بررسی مراحل تجزیه و تحلیل VPRS در یک سیستم خبره: کاربرد رتبه بندی اعتبار بانکی

The variable precision rough sets model (VPRS) along with many derivatives of rough set theory (RST) necessitates a number of stages towards the final classification of objects. These include, (i) the identification of subsets of condition attributes (β-reducts in VPRS) which have the same quality of classification as the whole set, (ii) the construction of sets of decision rules associated with the reducts and (iii) the classification of the individual objects by the decision rules. The expert system exposited here offers a decision maker (DM) the opportunity to fully view each of these stages, subsequently empowering an analyst to make choices during the analysis. Its particular innovation is the ability to visually present available β-reducts, from which the DM can make their selection, a consequence of their own reasons or expectations of the analysis undertaken. The practical analysis considered here is applied on a real world application, the credit ratings of large banks and investment companies in Europe and North America. The snapshots of the expert system presented illustrate the variation in results from the ‘asymmetric’ consequences of the choice of β-reducts considered.

Since the introduction of Rough Set Theory (RST) about twenty years ago (Pawlak, 1982 and Pawlak, 1991), it has become a popular technique for the classification of objects (Tsumato, Slowinski, Komorowski, & Grzymala-Busse, 2004). Its popularity is a direct consequence of its operational processes, which adhere most closely to the notions of knowledge discovery and data mining (Li & Wang, 2004). These include; operating on the data to identify facts, only from that data which has been utilised and there are no externally imposed assumptions on the data (Jensen, 2004). There is for example no need for normally distributed attribute values as in multivariate discriminant analysis (see Lin & Piesse, 2004). These issues mitigate external concerns placed on a decision maker (DM), moreover they leave the decision maker to undertake their particular analysis (based on a known research theme). An illustration of the popularity of RST has been its nascent development (Alpigini et al., 2002 and Tsumato et al., 2004), which has included advances in the areas such as medical applications, bioinfornmatics, image recognition and information retrieval. Here the variable precision rough set (VPRS) approach is considered, which as its name may suggest allows for a level of miss-classification to exist in the decision rules constructed (see Ziarko, 1993 and Ziarko, 1993; Beynon, 2001). Moreover, central to this study is the exposition of an expert system that undertakes the various stages of VPRS analysis, with emphasis on the appropriate interaction with the DM throughout. The particular application of the described VPRS expert system, is in the area of bank ratings. Moreover, North American and European banks that have been assigned Moody's Bank Financial Strength Rating (BFSR) are considered (Moody's Europe, 2004). As with the general rating problem, there is a dearth of specific ‘public’ knowledge on how the credit agencies like Moody's and Standard and Poor's (S&Ps) make their classification decisions (Singleton & Surkan, 1991). This itself has encouraged analysis using a variety of techniques, including multiple regression models (Horrigan, 1966, Molinero et al., 1996 and West, 1970), probit and logit models (Bouzouita & Young, 1998) and neural networks (Singleton & Surkan, 1991). With the use of VPRS producing sets of readable decision rules then a novel (initial) analysis in this area is also a part of this study. As an expert system, here its purpose is many-fold; firstly to adequately undertake the necessary analysis (in this case VPRS), secondly to present the results to a DM in a way that benefits them, thirdly control over the analysis is placed fully with the DM. This control issue, with respect to VPRS in particular includes the choice of β-reduct from those identified. Moreover, VPRS is one of a number of techniques that centers around knowledge reduction, the expert system places a level of choice on this reduction with the DM themselves. In the bank rating problem there needs to be details available on the individual banks and their correct or in-correct classification. The snapshots of the VPRS expert system presented in this study elucidate these issues. The structure of the rest of the paper is as follows: In Section 2, the rudiments of VPRS are described with initial snapshots of the expert system utilized on a small example data set. In Section 3, the bank data set is described. In 4 and 5, the VPRS expert system is applied to the aforementioned bank data set, including snapshots describing the three stages of VPRS outlined previously. In Section 6, conclusions are given as well as directions for future research.

This study has elucidated an expert system based on the variable precision rough set theory (VPRS) technique for object classification. Its emphasis is on the identification of certain stages of the VPRS, each of them offering information to the decision maker (analyst). Throughout the majority of the paper a bank problem is considered over European and North American banks, which have been assigned Moody's recently introduced bank financial strength rating. An important stage of VPRS is the identification and selection of subsets of condition attributes (termed β-reducts) which adequately characterize the objects as would the whole set. The expert system reports a list of available β-reducts and the β sub-domain it exists over. Each identified β-reduct can be efficiently selected and concomitant results accrued. This is a subtle facet of the expert system, since it empowers the analyst the fullest opportunity to follow their particular research direction. That is, the emphasis with VPRS (and RST) is the imposing of a β-reduct to the analyst, here the honest priority is for the analyst to make that choice if they prefer. As long as a subset of condition attributes is a β-reduct then it satisfies the necessary properties and is equally selectable to any other. The other snapshots offer insights into the VPRS analysis to the decision maker. The sets of decision rules offer interpretability, while information on which rule classifies the individual objects offer object by object elucidation to the analysis. The future for this expert system, from its conception, is based on the analysts who will ‘hopefully’ utilise it and continue to identify what they want. One future development is the ability to undertake cross validation analyses, thus offering possible statistical inference to the classification of objects.