Abstract. Numerous authors have proposed functions to quantify the degree of similarity between two fuzzy numbers using various descriptive parameters, such as the geometric distance, the distance between the centers of gravity or the perimeter. However, these similarity functions have drawbacks for specific situations. We propose a new similarity measure for generalized trapezoidal fuzzy numbers aimed at overcoming such drawbacks. This new measure accounts for the distance between the centers of gravity and the geometric distance but also incorporates a new term based on the shared area between the fuzzy numbers. The proposed measure is compared against other measures in the literature.

Several methodologies based on ISO/IEC 27000 international standard have been developed to deal with risk analysis in information systems (IS). These methodologies do not, however, consider imprecise val-uations, but use precise values on different, usually percentage, scales.We propose an extension of the MAGERIT methodology based on classical fuzzy computational models. A linguistic term scale is used to represent asset values, their dependencies and frequency and asset deg-radation associated with threats. Computations are based on trapezoidal fuzzy numbers associated with linguistic terms. A similarity function is used to associate a linguistic term on the previously defined scale to the trapezoidal fuzzy numbers resulting from computations. Finally, regarding the selection of preven-tive safeguards to reduce risks in IS, we propose a dynamic programming-based method that incorpo-rates simulated annealing to tackle optimizations problems with the aim of minimizing costs while keeping the risk at acceptable levels.An example of an administrative unit using in-house and third-party information systems internally and to provide public information services is used to illustrate the methodology.

This paper proposes a new method, ConvGraph, to detect communities in highly cohesive and isolated weighted graphs, where the sum of the weights is significantly higher inside than outside the communities. The method starts by transforming the original graph into a line graph to apply a convolution, a common technique in the computer vision field. Although this technique was originally conceived to detect the optimum edge in images, it is used here to detect the optimum edges in communities identified by their weights rather than by their topology. The method includes a final refinement step applied to communities with a high vertex density that could not be detected in the first phase. The proposed algorithm was tested on a series of highly cohesive and isolated synthetic graphs and on a real-world export graph, performing well in both cases.

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Different functions for quantifying the degree of similarity between two fuzzy numbers have been proposed in the literature on the basis of various descriptive parameters, such as the geometric distance, the distance between the centers of gravity, the perimeters or the shared area between the fuzzy numbers. However, these similarity functions are not equally applicable across all situations. Consequently, comparative analyses have been performed on the basis of different sets of fuzzy number pairs. In this paper we thoroughly review the similarity functions proposed in the literature, identify their properties and possible drawbacks and compare them on the basis of an extended set of fuzzy numbers.