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Operations on fuzzy numbers
Abstract
A fuzzy number is a fuzzy subset of the real line whose highest membership values are clustered around a given real number called the mean value ; the membership function is monotonia on both sides of this mean value. In this paper, the usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification principle. The practical use of fuzzified operations is shown to be easy, requiring no more computation than when dealing with error intervals in classic tolerance analysis. The field of applications of this approach seems to be large, since it allows many known algorithms to be fitted to fuzzy data.
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Citations
Cited by
Karnik, N. N., Mendel, J. M., & Liang, Q. (1999) · IEEE Transactions on Fuzzy Systems · doi:10.1109/91.811231 · Cited by 1,643
General Type-2 Fuzzy Logic Systems Made Simple: A Tutorial
Mendel, J. M. (2014) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2013.2286414 · Cited by 311
Buckley, J. J., Siler, W., & Tucker, D. (1986) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(86)80027-6 · Cited by 118
Bimodal fuzzy analytic hierarchy process (BFAHP) for coronary heart disease risk assessment
Sabahi, F. (2018) · Journal of Biomedical Informatics · doi:10.1016/j.jbi.2018.03.016 · Cited by 36
Metadata
- Authors
- DUBOIS, D., & PRADE, H.
- Venue
- International Journal of Systems Science
- Publisher
- Informa UK Limited
- Published
- 1978-06
- Volume
- 9
- Issue
- 6
- Pages
- 613-626
- ISSN
- 0020-7721 (ISSN-L)
- 1464-5319
- OpenAlex
- W2069069851
- Cited by
- 2,696
- References
- 0
- FWCI
- 9.42
- Type
- journal article
- Language
- en
- Open access
- closed
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Cite CoChat for the checks on this page, and the paper for its own findings.
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- CoChat. (2026). Citation check: Operations on fuzzy numbers. https://app.cochat.ai/papers/10.1080/00207727808941724
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- DUBOIS, D., & PRADE, H. (1978). Operations on fuzzy numbers. International Journal of Systems Science. https://doi.org/10.1080/00207727808941724
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
