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Z-Numbers and Type-2 Fuzzy Sets: A Representation Result


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Abstract

Traditional [0; 1] based fuzzy sets were originally invented to describe expert knowledge expressed in terms of imprecise “fuzzy” words from the natural language. To make this description more adequate, several generalizations of the traditional [0; 1] based fuzzy sets have been proposed, among them type-2 fuzzy sets and Z-numbers. The main objective of this paper is to study the relation between these two generalizations. As a result of this study, we show that if we apply data processing to Z-numbers, then we get type-2 sets of special type —that we call monotonic. We also prove that every monotonic type-2 fuzzy set can be represented as a result of applying an appropriate data processing algorithm to some Z-numbers.


Keywords


Pages

Total Pages: 5
Pages: 205-210

DOI
10.1080/10798587.2017.1330310


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Published

Volume: 24
Issue: 1
Year: 2018

Cite this document


References

Aliev, Rafik A et al. "The Arithmetic of Z-Numbers." (2015): n. pag. Crossref. Web. https://doi.org/10.1142/9575

Klir G. Fuzzy sets and fuzzy logic

Mendel J.M. Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions

Mendel, Jerry M., and Dongrui Wu. "Perceptual Computing." (2010): n. pag. Crossref. Web. https://doi.org/10.1002/9780470599655

Nguyen H.T. A First Course in Fuzzy Logic

Nguyen, Hung T., Vladik Kreinovich, and Qiang Zuo. "Interval-Valued Degrees of Belief: Applications of Interval Computations to Expert Systems and Intelligent Control." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05.03 (1997): 317-358. Crossref. Web. https://doi.org/10.1142/S0218488597000257

Zadeh, L.A. "Fuzzy Sets." Information and Control 8.3 (1965): 338-353. Crossref. Web. https://doi.org/10.1016/S0019-9958(65)90241-X

Zadeh, Lotfi A. "A Note on Z-Numbers." Information Sciences 181.14 (2011): 2923-2932. Crossref. Web. https://doi.org/10.1016/j.ins.2011.02.022

JOURNAL INFORMATION


ISSN PRINT: 1079-8587
ISSN ONLINE: 2326-005X
DOI PREFIX: 10.31209
10.1080/10798587 with T&F
IMPACT FACTOR: 0.652 (2017/2018)
Journal: 1995-Present




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