I)”, Fuzzy Sets Syst. 40 (1991) 143202; doi:10.1016/0165-0114(91)90050-Z.
[4] Fodor, J. and Torrens, J., “An overview of fuzzy logic connectives on the unit interval”, Fuzzy Sets Syst. 281 (2015) 183187; doi:10.1016/j.fss.2015.05.016.
[5] Gottwald, S., A treatise on many-valued logics, Volume 9 of Studies in Logic and Computation (Research Studies Press Ltd, Baldock, 2001).
[6] Hilnena, D., Kalina, M. and Kral, P., “A class of implications related to Yager’s $f$ -implications”, Inform. Sci. 260 (2014) 171184; doi:10.1016/j.ins.2013.09.045.
[7] Liu, H. W., “A new class of fuzzy implications derived from generalized $h$ -generators”, Fuzzy Sets Syst. 24 (2013) 6392; doi:10.1016/j.fss.2012.11.022.
[8] Mas, M., Monserrat, M., Torrens, J. and Trillas, E., “A survey on fuzzy implications functions”, IEEE Trans. Fuzzy Syst. 15 (2007) 11071121; doi:10.1109/TFUZZ.2007.896304.
[9] Massanet, S. and Torrens, J., “On the characterization of Yager’s implications”, Inform. Sci. 201 (2012) 118; doi:10.1016/j.ins.2012.03.008.
[10] Massanet, S. and Torrens, J., “On a new class of fuzzy implications: $h$ -implications and generalizations”, Inform. Sci. 181 (2014) 21112127; doi:10.1016/j.ins.2011.01.030.
[11] Pei, D., “ $R_{0}$ implication: characteristics and applications”, Fuzzy Sets Syst. 131 (2002) 297302; doi:10.1016/S0165-0114(02)00053-2.
[12] Pei, D., “The unified algorithms of triple I methods for fuzzy reasoning”, Inform. Sci. 178 (2008) 520530; doi:10.1016/j.ins.2007.09.003.
[13] Wang, G. J., “On the logic foundation of fuzzy reasoning”, Inform. Sci. 117 (1999) 4788; doi:10.1016/S0020-0255(98)10103-2.
[14] Xie, A. F. and Liu, H. W., “A generalization of Yager’s $f$ -generated implications”, Internat. J. Approx. Reason. 54 (2013) 3546; doi:10.1016/j.ijar.2012.08.005.
[15] Yager, R. R., “On some new classes of implication operators and their role in approximate reasoning”, Inform. Sci. 167 (2004) 193216; doi:10.1016/j.ins.2003.04.001.
[16] Zhu, Y. and Pei, D., “On the characterizations of D-implications”, Fuzzy Syst. Math. 29 (2015) 8898.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed