Optimizing binary questionnaires (Q1084372)

A solution to the problem of constructing optimal questionnaires is examined. The principles of choosing a root question are presented. Questionnaires are broken down into transitive and intransitive on the basis of a binary relationship presented in the set of questions. Theorems are formulated which allow the choice of a root question to be restricted for both classes. Relationships are obtained for a unique choice of root question from which an algorithm for constructing an optimal questionnaire when auxiliary conditions are satisfied is proposed and an algorithm for constructing a quasioptimal questionnaire when these conditions are not satisfied is presented.