Intersections Between Basic Families of Fuzzy Implications: (S, N)-, R- and QL-Implications

In this work, our primary focus is to determine the intersections that exist between the family of QL-implications and the families of (S, N)- and R-implications. Toward this end, firstly, we investigate the conditions under which a QL-operation becomes a fuzzy implication. Since the exchange principle and the ordering property of fuzzy implications play an important role in this study, we propose some necessary and/or sufficient conditions on the underlying operations under which QL-operations satisfy them. As part of this attempt some interesting results pertaining to natural negations from t-conorms and the exact intersection between (S, N)and R-implications have been obtained. We also mention some open problems relating to QL-implications.

• Type: Conference
• Year: 2007
• Where: EUSFLAT
• Authors: Balasubramaniam Jayaram, Michal Baczynski
• Keywords: EUSFLAT 2007, Exchange Principle, Fuzzy Implications, Primary Focus