Measuring Inter-group Agreement on zSlice Based General Type-2 Fuzzy
  Sets
  Recently, there has been much research into modelling of uncertainty in human
perception through Fuzzy Sets (FSs). Most of this research has focused on
allowing respondents to express their (intra) uncertainty using intervals.
Here, depending on the technique used and types of uncertainties being modelled
different types of FSs can be obtained (e.g., Type-1, Interval Type-2, General
Type-2). Arguably, one of the most flexible techniques is the Interval
Agreement Approach (IAA) as it allows to model the perception of all
respondents without making assumptions such as outlier removal or predefined
membership function types (e.g. Gaussian). A key aspect in the analysis of
interval-valued data and indeed, IAA based agreement models of said data, is to
determine the position and strengths of agreement across all the
sources/participants. While previously, the Agreement Ratio was proposed to
measure the strength of agreement in fuzzy set based models of interval data,
said measure has only been applicable to type-1 fuzzy sets. In this paper, we
extend the Agreement Ratio to capture the degree of inter-group agreement
modelled by a General Type-2 Fuzzy Set when using the IAA. This measure relies
on using a similarity measure to quantitatively express the relation between
the different levels of agreement in a given FS. Synthetic examples are
provided in order to demonstrate both behaviour and calculation of the measure.
Finally, an application to real-world data is provided in order to show the
potential of this measure to assess the divergence of opinions for ambiguous
concepts when heterogeneous groups of participants are involved.
