Rough Fuzzy Set Theory and Neighbourhood Approximation Based Modelling for Spatial Epidemiology

Background

Recent and past literatures have documented the relationship between locations, individuals and diseases. Geographic Information Systems (GIS) have been widely used to study problems involving public health. Spatial analysis with respect to epidemiology has been addressed in recent researches. Transmission and distribution of SARS - severe acute respiratory syndrome was studied and analysed by Meng et al. (2002), Wang (2006) documented risk exposure pattern, Ulegtekin et al. (2007) analysed distribution of measles in Turkey, Slowinski et al. (1996) predicted pancreatitis using Rough Set Theory, Rowland et al. (1998) predicted ambulation after spinal cord injuries, Vinterbo and Øhrn (1999) built a rough set based predictor for myocardial infarction, Bai et al. (2010) used RST to uncover spatial decision rules in neural-tube birth defect. Spatial analysis employing statistical models and spatial regression methods to study population dynamics is reported in Chi and Zhu (2008) and the use of weighted centroid method to predict outbreak of Escherichia Coli in Buscema et al (2013). The results have depended on specific features of dataset like configuration, distribution, spatial heterogeneity and autocorrelation. Bai et al. (2010) substantiate that being discernibility based, ability to handle inconsistent data, applicability to any number of outcomes, dimensionality reduction, suitability for spatial data are some of the features that make Rough Sets very conducive to epidemiological study.

To better express the multifaceted nature of the real world and address the limitation of knowledge and uncertainty of factual data, fuzziness can be used to represent some attributes of data. It has been used to represent the classification of land-cover types in Shi (2005) and effect of environmental factors on birth defects in Bai et al. (2010). A geographic phenomenon may tend to be closely related and distant related entities based on the distance. This is spatial auto correlation and upheld by Tobler’s law of geography as in Miller (2004). In RST, an object tends to have roughness where the object is a subset of universe with some property states Pawlak (1984). Lower and Upper approximations are used to define an object. The roughness of an object can be précised upon collecting more attributes about the object. Bai et al. (2014) affirm that roughness is not a fuzzy concept by nature and so fuzzy sets cannot be used to represent roughness Rough Fuzzy Sets which is an extension of rough sets can be used to construct the decision system for spatial analytics. Combining Intuitionistic approach along with rough fuzzy sets will tend to better accuracy of results leading to crisp conditions and probability based fuzzy decisions.

Dimensionality reduction which is also addressed by RST needs an extra step on dealing with spatial and non-spatial attributes of the decision system. Spatial attributes which are continuous in nature will have to be discretised for RST to construct equivalence classes. Jensen and Shen (2004) approve that the discretization may sometimes lead to loss of information. Liao (2012) substantiated the use of Neighborhood Rough Set approximation to work with continuous attributes without discretising them.