@article {
author = {Alavi, S.M.},
title = {Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system},
journal = {Iranian Journal of Numerical Analysis and Optimization},
volume = {13},
number = {3},
pages = {532-552},
year = {2023},
publisher = {Ferdowsi University of Mashhad},
issn = {2423-6977},
eissn = {2423-6969},
doi = {10.22067/ijnao.2023.79051.1187},
abstract = {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.},
keywords = {Fuzzy Number of type L-R,Nearest Trapezoidal Fuzzy Number,Shape Function,Fuzzy approximation},
url = {https://ijnao.um.ac.ir/article_43823.html},
eprint = {https://ijnao.um.ac.ir/article_43823_c6b08ef6fc30ebe55469b60a4b856ced.pdf}
}