Conjugacy in pattern recognition and choice problems (Q2724055)

General approaches (immersional, existential and logical) to the construction of conjugate (dual) problems of decision making and mathematical diagnostics are considered. Two of the approaches are related to hereditary existence (of solutions and generalized solutions to choice and diagnostics problems) and to sequence conditions (which provide that some inequalities are consequences of the system of some other inequalities). The paper presents a short review of models of conjugate problems of an effective choice of decision variants and their diagnosis in operations research. New models of pattern recognition and decision making problems are also given.NEWLINENEWLINENEWLINEThe models considered (all based on conjugacy) include: discrimination of sets defined parametrically (contraction method can be used for finding committee solutions of the discriminant analysis problems), committees in nonformalized problems, separation of infinite sets, choice of feature space, conjugate problems in taxonomy, descriptions of complex systems, ambiguous interpretation of contradictory information. Appropriate numerical examples are provided.NEWLINENEWLINENEWLINEIt is concluded that conjugacy in pattern recognition can help (similarly as in mathematical programming) to estimate the stability of solutions to choice and diagnosing problems and of corresponding decision rules, as well as to resolve the contradictions in the observed data and in the corresponding mathematical models.