Scales and covers in general measurement problem

A demonstration is given that in terms of representational theory the general measurement problem (GMP) can be treated as a discrete optimization problem. Moreover, particular discrete optimization problems appear at every stage of the GMP solution. There is a sufficiently compact family of problems that is universal to a considerable extent. They permit the management of many concrete practical tasks appearing in the arrangement of the measurement process with both quantitative and qualitative scales. It is demonstrated that these universal problems are covering problems. Several variants of these problems are discussed in the context of measurement with numerical examples. This approach also allows consideration from an integrated point of view of any kind of functions of measurement information systems: check, diagnosis, and pattern recognition.