Expositing stages of VPRS analysis in an expert system: Application with bank credit ratings


Expositing stages of VPRS analysis in an expert system:

Application with bank credit ratings

Benjamin Griffiths, Malcolm J. Beynon*

Cardiff Business School, Cardiff University, Colum Drive, Cardiff, CF10 3EU, Wales, UK

Abstract

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 (b-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 b-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 b-reducts considered.

q 2005 Published by Elsevier Ltd.

Keywords: Bank ratings; Data visualisation; Decision rules; Expert system; VPRS

1. Introduction

Since the introduction of Rough Set Theory (RST) about

twenty years ago (Pawlak, 1982, 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, Peters, Skowron, & Zhong,

2002; 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, 1993a, b; 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,

Gomez, & Cinca, 1996; West, 1970;), probit and logit

models (Bouzouita & Young, 1998) and neural networks

Expert Systems with Applications 29 (2005) 879–888

www.elsevier.com/locate/eswa

0957-4174/$ - see front matter q 2005 Published by Elsevier Ltd.

doi:10.1016/j.eswa.2005.06.008

* Corresponding author. Tel: C44 029 2087 5747; fax: C44 029 2087

4419.

E-mail address: beynonmj@cardiff.ac.uk (M.J. Beynon).

http://www.elsevier.com/locate/eswa


(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 b-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

Sections 4 and 5, the VPRS expert system is applied to the

aforementioned bank data set, including snapshots describ-

ing the three stages of VPRS outlined previously. In Section 6,

conclusions are given as well as directions for future

research.

2. VPRS and concomitant expert system (using a small

example)

This section briefly describes fundamental aspects of

VPRS through a small example and use of the concomitant

expert system, for further reading on VPRS and related

methodologies see Ziarko (1993a, b), Beynon (2001);

Tsumato et al. (2004). The information system, central to

VPRS, is made up of objects described by sets of condition

(C) and decision attributes and (D). Objects characterized

and categorized by the same condition and decision attribute

values are grouped into condition (E(C)) and decision

(E(D)) classes, respectively.
1

The VPRS expert system

described in this study includes the ability to view such an

information system, see Fig. 1.

In Fig. 1, the presented information system is made up of

seven objects, described by six condition and one decision

attribute. The 0 and 1 descriptor values
2

enable the

construction of condition and decision classes. In summary,

the condition classes of objects (using all the condition

attributes, C) as groupings (X1, X2, X3, X4 and X5) of

indiscernible objects are:

X1 Z fo0g; X2 Z fo1; o4; o6g; X3 Z fo2g;

X4 Z fo3g and X5 Z fo5g:

Similarly, the decision classes (Y0 and Y1) associated

with the decision attribute are:

Y0 Z fo3; o4; o5; o6g and Y1 Z fo0; o1; o2g:

The relationship (memberships of objects) between these

condition and decision classes is fundamental to VPRS (and

other RST based methodologies). Subject to a majority

inclusion relation with threshold value b2(0.5, 1] (see An,
Shan, Chan, Cercone, & Ziarko, 1996), VPRS looks at the

condition classes that can be considered associated

(classified) with a particular decision class. Moreover,

those condition classes which have the property that the

largest group proportion of objects classified to a decision

class is at least b. The proportion of the objects in these

classified condition classes is defined as the quality of the

classification, more formally defined by Ziarko (1993a, b):

g
b
ðP; DÞ Z

cardgPrðZjXiÞRbfXi 2EðPÞg

cardðUÞ
;

where Z 2EðDÞ and P 4C;

for a specified value of b.
3

An integral part of VPRS is rule

construction through the use of b-reducts which are

particular subsets of condition attributes (P) providing the

classification of objects with the same gb(P, D) as the full
set of attributes C (ibid.). Formally in VPRS, a b-reduct

(RED
b

(P, D)), has the twin properties:

(1) gb(C, D)Zgb(REDb (C, D), D),
(2) No proper subset of RED

b
(C, D), subject to the same b

value can also give the same quality of classification.

Based on an identified b-reduct, a number of different

sets of decision rules can be identified (maximal, minimal -

see An et al., 1996). Here the minimal rule set is

constructed, found through the identification of prime

implicants and then further reduction in conditions

(descriptor values) in the individual rules (ibid.). The details

of VPRS presented so far, are its near original form (from

Ziarko, 1993a, b), recent developments include those

reported in Beynon (2001); Mi, Wu, and Zhang (2004)

and Li and Wang (2004). The VPRS expert system

exposited here incorporates the work in Beynon (2001),

where information over the whole b domain (0.5, 1.0] is

utilised. With a possible infinite number of different b

values identified to choose from, more than one b-reduct

(finite number) may be identified. For the information
1

These are equivalence classes E($), where a single member is made up

of a group of objects indiscernible with each other based on the attribute

values it is associated with (see Beynon, 2001).
2

VPRS works on a level of discretised data (rather than continuous

values), hence may require the lowering of the level of granularity of the

considered data set (see Beynon, 2004).

3
The full description of VPRS involves the identification of certain

approximation regions (positive, boundary and negative), each containing

groups of objects, see Beynon (2001) and Ziarko (1993a, b). For brevity this

paper purposely limits the level of formal notation described herein.

B. Griffiths, M.J. Beynon / Expert Systems with Applications 29 (2005) 879–888880



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