Generalized modus ponens using Fodor's implication and a parametric T-norm

Authors:
Ion Iancu
Affiliations:
Department of Mathematics and Computer Science, University of Craiova, Craiova, Romania
Venue:
WSEAS TRANSACTIONS on SYSTEMS
Year:
2008

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Abstract

Using Generalized Modus Ponens reasoning, we examine the values of the inferred conclusion by using 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)-λ≥-1, for composition operation. This t-norm is important to use because for λ=-1 and λ=0 it gives the commonly used t-norms t1(x,y)=xy and t2(x,y)=max(0,x+y-1), respectively.