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NEW GENERALIZED $h$ -IMPLICATIONS

  • D. PEI (a1) and Y. ZHU (a1)
Abstract

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.

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[1] Baczyński, M. and Jayaram, B., “Yager’s classes of fuzzy implications: some properties and intersections”, Kybernetika 43 (2007) 157182; http://eudml.org/doc/33849.
[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.
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The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
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