Continuity issues of the implicational interpretation of fuzzy rules

Martin Štěpnička, Ulrich Bodenhofer, Martina Daňková, Vilém Novák

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1959-1972
Number of pages14
JournalFuzzy Sets and Systems
Issue number14
Publication statusPublished - 16 Jul 2010
Externally publishedYes


  • Conjunctive normal form
  • Continuity
  • Fuzzy rules
  • Implicational interpretation
  • Linguistic description


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