Algebraic framework of an optimization problem in diagnosis

A formal analysis of an optimization problem in medical diagnosis is presented. The mathematical model of the diagnostic process corresponds in this work to an abstract machine definition which is based on the following sets and functions: Set of possible pathological states (diseases) of a patient, set of diagnostic tests (examination methods), set of all possible results of the tests (symptoms and signs), function which chooses successive tests, function performing a test (i.e., assigning to a given test its result), function assigning to each symptom a certain subset of the set of diseases. For a given abstract machine a class of pairs of graphs is formed; their analysis leads to the identification of a class of pairs of subgraphs which corresponds to an optimized diagnostic procedure. The optimization consists of a comparison of the distances between the initial and terminal vertices of the graphs and of a choice of a shortest route to a final diagnosis. For the considered class of pairs of subgraphs a mathematical model of the optimized diagnostic process is reconstructed.