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A solution for systems of linear fuzzy equations in spite of the non-existence of a field of fuzzy numbers

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Organization
Abstract
In this paper we investigate whether the fuzzy arithmetic based on Zadeh's extension principle could be improved by redefining the fuzzy addition and multiplication so that the class of fuzzy numbers combined with these operations would constitute a field. We will prove that such a fuzzy arithmetic does not exist. This has important consequences for solving systems of linear fuzzy equations. Despite the lack of inverses, we propose a method to solve approximately such systems.
Keywords
lack of inverses, field, fuzzy arithmetic, fuzzy numbers, solving systems of fuzzy linear equations

Citation

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MLA
Vroman, Annelies, Glad Deschrijver, and Etienne Kerre. “A Solution for Systems of Linear Fuzzy Equations in Spite of the Non-existence of a Field of Fuzzy Numbers.” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 13.3 (2005): 321–335. Print.
APA
Vroman, Annelies, Deschrijver, G., & Kerre, E. (2005). A solution for systems of linear fuzzy equations in spite of the non-existence of a field of fuzzy numbers. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 13(3), 321–335.
Chicago author-date
Vroman, Annelies, Glad Deschrijver, and Etienne Kerre. 2005. “A Solution for Systems of Linear Fuzzy Equations in Spite of the Non-existence of a Field of Fuzzy Numbers.” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 13 (3): 321–335.
Chicago author-date (all authors)
Vroman, Annelies, Glad Deschrijver, and Etienne Kerre. 2005. “A Solution for Systems of Linear Fuzzy Equations in Spite of the Non-existence of a Field of Fuzzy Numbers.” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 13 (3): 321–335.
Vancouver
1.
Vroman A, Deschrijver G, Kerre E. A solution for systems of linear fuzzy equations in spite of the non-existence of a field of fuzzy numbers. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. WORLD SCIENTIFIC PUBL CO PTE LTD; 2005;13(3):321–35.
IEEE
[1]
A. Vroman, G. Deschrijver, and E. Kerre, “A solution for systems of linear fuzzy equations in spite of the non-existence of a field of fuzzy numbers,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 13, no. 3, pp. 321–335, 2005.
@article{321023,
  abstract     = {{In this paper we investigate whether the fuzzy arithmetic based on Zadeh's extension principle could be improved by redefining the fuzzy addition and multiplication so that the class of fuzzy numbers combined with these operations would constitute a field. We will prove that such a fuzzy arithmetic does not exist. This has important consequences for solving systems of linear fuzzy equations. Despite the lack of inverses, we propose a method to solve approximately such systems.}},
  author       = {{Vroman, Annelies and Deschrijver, Glad and Kerre, Etienne}},
  issn         = {{0218-4885}},
  journal      = {{International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems}},
  keywords     = {{lack of inverses,field,fuzzy arithmetic,fuzzy numbers,solving systems of fuzzy linear equations}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{321--335}},
  publisher    = {{WORLD SCIENTIFIC PUBL CO PTE LTD}},
  title        = {{A solution for systems of linear fuzzy equations in spite of the non-existence of a field of fuzzy numbers}},
  volume       = {{13}},
  year         = {{2005}},
}

Web of Science
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