A vector visualization of uncertainty complementing the traditional fuzzy approach with applications in project management

Abstract

In view of recent technological developments and new computational and graphical possibilities, scientists and practitioners have become increasingly interested in studying how data and information should be presented. For instance, in project management, it is now recommended to employ dashboards instead of traditional reports. It is also believed that the usage of vectors, resembling the hands of a clock, may increase the efficiency and effectiveness of data presentation and information processing. In light of this, we propose a novel approach to visualization of uncertainty as defined by triangular fuzzy numbers. This new representation is based on vectors whose length represents the range of possible values of an uncertain parameter, while the slope reflects tendencies within possible scenarios. The mathematical foundations and definitions along with the basic properties of this approach are demonstrated in detail. In particular, we show how to transform triangular representations into vector ones and vice versa. The arithmetic operations of addition and multiplication by a crisp number on these vectors are demonstrated as well. Possible applications of the new vector visualization to project uncertainty representation and in project management are described. We also discuss both the advantages and disadvantages of our approach in relation to the traditional visualization as graphs of membership functions. Our proposal is complementary to the traditional one, and they should be used in combination. The new graphical representation of triangular fuzzy numbers expands the available toolbox for visualizing uncertainty not only in project management but in any other area.