Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system
| Autor: | S.M. Alavi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Iranian Journal of Numerical Analysis and Optimization, Vol 13, Iss 3, Pp 532-552 (2023) |
| Druh dokumentu: | article |
| ISSN: | 2423-6977 2423-6969 |
| DOI: | 10.22067/ijnao.2023.79051.1187 |
| Popis: | The fuzzy operations on fuzzy numbers of type L-R are much easier than general fuzzy numbers. It would be interesting to approximate a fuzzy number by a fuzzy number of type L-R. In this paper, we state and prove two significant application inequalities in the monotonic functions set. These inequalities show that under a condition, the nearest fuzzy number of type L-R to an arbitrary fuzzy number exists and is unique. After that, the nearest fuzzy number of type L-R can be obtained by solving a linear system. Note that the trapezoidal fuzzy numbers are a particular case of the fuzzy numbers of type L-R. The proposed method can represent the nearest trapezoidal fuzzy number to a given fuzzy number. Finally, to approximate fuzzy solutions of a fuzzy linear system, we apply our idea to construct a framework to find solutions of crisp linear systems instead of the fuzzy linear system. The crisp linear systems give the nearest fuzzy numbers of type L-R to fuzzy solutions of a fuzzy linear system. The proposed method is illustrated with some examples. |
| Databáze: | Directory of Open Access Journals |
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