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Abstract 
 The pioneer work of image compression/reconstruction based on fuzzy relational equations (ICF) and the related works are introduced. The ICF regards an original image as a fuzzy relation by embedding the brightness level into [0،1]. The compression/reconstruction of ICF correspond to the composition/solving inverse problem formulated on fuzzy relational equations. Optimizations of ICF can be consequently deduced based on fuzzy relational calculus، i.e.، computation time reduction/improvement of reconstructed image quality are correspond to a fast solving method/finding an approximate solution of fuzzy relational equations، respectively. Through the experiments using test images extracted from Standard Image DataBAse (SIDBA)، the effectiveness of the ICF and its optimizations are shown