The Compositional Rule of Inference and Zadeh’s Extension Principle for Non-normal Fuzzy Sets

P.M. van den Broek; J.A.R. Noppen

doi:10.1007/978-3-540-72434-6_63

The Compositional Rule of Inference and Zadeh’s Extension Principle for Non-normal Fuzzy Sets

P.M. van den Broek, J.A.R. Noppen

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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Abstract

Defining the standard Boolean operations on fuzzy Booleans with the compositional rule of inference (CRI) or Zadeh's extension principle gives counter-intuitive results. We introduce and motivate a slight adaptation of the CRI, which only effects the results for non-normal fuzzy sets. It is shown that the adapted CRI gives the expected results for the standard Boolean operations on fuzzy Booleans. As a second application, we show that the adapted CRI enables a don't-care value in approximate reasoning. From the close connection between the CRI and Zadeh's extension principle, we derive an adaptation of the extension principle, which, like the modified CRI, also gives the expected Boolean operations on fuzzy Booleans.

Original language	Undefined
Title of host publication	Theoretical Advances and Applications of Fuzzy Logic and Soft Computing
Editors	Oscar Castillo
Place of Publication	Berlin Heidelberg, Germany
Publisher	Springer
Pages	621-628
Number of pages	8
ISBN (Print)	978-3-540-72433-9
DOIs	https://doi.org/10.1007/978-3-540-72434-6_63
Publication status	Published - 2007

Publication series

Name	Advances in Soft Computing
Publisher	Springer
Number	7/42
Volume	42
ISSN (Print)	1615-3871

Keywords

SE-SC: Soft Computing applied to Software Engineering
METIS-246020
IR-62172
EWI-11918

Access to Document

10.1007/978-3-540-72434-6_63

ifsa2007final-paper_128

Cite this

van den Broek, P. M., & Noppen, J. A. R. (2007). The Compositional Rule of Inference and Zadeh’s Extension Principle for Non-normal Fuzzy Sets. In O. Castillo (Ed.), Theoretical Advances and Applications of Fuzzy Logic and Soft Computing (pp. 621-628). Article 10.1007/978-3-540-72434-6_63 (Advances in Soft Computing; Vol. 42, No. 7/42). Springer. https://doi.org/10.1007/978-3-540-72434-6_63

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van den Broek, PM & Noppen, JAR 2007, The Compositional Rule of Inference and Zadeh’s Extension Principle for Non-normal Fuzzy Sets. in O Castillo (ed.), Theoretical Advances and Applications of Fuzzy Logic and Soft Computing., 10.1007/978-3-540-72434-6_63, Advances in Soft Computing, no. 7/42, vol. 42, Springer, Berlin Heidelberg, Germany, pp. 621-628. https://doi.org/10.1007/978-3-540-72434-6_63

The Compositional Rule of Inference and Zadeh’s Extension Principle for Non-normal Fuzzy Sets. / van den Broek, P.M.; Noppen, J.A.R.
Theoretical Advances and Applications of Fuzzy Logic and Soft Computing. ed. / Oscar Castillo. Berlin Heidelberg, Germany: Springer, 2007. p. 621-628 10.1007/978-3-540-72434-6_63 (Advances in Soft Computing; Vol. 42, No. 7/42).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

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van den Broek PM, Noppen JAR. The Compositional Rule of Inference and Zadeh’s Extension Principle for Non-normal Fuzzy Sets. In Castillo O, editor, Theoretical Advances and Applications of Fuzzy Logic and Soft Computing. Berlin Heidelberg, Germany: Springer. 2007. p. 621-628. 10.1007/978-3-540-72434-6_63. (Advances in Soft Computing; 7/42). doi: 10.1007/978-3-540-72434-6_63