On Fuzzy Concepts

C. Hoede, X. Wang

Research output: Book/ReportReportProfessional

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Abstract

In this paper we try to combine two approaches. One is the theory of knowledge graphs in which concepts are represented by graphs. The other is the axiomatic theory of fuzzy sets (AFS). The discussion will focus on the idea of fuzzy concept. It will be argued that the fuzziness of a concept in natural language is mainly due to the difference in interpretation that people give to a certain word. As different interpretations lead to different knowledge graphs, the notion of fuzzy concept should be describable in terms of sets of graphs. This leads to a natural introduction of membership values for elements of graphs. Using these membership values we apply AFS theory as well as an alternative approach to calculate fuzzy decision trees, that can be used to determine the most relevant elements of a concept.
Original languageUndefined
Place of PublicationEnschede
PublisherToegepaste Wiskunde
Number of pages29
Publication statusPublished - Dec 2006

Publication series

NameApplied Mathematics Memoranda
PublisherDepartment of Applied Mathematics, University of Twente
No.1814
ISSN (Print)0169-2690

Keywords

  • IR-66585
  • EWI-8066
  • METIS-237581
  • MSC-05C99
  • MSC-03E72

Cite this

Hoede, C., & Wang, X. (2006). On Fuzzy Concepts. (Applied Mathematics Memoranda; No. 1814). Enschede: Toegepaste Wiskunde.
Hoede, C. ; Wang, X. / On Fuzzy Concepts. Enschede : Toegepaste Wiskunde, 2006. 29 p. (Applied Mathematics Memoranda; 1814).
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Hoede, C & Wang, X 2006, On Fuzzy Concepts. Applied Mathematics Memoranda, no. 1814, Toegepaste Wiskunde, Enschede.

On Fuzzy Concepts. / Hoede, C.; Wang, X.

Enschede : Toegepaste Wiskunde, 2006. 29 p. (Applied Mathematics Memoranda; No. 1814).

Research output: Book/ReportReportProfessional

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N2 - In this paper we try to combine two approaches. One is the theory of knowledge graphs in which concepts are represented by graphs. The other is the axiomatic theory of fuzzy sets (AFS). The discussion will focus on the idea of fuzzy concept. It will be argued that the fuzziness of a concept in natural language is mainly due to the difference in interpretation that people give to a certain word. As different interpretations lead to different knowledge graphs, the notion of fuzzy concept should be describable in terms of sets of graphs. This leads to a natural introduction of membership values for elements of graphs. Using these membership values we apply AFS theory as well as an alternative approach to calculate fuzzy decision trees, that can be used to determine the most relevant elements of a concept.

AB - In this paper we try to combine two approaches. One is the theory of knowledge graphs in which concepts are represented by graphs. The other is the axiomatic theory of fuzzy sets (AFS). The discussion will focus on the idea of fuzzy concept. It will be argued that the fuzziness of a concept in natural language is mainly due to the difference in interpretation that people give to a certain word. As different interpretations lead to different knowledge graphs, the notion of fuzzy concept should be describable in terms of sets of graphs. This leads to a natural introduction of membership values for elements of graphs. Using these membership values we apply AFS theory as well as an alternative approach to calculate fuzzy decision trees, that can be used to determine the most relevant elements of a concept.

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Hoede C, Wang X. On Fuzzy Concepts. Enschede: Toegepaste Wiskunde, 2006. 29 p. (Applied Mathematics Memoranda; 1814).