Openings and closures of fuzzy preorderings: Theoretical basics and applications to fuzzy rule-based systems

Ulrich Bodenhofer; Martine De Cock; Etienne E. Kerre

doi:10.1080/0308107031000135026

Openings and closures of fuzzy preorderings: Theoretical basics and applications to fuzzy rule-based systems

Ulrich Bodenhofer^*
, Martine De Cock
, Etienne E. Kerre

^*Corresponding author for this work

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

56 Citations (Scopus)

Abstract

The purpose of this paper is two-fold. Firstly, a general concept of closedness of fuzzy sets under fuzzy preorderings is proposed and investigated along with the corresponding opening and closure operators. Secondly, the practical impact of this notion is demonstrated by applying it to the analysis of ordering-based modifiers.

Original language	English
Pages (from-to)	343-360
Number of pages	18
Journal	International Journal of General Systems
Volume	32
Issue number	4
DOIs	https://doi.org/10.1080/0308107031000135026
Publication status	Published - 2003
Externally published	Yes

Keywords

Closedness
Fuzzy preordering
Fuzzy relation
Linguistic modifier

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10.1080/0308107031000135026

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title = "Openings and closures of fuzzy preorderings: Theoretical basics and applications to fuzzy rule-based systems",

abstract = "The purpose of this paper is two-fold. Firstly, a general concept of closedness of fuzzy sets under fuzzy preorderings is proposed and investigated along with the corresponding opening and closure operators. Secondly, the practical impact of this notion is demonstrated by applying it to the analysis of ordering-based modifiers.",

keywords = "Closedness, Fuzzy preordering, Fuzzy relation, Linguistic modifier",

author = "Ulrich Bodenhofer and \{De Cock\}, Martine and Kerre, \{Etienne E.\}",

note = "Funding Information: *Corresponding author. Fax: {\th}43-7236-3343-888. E-mail: [email protected] †This work was supported by the Kplus Competence Center Program which is funded by the Austrian Government, the Province of Upper Austria, and the Chamber of Commerce of Upper Austria. ‡This work was supported by the Fund for Scientific Research of Flanders (FWO). Parts of this work were done during a COST Action 15 short-term scientific mission of Martine De Cock at the Fuzzy Logic Laboratory Linz-Hagenberg in April 2000.",

year = "2003",

doi = "10.1080/0308107031000135026",

language = "English",

volume = "32",

pages = "343--360",

journal = "International Journal of General Systems",

issn = "0308-1079",

publisher = "Taylor and Francis Ltd.",

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TY - JOUR

T1 - Openings and closures of fuzzy preorderings

T2 - Theoretical basics and applications to fuzzy rule-based systems

AU - Bodenhofer, Ulrich

AU - De Cock, Martine

AU - Kerre, Etienne E.

N1 - Funding Information: *Corresponding author. Fax: þ43-7236-3343-888. E-mail: [email protected] †This work was supported by the Kplus Competence Center Program which is funded by the Austrian Government, the Province of Upper Austria, and the Chamber of Commerce of Upper Austria. ‡This work was supported by the Fund for Scientific Research of Flanders (FWO). Parts of this work were done during a COST Action 15 short-term scientific mission of Martine De Cock at the Fuzzy Logic Laboratory Linz-Hagenberg in April 2000.

PY - 2003

Y1 - 2003

N2 - The purpose of this paper is two-fold. Firstly, a general concept of closedness of fuzzy sets under fuzzy preorderings is proposed and investigated along with the corresponding opening and closure operators. Secondly, the practical impact of this notion is demonstrated by applying it to the analysis of ordering-based modifiers.

AB - The purpose of this paper is two-fold. Firstly, a general concept of closedness of fuzzy sets under fuzzy preorderings is proposed and investigated along with the corresponding opening and closure operators. Secondly, the practical impact of this notion is demonstrated by applying it to the analysis of ordering-based modifiers.

KW - Closedness

KW - Fuzzy preordering

KW - Fuzzy relation

KW - Linguistic modifier

UR - https://www.scopus.com/pages/publications/5644293155

U2 - 10.1080/0308107031000135026

DO - 10.1080/0308107031000135026

M3 - Article

AN - SCOPUS:5644293155

SN - 0308-1079

VL - 32

SP - 343

EP - 360

JO - International Journal of General Systems

JF - International Journal of General Systems

IS - 4

ER -

Openings and closures of fuzzy preorderings: Theoretical basics and applications to fuzzy rule-based systems

Abstract

Keywords

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