Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system
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 inequali...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2023-09-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_43823_c6b08ef6fc30ebe55469b60a4b856ced.pdf |
| Summary: | 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. |
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| ISSN: | 2423-6977 2423-6969 |