The Quantification of Subjectivity: The R-fuzzy Grey Analysis Framework

This paper puts forward a newly derived framework for capturing and inferring from subjective based uncertainty for any given observation. The framework is referred to as the R-fuzzy grey analysis framework (RfGAf), which itself is comprised of 3 distinct components: 1. R-fuzzy sets - to capture the uncertainty, which utilises crisp rough set bounding of uncertain possible fuzzy membership values. 2. A significance measure - to provide a means to allow for conditional probability to be undertaken, and also to allow for the translation of the data to that of a time series, allowing for the linking to that of the third component. 3. Grey analysis, more specifically, the absolute degree of grey incidence, where post-analysis can be undertaken and additional metrics obtained. The hybridisation of all three has allowed for the creation of a framework ideally suited for the quantification of perception based uncertainty, which by proxy will be inherently associated to subjectivity. It will be shown and demonstrated how such a framework can be made use of, showcasing the advantages of such an approach. By making use of R-fuzzy sets and the significance measure, an intermediary approach to that of a generalised type-2 fuzzy set can be obtained. As it is widely agreed upon that a generalised type-2 fuzzy approach is ideal for capturing higher degrees of resolution with regards to uncertainty, the associated computational burden of its complexity makes it unfavourable, hence why the interval-valued type-2 approach is favoured. The findings indicate the RfGAf can allow for the high capacity and detail one would expect when considering a type-2 fuzzy set representation, with that of the simplistic objectiveness one would associate to a typical type-1 fuzzy set. The novelty of the framework allows for one to fully capture all the nuances and individualities of a population without a single loss of information. That snapshot in time can tell an awful lot with regards to perceived perception. The framework can be deployed on varying sizes of populations, from the intrinsically small to the overtly large. Potentially, one can use that snapshot to predict how an observation could be perceived in future events. If one can forecast the perception ahead of time, one can improve drastically on efficacy and efficiency. Such a framework has a strong applicability with regards to expert and intelligent systems in allowing for more detailed inference to be utilised and acted upon.