An R-fuzzy and Grey Analysis Framework

This paper puts forward the notion of an R-fuzzy and grey analysis framework. This is based on our previous works which involved enhancing the R-fuzzy set and the research undertaken on grey analysis, we believe that this newly proposed framework - the R-fuzzy grey analysis framework (RfGAf), to be a viable methodology to adopt when considering uncertainty modelling. It will be shown that the framework is very well suited in application areas involving perception modelling, where group consensus and subjectivity are prevalent. In such domains a single observation can have a multitude of different perspectives, choosing a single fuzzy value as a representative becomes problematic. The fundamental concept of an R-fuzzy set is that it allows for the collective perception of a populous, and also individualised perspectives to be encapsulated within its membership set. The introduction of a significance measure allowed for the quantification of any membership value contained within any generated R-fuzzy set. This in addition provided one the means to infer from the conditional probability of each contained fuzzy membership value. Such is the pairing of the significance measure and the R-fuzzy concept, it replicates in part, the higher order of complex uncertainty which can be garnered using a type-2 fuzzy approach, with the computational ease and objectiveness of a typical type-1 fuzzy set. This paper utilises the use of grey analysis, in particular, the use of the absolute degree of grey incidence for the inspection of the sequence generated when using the significance measure, when quantifying the degree of significance for each contained fuzzy membership value. Using the absolute degree of grey incidence provides a means to measure the metric spaces between sequences, so that perception divergence can be quantified.