Variableprecisionroughsettheoryanddatadiscretisationanapplicationtocorporatefailureprediction资源-CSDN文库

需积分: 9 187 浏览量 2011-01-17 20:22:49 上传评论收藏 169KB PDF 举报

### 变精度粗糙集理论与数据离散化：在企业破产预测中的应用 #### 概述本文讨论了变精度粗糙集（Variable Precision Rough Set, VPRS）理论及其在企业破产预测中的应用，并通过实证研究比较了VPRS与其他传统统计方法的有效性。自帕瓦拉克（Pawlak）在1982年提出粗糙集理论以来，该理论已成为一种基于规则的决策技术。尽管如此，在商业和金融领域的实际应用中，关于粗糙集方法的研究相对较少。本文作者利用VPRS模型和FUSINTER离散化方法进行实验，旨在预测英国企业的成功与否。 #### 变精度粗糙集理论 **粗糙集理论**是一种处理不完整或模糊信息的方法，最初由波兰科学家Zdzisław Pawlak提出。该理论提供了一种在无需额外信息的情况下对数据进行分类的框架。传统的粗糙集理论主要关注边界区域的不确定性，并且假设所有对象都具有相同的精度要求。 **变精度粗糙集（VPRS）**是粗糙集理论的一个扩展版本，它允许根据具体的应用场景调整精度参数。这意味着可以根据不同决策问题的需求来改变精度阈值，从而更灵活地处理数据的不确定性和复杂性。VPRS模型通过引入一个可变的精度参数，能够在处理噪声数据时减少错误分类的风险，提高模型的准确性和实用性。 #### 数据离散化方法 **数据离散化**是指将连续属性转换为离散区间的过程，这对于许多机器学习算法来说至关重要。离散化可以简化数据结构、减少计算复杂度，并有助于提高模型的解释性。文中提到的**FUSINTER数据离散化方法**是一种无监督的数据离散化技术，它不依赖于专家意见或其他先验知识，而是根据数据本身的分布特征自动确定最优的分割点。这种方法能够有效降低数据维度，同时保留关键的信息。 #### 实证研究在本文中，作者运用VPRS模型和FUSINTER离散化方法进行了实证研究，以预测英国企业的破产情况。研究结果与传统的逻辑回归、多元判别分析以及非参数决策树方法进行了比较。通过对比发现，VPRS不仅在预测准确性上表现出色，还能生成明确的概率规则，为决策者提供了有价值的见解，帮助他们更好地理解分类问题的本质。 #### 结论本文通过实验表明，VPRS作为一种实用工具，能够从给定的信息系统中生成明确的概率规则，为企业破产预测提供了一种新的视角。相比于传统的统计方法，VPRS在处理不确定性和噪声数据方面展现出更强的能力。此外，FUSINTER离散化方法的使用进一步提高了模型的性能和稳定性。因此，VPRS和FUSINTER的结合为企业失败预测提供了一个强有力的分析工具，对于学术界和实务界来说都是一个值得进一步探索的方向。变精度粗糙集理论及其在企业破产预测中的应用展示了这一理论的强大功能，尤其是在处理复杂的商业数据时。未来的研究可以从更多维度出发，探索VPRS与其他机器学习技术相结合的可能性，以应对更加多样化的决策挑战。

资源推荐

资源详情

资源评论

Omega 29 (2001) 561–576

www.elsevier.com/locate/dsw

Variable precision rough set theory and data discretisation:

an application to corporate failure prediction

Malcolm J. Beynon

∗

, Michael J. Peel

Cardi Business School, Aberconway Building, Colum Drive, Cardi, CF10 3EU, UK

Received 18 February 2000; accepted 6 June 2001

Abstract

Since the seminal work of Pawlak (International Journal of Information and Computer Science, 11 (1982) 341–356) rough

set theory (RST) has evolved into a rule-based decision-making technique. To date, however, relatively little empirical research

has been conducted on the ecacy of the rough set approach in the context of business and nance applications. This paper

extends previous research by employing a development of RST, namely the variable precision rough sets (VPRS) model, in

an experiment to predict between failed and non-failed UK companies. It also utilizes the FUSINTER discretisation method

which neglates the inuence of an ‘expert’ opinion. The results of the VPRS analysis are compared to those generated by

the classical logit and multivariate discriminant analysis, together with more closely related non-parametric decision tree

methods. It is concluded that VPRS is a promising addition to existing methods in that it is a practical tool, which generates

explicit probabilistic rules from a given information system, with the rules oering the decision maker informative insights

into classication problems.

