Fuzzy multicriteria decision support for budget allocation in the transport sector

Summary This paper compares two ways of providing decision support for the allocation of a fixed financial budget among a set of competing highway investment proposals. The first, which is described only in outline, uses a broadly conventional, hierarchically structured linear additive multicriteria model. The technical focus of the paper, however, is on the second, and approach based in fuzzy multicriteria modelling. The thinking which led us to explore this approach is set out, together with the formal structure of the model. The results of a small case study are given and an assessment is made of how decision makers' understanding of the investment options available can be enhanced by using the two models in tandem.     

A finite element approach for analysis and computational modelling of coupled reaction diffusion models

In this article, we establish the existence and uniqueness of solutions to the coupled reaction–diffusion models using Banach fixed point theorem. The Galerkin finite element method is used for the approximation of solutions, and an a priori error estimate is derived for such approximations. A scheme is proposed by combining the Crank–Nicolson and the predictor–corrector methods for the time discretization. Some numerical examples are considered to illustrate the accuracy and efficiency of the proposed scheme. It is found that the scheme is second‐order convergent. In addition, nonuniform grids are used in some cases to enhance the accuracy of the scheme.     

A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral

In the context of aggregation, the Choquet integral arises as a natural generalization of the weighted arithmetic mean. In their seminal work on bi-capacities, Grabisch and Labreuche have recently proposed an extension of the Choquet integral adapted to the situation where the values to be aggregated lie on a bipolar scale. In such a framework, they have derived generalizations of the Shapley value and of the Shapley interaction index that can be used to apprehend the main behavioral characteristics of the aggregation. Founding our approach on the intuitive notion of weight of a criterion, we propose alternative definitions of importance and interaction indices that may be more easily interpretable and we study their properties.