Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697713320230901Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system5325524382310.22067/ijnao.2023.79051.1187ENS.M.AlaviDepartment of Mathematics, Faculty of Basic Sciences, Arak Branch, Islamic Azad University, Arak, Iran.00000001794418159Journal Article20221005The 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.https://ijnao.um.ac.ir/article_43823_c6b08ef6fc30ebe55469b60a4b856ced.pdf