Blockwise similarity in [0,1] via triangular norms and Sugeno integrals - Application to cluster validity

In many fields, e.g. decision-making, numerical values in [0,1] are available and one is often interested in detecting which are similar. In this paper, we propose an operator which is able to detect whether some values can be gathered by blocks with respect to their similarity or not. It combines the values and a kernel function using triangular norms and Sugeno integrals. This operator allows to estimate this blockwise similarity at different levels. For illustration purpose, we use it to define an index suitable for the cluster validity problem in pattern recognition.