Generalized modus ponens using Fodor's implication

Authors:
Ion Iancu
Affiliations:
University of Craiova, Faculty of Mathematics and Computer Science, Craiova, Romania
Venue:
ICAI'08 Proceedings of the 9th WSEAS International Conference on International Conference on Automation and Information
Year:
2008

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Abstract

Using generalized modus ponens reasoning, we examine the values of the inferred conclusion using the Fodor's implication in order to interpret a fuzzy if-then rule with a single input single output and the t-norm t(x,y) = max(1+λ)(x+y-1)-λxy,0), λ ≥ -1, for composition operation. This t-norm is important to use because for λ = -1 and λ = 0 it gives the very used t-norms t1(x,y) = xy and t2(x,y) = max(0,x+y-1), respectively.