%0 Journal Article
%T Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system
%J Iranian Journal of Numerical Analysis and Optimization
%I Ferdowsi University of Mashhad
%Z 2423-6977
%A Alavi, S.M.
%D 2023
%\ 09/01/2023
%V 13
%N 3
%P 532-552
%! Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system
%K Fuzzy Number of type L-R
%K Nearest Trapezoidal Fuzzy Number
%K Shape Function
%K Fuzzy approximation
%R 10.22067/ijnao.2023.79051.1187
%X 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.
%U https://ijnao.um.ac.ir/article_43823_c6b08ef6fc30ebe55469b60a4b856ced.pdf