Contrapositive symmetry of distributive fuzzy implications

Authors:
Michal Baczyński
Affiliations:
Institute of Mathematics, University of Silesia, 40-007 Katowice, ul. Bankowa 14, Poland
Venue:
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Year:
2002

Citing 6
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Abstract

Recently, we have examined the solutions of the system of the functional equations I(x, T(y,z)) = T(I(x,y), I(x,z)), I(x, I(y,z)) = I(T(x,y),z), where T: [0,1]2 → [0,1] is a strict t-norm and I : [0,1]2 → [0,1] is a non-continuous fuzzy implication. In this paper we continue these investigations for contrapositive implications, i.e. functions which satisfy the functional equation I(x, y) = I(N(y), N(x)), with a strong negation N : [0,1] → [0,1]. We show also the bounds for two classes of fuzzy implications which are connected with our investigations.