Continuity issues of the implicational interpretation of fuzzy rules

Authors:
Martin Štěpnička;Ulrich Bodenhofer;Martina Daňková;Vilém Novák
Affiliations:
Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic;Institute of Bioinformatics, Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria;Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic;Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
Venue:
Fuzzy Sets and Systems
Year:
2010

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Abstract

The implicational interpretation of fuzzy rules has received little attention in real-world applications so far. This is largely due to the fact that ensuring continuity of the resulting function is not a straightforward task. This paper targets this subject. Departing from consistent linguistic descriptions/rule bases, we introduce sufficient conditions for the continuity of the implicational interpretation with mean of maximum defuzzification. We demonstrate that continuity can be achieved under practically feasible conditions, regardless of the dimensionality of the input.