Досяжнiсть нечiтких альтернативних залежних цiлей у заданiй субординацiї строгого ранжування

Abstract

Розглядається задача прийняття рiшень iз нечiтко визначеними цiлями, якi упорядковано за важливiстю i для них визначено умови допустимостi та залежностi вiд допустимостi цiлей вищого рангу. Для розв'язання даної задачi запропоновано модифiкацiю схеми скаляризацiї та пiдхiд, що ґрунтуться на зведеннi її до задачi однокритерiальної оптимiзацiї, цiльова функцiя у якiй є скалярною згорткою критерiїв часткових критерiїв.

The decision-making problem with fuzzy goals are considered. Such problems, for example, are in the case of decision-making based on the opinions of several experts who formulate the estimation not clearly. Goals are ranking by importance, i.e. the strict subordination ranking on set of corresponding membership functions are defined. The set of allowed solutions (alternatives) is a subset of the integer numbers. For each of the membership functions defined the minimum value at which criterion is acceptable. It is required to find an optimal solution of the problem considering only acceptable criteria. Based on the properties of the considered problem is proposed to reduce this decision-making problem which is the lexicographic optimization problem with alternative criteria to the one criterion optimization problem with objective function, which is a positive linear convolution of partial criteria. This method allows to reduce the optimization problem with vector criterion function to an optimization problem with scalar objective function, which allows to apply known methods for its solve. The proved theorem, justifying that ability. The cases with different kinds of membership functions are considered, and for each of them the corresponding rules for calculating of the coefficients of positive linear convolution are described. Also the modification of scalar scheme for solving lexicographic problem with alternative criteria is proposed.