Unless specified otherwise, by “manifolds” and “varieties” we shall always mean, respectively, complex manifolds and complex algebraic varieties. Consequently, “dimension” (of a manifold or variety) always refers to the complex dimension. We also fix, once and for all, a commutative Noetherian ring k of finite global dimension as our ring of “coefficients”; the reader is welcome to take k = Z,Q...

the pioneer work of image compression/reconstruction based onfuzzy relational equations (icf) and the related works are introduced. theicf regards an original image as a fuzzy relation by embedding the brightnesslevel into [0,1]. the compression/reconstruction of icf correspond to thecomposition/solving inverse problem formulated on fuzzy relational equations.optimizations of icf can be consequ...