Geodesic
Mathematical models for performing unified arithmetic operations with fuzzy numbers in the formalization of expert knowledge
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 75-84

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The paper considers fuzzy representation and manipulation of explicit and implicit expert knowledge. It proposes to use fuzzy numbers that allow describing uncertainty factors. It also presents a new form of specifying symmetrized forms of representation of fuzzy numbers, as well as extended and additional arithmetic operations on them which preserve the original level of fuzzy knowledge of experts and simplify the process of their formalization in solving applied problems.
Keywords: fuzzy numbers, extended and additional arithmetic operations, simulation modeling, accuracy, reliability, adequacy of the model, complex technical system. 
@article{VYURM_2024_16_4_a8,
     author = {A. V. Spesivtsev and B. V. Sokolov},
     title = {Mathematical models for performing unified arithmetic operations with fuzzy numbers in the formalization of expert knowledge},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {75--84},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2024_16_4_a8/}
}
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A. V. Spesivtsev; B. V. Sokolov. Mathematical models for performing unified arithmetic operations with fuzzy numbers in the formalization of expert knowledge. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 16 (2024) no. 4, pp. 75-84. http://geodesic.mathdoc.fr/item/VYURM_2024_16_4_a8/