Implications Generated by Triples of Monotone Functions

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 228)


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.


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Dept. of MathematicsFEEC Brno Uni. of TechnologyBrnoCzech Republic
  2. 2.Faculty of Civil Engineering, Department of MathematicsSlovak University of Technology in BratislavaBratislavaSlovakia
  3. 3.Dept. of Quantitative Methods and Information Systems, Faculty of EconomicsMatej Bel UniversityBanská BystricaSlovakia

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