Structuring of the ctriterional space by an angle similarity measure

Abstract

Multicriteria decision-making is a particularly hard complex of tasks for a person’s information processing system. As a rule, the more the problem model is constructed and reflects the real problem or task that caused it, the more criteria it has to take into account. With this dimension, classical methods of mathematical programming are ineffective. This necessitates the development of specific methods and approaches designed to structure the criterion space of large dimension problems. This paper describes a fuzzy binary relation and its belonging function that determine the angular measure of similarity of efficiency criteria. It characterizes the degree of similarity between the vector gradients of the objective functions of the efficiency criteria between them. The one-tier clustering method was modified based on fuzzy binary relations to use the angular similarity measure. This allowed clustering of the criterion space into conical clusters on the basis of similarity - a consistent strong link between the performance criteria. The complex approach to structuring the criterion space of vector linear programming problems is presented. On the basis of the proposed mathematical apparatus, software was developed that implements clustering with conical clusters. Conducting hands-on experiments has shown its effectiveness in solving certain classes of application tasks. This work is an evolution of the direction of structuring the set of efficiency criteria for a class of multicriteria linear programming problems with a large dimensional criterion space in conditions where it is difficult or impossible to group, compare or order partial criteria, preferably for the decision maker. Prospective research is to develop a proposed clustering approach which is based on method of fuzzy binary angular similarity measures for solving other classes of applied problems.

Keywords

• кластеризацiя
• багатокритерiальна оптимiзацiя
• структурування
• кутова мiра подiбностi
• мiра подiбностi