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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     author = {I. S. Soldatenko},
     title = {On generalization of {Nguyen's} theorem for fuzzy numbers with unbounded support},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {17--29},
     publisher = {mathdoc},
     number = {4},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2024_4_a1/}
}
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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/