caa a22 4500 605468354 CHVBK 20210128100316.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00500-014-1243-7 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1243-7 Fuzzy LR linear systems: quadratic and least squares models to characterize exact solutions and an algorithm to compute approximate solutions [Elektronische Daten] [Reza Ghanbari, Nezam Mahdavi-Amiri] We first establish some necessary and sufficient conditions for solvability of fuzzy LR linear systems. We then propose a concept for an approximate solution when a fuzzy LR linear system lacks a solution. Recently, we have proposed an approximate solution for a fuzzy LR linear system under the condition that a corresponding crisp linear system was solvable. Here, we remove this condition by presenting a more general concept of an approximate solution based on a least squares model. We also develop the conditions for the uniqueness of the approximate solution. To compute an approximate solution, we propose an algorithm based on a quadratic programming model with bound constraints on some variables. Finally, we show numerically the appropriateness of our proposed approximate solution for large scale problems in comparison with other recently proposed approximate solutions. The numerical results show that our proposed algorithm produces significantly more accurate solutions. Springer-Verlag Berlin Heidelberg, 2014 Fuzzy linear systems nationallicence Fuzzy numbers nationallicence Approximate solution nationallicence Quadratic programming nationallicence Least squares approximation nationallicence Solvability nationallicence Ghanbari Reza Department of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box: 9177948953, Mashhad, Iran aut Mahdavi-Amiri Nezam Faculty of Mathematical Sciences, Sharif University of Technology, P. O. Box: 11155-9415, Tehran, Iran aut Soft Computing Springer Berlin Heidelberg 19/1(2015-01-01), 205-216 1432-7643 19:1<205 2015 19 500 https://doi.org/10.1007/s00500-014-1243-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1243-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ghanbari Reza Department of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box: 9177948953, Mashhad, Iran aut NATIONALLICENCE 700 1- Mahdavi-Amiri Nezam Faculty of Mathematical Sciences, Sharif University of Technology, P. O. Box: 11155-9415, Tehran, Iran aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/1(2015-01-01), 205-216 1432-7643 19:1<205 2015 19 500