Exploring statistical attributes obtained from fuzzy agreement models

In this paper we explore the characteristics of Type-1 Fuzzy Set agreement models based on interval data through contrasting statistical measures of the fuzzy models and the raw data respectively. We create Type-1 Fuzzy Set models using the Interval Agreement Approach, and then extract a preliminary set of attributes that encapsulate aspects of the agreement models. In order to explore what these attributes can tell us, we compare them with a set of traditional statistical measures of consensus which are applied to the raw data. Two interval-valued survey data sets are employed in this study, a synthetic data set consisting of 30 groups of 10 experts rating 25 objects which is used to provide a large example, and a real-world data set consisting of 7 groups of 4-8 cyber-security experts rating 26 security components that was collected during a decision making exercise at GCHQ, Cheltenham, UK. We show that while there are areas in which traditional methods and the attributes extracted from the Type-1 Fuzzy Set agreement models overlap, there are also attributes that do not appear to be replicated, suggesting that these attributes contain additional information about the consensus within the groups. A discussion of the results is provided, along with the conclusions that can be drawn and considerations for future work on this subject.