Geodesic
On generalization of Nguyen's theorem for fuzzy numbers with unbounded support
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2024), pp. 17-29
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The article provides a generalization of Nguyen's theorem for identification of $\alpha$-level set of a function from fuzzy arguments through a function from their $\alpha$-levels in the case when fuzzy quantities have unbounded support. The results are specified for the simplest arithmetic operations, as well as for weighted sums of fuzzy quantities. For the weakest triangular norm, formulas are written for calculating the boundaries of these level sets.
Keywords: fuzzy values, possibilistic values, $\alpha$-level set, Nguyen's theorem, theory of possibilities, calculus of possibilities. 
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I. S. Soldatenko. On generalization of Nguyen's theorem for fuzzy numbers with unbounded support. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2024), pp. 17-29. http://geodesic.mathdoc.fr/item/VTPMK_2024_4_a1/

[1] Nguen H. T., “A note on the extension principle for fuzzy sets”, Journal of Mathematical Analysis and Applications, 64 (1978), 369–380 | DOI | MR

[2] Full$\rm\acute~e$r.R., Keresztfalvi T., “On generalization of Nguyen’s theorem”, Fuzzy Sets and Systems, 41 (1991), 371–374 | DOI | MR | Zbl

[3] Yazenin A. V., Basic concepts of the theory of possibilities. Mathematical decision-making apparatus in a hybrid uncertainty, Fizmatlit Publ., Moscow, 2016, 144 pp. (in Russian)

[4] Nahmias S., “Fuzzy variables”, Fuzzy Sets and Systems, 1:2 (1978), 97–110 | DOI | MR | Zbl

[5] Nguyen H. T., Walker C. L., Walker E. A., A First Course in Fuzzy Logic, 4th ed., CRC Press, Boca Raton, 2018 | DOI | MR | Zbl

[6] Hong D. H., “Parameter estimations of mutually t-related fuzzy variables”, Fuzzy Sets and Systems, 123:1 (2001), 63–71 | DOI | MR | Zbl

[7] Dubois D., Prade H., Theorie des Possibilites, Application a la Representation des Connaissances en Informatique, Masson, Paris, 1988 | MR

[8] Full$\rm\acute~e$r.R., Keresztfalvi T., “t-Norm-based addition of fuzzy numbers”, Fuzzy Sets and Systems, 51 (1992), 155–159 | DOI | MR

[9] Alefeld G., Herzberger J., Introduction to Interval Computation, Academic Press, 2012 | MR

[10] Yazenin A., Wagenknecht M., Possibilistic Optimization. A Measure-Based Approach, Brandenburgische Technische Universitat, Cotbus, Germany, 1996, 133 pp.