\(S\)-approximation: a new approach to algebraic approximation (Q2249956)

Summary: We intend to study a new class of algebraic approximations, called \(S\)-approximations, and their properties. We have shown that \(S\)-approximations can be used for applied problems which cannot be modeled by inclusion based approximations. Also, in this work, we studied a subclass of \(S\)-approximations, called \(S_{\mathcal{M}}\)-approximations, and showed that this subclass preserves most of the properties of inclusion based approximations but is not necessarily inclusion based. The paper concludes by studying some basic operations on \(S\)-approximations and counting the number of \(S\)-min functions.