Метод формалізації процесу прийняття рішення на базі теорії порогових елементів

Abstract

The conceptual principles and the theoretical substantiation of the peculiarities of the threshold elements mathematical apparatus application for the making decision of complex classification problems are formulated. This makes it possible to significantly simplify the procedure for formalizing the DSS for objects with quantitative evaluation parameters. The method of formalizing the making decision process based on the theory of threshold elements for objects with quantitative evaluation parameters is suggested, which, unlike existing approaches, in particular the method of linear weighted sums, allows us to substantiate weighting of estimating parame-ters. This allows for making decision of a clear and one-valued solution provided that the combinations of valuation parameters are incompletely checked. The process of constructing the logical function of choice is formalized and the algorithm of the transition from the logical selection function to the threshold function is proposed. Construction of the logical choice function requires the definition of its minimum disjunctive normal form. This led to the need to find the number of simple implicants that should have this form of function. Such a process was identified by proving the authors of the corresponding theorem. A corresponding approach to the making classification decision, when functionally meaningless elements that are theoretically possible to be ignored can’t be taken into account, and threshold selection functions will not ensure the attribution of an element to any class is formulated. The algorithm of making decision in the process of application of the method described above is produced. The peculiarities of such an algorithm are that it is clearly and cardinally described and quite simply implemented with the use of modern computer technology.