TY - JOUR
T1 - Continuity issues of the implicational interpretation of fuzzy rules
AU - Štěpnička, Martin
AU - Bodenhofer, Ulrich
AU - Daňková, Martina
AU - Novák, Vilém
N1 - Funding Information:
This work has been supported by projects MSM6198898701 of the MŠMT Cˇ R and IAA108270902 of the GAAV Cˇ R. Significant parts of this paper have been written when Ulrich Bodenhofer was still affiliated with Software Competence Center Hagenberg GmbH (SCCH), mainly during a research visit of Martina Danˇková and Martin Šteˇpnicˇka that was supported by SCCH. Therefore, partial support by the Austrian Government, the State of Upper Austria, and the Johannes Kepler University Linz in the framework of the Kplus Competence Center Program is gratefully acknowledged.
PY - 2010/7/16
Y1 - 2010/7/16
N2 - 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.
AB - 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.
KW - Conjunctive normal form
KW - Continuity
KW - Fuzzy rules
KW - Implicational interpretation
KW - Linguistic description
UR - http://www.scopus.com/inward/record.url?scp=77955274850&partnerID=8YFLogxK
U2 - 10.1016/j.fss.2010.03.009
DO - 10.1016/j.fss.2010.03.009
M3 - Article
AN - SCOPUS:77955274850
SN - 0165-0114
VL - 161
SP - 1959
EP - 1972
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
IS - 14
ER -