Implications Generated by Triples of Monotone Functions
In this paper we deal with fuzzy implications generated via triples of monotone functions f,g,h. This idea has been presented for the first time at the IPMU 2012 conference, where we have introduced the generating formula and studied some special cases of these fuzzy implications. In our contribution we further develop this concept and study properties of generated fuzzy implications. More precisely,we study how some specific properties of generators f,g,h influence properties of the corresponding fuzzy implications.
We give also some examples of such generated fuzzy implications and examples illustrating the intersection of the system of fuzzy implications generated by this method with known types of generated fuzzy implications.
Unable to display preview. Download preview PDF.
- 10.Hájek, P.: Mathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)Google Scholar
- 13.Jayaram, B.: Contrapositive symmetrisation of fuzzy implications-revisited. Fuzzy Sets and Systems 157, 2291–2310 (2006) Google Scholar
- 14.Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms, 1st edn. Springer (2000)Google Scholar
- 22.Smutná, D.: On many valued conjunctions and implications. Journal of Electrical Engineering 50, 8–10 (1999)Google Scholar