Generalized modus ponens reasoning for rules with partial overlapping between premise and observation

Authors:
Ion Iancu
Affiliations:
University of Craiova, Department of Mathematics and Computer Science, Craiova, Romania
Venue:
ECC'08 Proceedings of the 2nd conference on European computing conference
Year:
2008

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Abstract

Using Generalized Modus Ponens reasoning, we examine the values of inferred conclusion when the premise of the rule and the observed fact have a partial overlapping. We work with fuzzy if-then rules 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. A set of eight implication operators are used, completing some of our previous results, where the method were used analyzing the possible inclusion relations between the premise and the observation.