Block similarity in fuzzy tuples

A common problem in decision-making is to analyze a tuple of numerical values associated with options, such as the degree of satisfaction assigned by experts to alternatives or probability values for hypotheses computed from data. With no loss of generality, it is assumed that the tuple contains values in the unit interval. For post-processing of typical value(s), singular values that may arise from noise in the data, or from unreliable experts, must not be taken into account. We present the concept of block similarity to address the problem of detecting subset(s) of typical values instead of extracting singular ones. The concept relies on suitable aggregation operators that combine the tuple components. Three different block similarity operators are proposed and discussed. These rely on Sugeno integrals of the tuple with respect to three different measures, namely cardinal weighting, symmetric kernel weighting and non-linear weighting. Numerical examples demonstrate their behaviors and their ability to detect blocks of similar values.