Continuity issues of the implicational interpretation of fuzzy rules

Martin Štěpnička; Ulrich Bodenhofer; Martina Daňková; Vilém Novák

doi:10.1016/j.fss.2010.03.009

Continuity issues of the implicational interpretation of fuzzy rules

Martin Štěpnička^*, Ulrich Bodenhofer, Martina Daňková, Vilém Novák

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1959-1972
Number of pages	14
Journal	Fuzzy Sets and Systems
Volume	161
Issue number	14
DOIs	https://doi.org/10.1016/j.fss.2010.03.009
Publication status	Published - 16 Jul 2010
Externally published	Yes

Keywords

Conjunctive normal form
Continuity
Fuzzy rules
Implicational interpretation
Linguistic description

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10.1016/j.fss.2010.03.009

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title = "Continuity issues of the implicational interpretation of fuzzy rules",

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.",

keywords = "Conjunctive normal form, Continuity, Fuzzy rules, Implicational interpretation, Linguistic description",

author = "Martin {\v S}t{\v e}pni{\v c}ka and Ulrich Bodenhofer and Martina Da{\v n}kov{\'a} and Vil{\'e}m Nov{\'a}k",

note = "Funding Information: This work has been supported by projects MSM6198898701 of the M{\v S}MT 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 Danˇkov{\'a} and Martin {\v S}teˇpnicˇka 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.",

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doi = "10.1016/j.fss.2010.03.009",

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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.

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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.

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KW - Conjunctive normal form

KW - Continuity

KW - Fuzzy rules

KW - Implicational interpretation

KW - Linguistic description

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SP - 1959

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JF - Fuzzy Sets and Systems

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ER -

Continuity issues of the implicational interpretation of fuzzy rules

Abstract

Keywords

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