Evidence theory and VPRS model

The Rough Set Theory (RST) was proposed by Pawlak [4] as a new mathematical approach to deal with uncertain knowledge in expert systems. In 1991 Ziarko [11] proposed the Variable Precision Rough Set Model (VPRSM) as a certain extension of the rough set theory. VPRSM approach makes it possible to use a certain level of misclassi cation. The aim of this paper is to introduce belief and plausibility functions de ned by the {approximation regions. On the basis of the {approximation regions, the {basic probability assignment is de ned and the Dempster's combination rule for product of two decision tables is constructed. This entire approach is illustrated by examples

Variable Precision Rough Set Model for Incomplete Information Systems and Its Beta-Reducts

As the original rough set model is quite sensitive to noisy data, Ziarko proposed the variable precision rough set (VPRS) model to deal with noisy data and uncertain information. This model allowed for some degree of uncertainty and misclassification in the mining process. In this paper, the variable precision rough set model for an incomplete information system is proposed by combining the VPRS model and incomplete information system, and the beta-lower and beta-upper approximations are defined. Considering that classical VPRS model lacks a feasible method to determine the precision parameter beta when calculating the beta-reducts, we present an approach to determine the parameter beta. Then, by calculating discernibility matrix and discernibility functions based on beta-lower approximation, the beta-reducts and the generalized decision rules are obtained. Finally, a concrete example is given to explain the validity and practicability of beta-reducts which is proposed in this paper

The investigation of the Bayesian rough set model

AbstractThe original Rough Set model is concerned primarily with algebraic properties of approximately defined sets. The Variable Precision Rough Set (VPRS) model extends the basic rough set theory to incorporate probabilistic information. The article presents a non-parametric modification of the VPRS model called the Bayesian Rough Set (BRS) model, where the set approximations are defined by using the prior probability as a reference. Mathematical properties of BRS are investigated. It is shown that the quality of BRS models can be evaluated using probabilistic gain function, which is suitable for identification and elimination of redundant attributes

The investigation of the Bayesian rough set model

AbstractThe original Rough Set model is concerned primarily with algebraic properties of approximately defined sets. The Variable Precision Rough Set (VPRS) model extends the basic rough set theory to incorporate probabilistic information. The article presents a non-parametric modification of the VPRS model called the Bayesian Rough Set (BRS) model, where the set approximations are defined by using the prior probability as a reference. Mathematical properties of BRS are investigated. It is shown that the quality of BRS models can be evaluated using probabilistic gain function, which is suitable for identification and elimination of redundant attributes

Challenging the 'local turn' in migrant integration in the South East of England under the Coalition and Conservative Governments 2010-2018: a whole policy approach

In recent years increasing bodies of research have supported the idea that integration takes place on the local level (Jimenez 2009, Penninx & Martiniello 2007, Rutter 2015, Jensen 2011). Consequently, when the Coalition government claimed to be ushering in a radical new form of Localism and designated integration as a ‘local issue’, there was an apparent consensus between policy and academia alike that this localist turn was to be ‘welcomed’ (Ali & Gidley, 2014, p. 23). Nevertheless, this apparent consensus makes two assumptions. The first is that Localism is always a positive thing for the local level and the second is that greater autonomy at the local level will materialise in greater migrant integration activities. Consequently, research in this area spans two bodies of academic literature, Localism, and that of the ‘local turn’ in integration policies, and is the first time these two related fields have been combined. The primary research question of this thesis is “Did the designation of migrant integration as a ‘local issue’ under the Coalition and Conservative Governments 2010-2018 help or hinder the ability of local authorities to facilitate migrant integration in their localities?”. The research uses as its case study the South East (SE) of England as the region is home to the highest number of migrants in the UK second only to London, and has also not been covered in academic research on this area to date. It is also a predominantly rural area and as such adds to much needed research on migrant integration outside of urban or peri-urban settings. The principal research question is broken down into the following sub questions designed to unpack the aforementioned assumptions. Did a local turn in migrant integration policy take place under the Localism of the Coalition and Conservative Governments 2010 to 2018? How can a whole policy approach help us to map the aggregate demand on local authorities when it comes to migrant integration?” Both these questions are analysed using a trio of qualitative research methods, policy analysis, participant observation and semi-structured interviews, in order to highlight the danger of relying on policy frame analysis alone. This mixed method approach is also used to map the effects of a policy at regional and at local level in order to best address the primary question about what impact was had on the local level for migrant integration as a result of Coalition and Conservative government Localism policies. The policy analysis undertaken uses a modified version of Emilsson’s (2015) power lens approach mapping the impacts of normative, legislative and economic power levers in order to assess the cumulative effects of a policy rather than relying on policy frame alone. The findings demonstrate that rather than providing enabling conditions for migrant integration, Coalition and Conservative Localism reduced the activities local authorities could undertake to their core statutory duties, of which migrant integration is not one. Furthermore, this research also highlighted how, once all policies impacting on migrant integration are taken into account, (such as immigration, housing or employment), these governments made it significantly harder for local authorities to facilitate migrant integration. In particular, the role of the hostile environment and the increasing neo-liberalisation of government policies are seen to have negatively impacted upon every aspect of the integration process. The research also saw that running parallel to these detrimental policies was the Vulnerable Persons Resettlement Scheme (VRPS). This scheme was voluntary for local authorities to opt into but fully funded and coordinated by central government. Contrary to the scaling back of all non-statutory services which Localism and its accompanying austerity had necessitated, the VPRS led to an expansion in services for migrants including cohorts which were not refugees. The scheme also meant that local authority officers working on the VPRS were forced to navigate the hostile policies migrants face when accessing accommodation, bank accounts, registering with GPs, obtaining driving licences and other such aspects. This research shows that there are many types of Localism and that it is essential to examine the policy levers accompanying them in order to assess the impact there may be on migrant integration. It also demonstrates that a whole policy approach must be taken when considering migrant integration and that as such, it is dangerous to designate integration as a purely ‘local issue’