Keywords: Data mining; Failure prediction; FUSINTER data discretisation; Rough set theory; Variable precision rough set theory

1. Introduction

Since the nascence of computerisation, together with the

evolution of Articial Intelligence (AI), there has been an

explosion in the application of advanced decision-making

techniques to solving business problems [1–5]. Following

the pioneering study of Altman [6], who used multivariate

discriminant analysis (MDA) to dierentiate between failed

and non-failed US rms, a large body of research has fo-

cused on corporate failure prediction (see [7–10] for litera-

ture reviews). The prediction of corporate failure continues

to be viewed as a matter of considerable interest to both aca-

demics and practitioners (including credit and investment

analysts), and has obvious importance for the stakehold-

ers (investors, creditors, employees, managers) of a rm.

∗

Corresponding author. Tel./fax: +44-29-2087-5747.

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

This is evidenced by the recent application of neural net-

works (NNs), recursive partitioning algorithm (RPA) and

case based reasoning to this issue [11–15]. A key advantage

of these contemporary methods over their traditional coun-

terparts (such as MDA and logit analysis) is that they do not

require pre-specication of a functional form, nor the adop-

tion of restrictive assumptions concerning the distributions

of model variables and errors [12,16,10].

More recently, a further non-parametric technique, rough

set theory (RST), which has its foundations in mathematical

set theory, has been applied to decision problems [17,18].

RST was originated by Pawlak [19] and has been described

as ‘a new mathematical tool to deal with vagueness and un-

certainty. This approach seems to be of fundamental impor-

tance to AI and cognitive sciences, especially in the areas

of machine learning, knowledge acquisition, decision anal-

ysis, knowledge discovery from databases, expert systems,

decision support systems, inductive reasoning and pattern

recognition ... One of the advantages of RST is that it does

PII: S0305-0483(01)00045-7

562 M.J. Beynon, M.J. Peel / Omega 29 (2001) 561–576

not need preliminary or additional information about data,

such as probability distributions in statistics, basic probabil-

ity assignment in the Dempster Shafer theory of evidence,

or grade of membership of the value of possibility in fuzzy

set theory’ [20, p. 89].

RST incorporates the use of indiscernibility (equivalence)

relations to approximate sets of objects by upper and lower

set approximations and, as noted by Slowinski and Zopouni-

dis [21, p. 79], ‘it is a formal framework for discovering

deterministic and non-deterministic rules from a given rep-

resentation of knowledge ... [it] ... assumes knowledge rep-

resentation in a decision table form which is a special case

of an information system’. Initial RST applications focused

on medical diagnosis, drug research and process control

[22,23], but more recently it has been extended to cover

credit fraud detection, stock market rule-generation, market

research, climate change and the development of expert sys-

tems for the NASA space centre [24,25,20].

Slowinski and Zopounidis [21] also investigated the use

of RST to assess the risk of a Greek bank’s clients (rms) in

terms of granting nance. Although they did not examine the

predictive accuracy of the RST rules, they did conclude [21,

p. 39] that (based on nancial ratios and other rm-specic

variables), RST ‘is a useful tool for discovering a prefer-

ential attitude of the decision maker in multi-attribute sort-

ing problems’. More recently, Dimitras et al. [26, p. 278]

reported that (on the basis of nancial ratios) a rough set

approach to predicting between failed and non-failed Greek

rms ‘was generally better than those obtained by classical

discriminant and logit models’. A limitation of these studies

is that the continuous data used to derive the rough set rules,

have been discretised (a requirement of RST) with the aid

of a selected ‘expert’. Clearly dierent experts may proer

dierent views and the operational costs and complexities

of using RST (and related techniques) will increase when

there is over-reliance on an expert. In this context An et

al. [27, p. 647] have stated that ‘It has to be emphasised ...

that the question of how to optimally discretise the attribute

(variable) values, is unsolved, and a subject of on-going

research’. This paper therefore employs a new (and more

objective) discretisation method, namely the FUSINTER

technique. However, the motivation for data discretisation

extends beyond the requirements of RST, to include dis-

cretising data of an imprecise quality (‘noisy’ data). The

ability to formulate rules from interval data (via discreti-

sation) may also facilitate a more informed understanding

of the interaction of the characteristics of objects. In this

context, it is of interest to note that, even with regard to

traditional statistical estimators (logit=discriminant analy-

sis), it has recently been advocated that continuous vari-

ables (nancial ratios) should be rank-transformed to im-

prove their distributional properties in a failure prediction

setting [28].

A further RST innovation has been the development by

Ziarko [29] of a variable precision rough sets (VPRS) model,

which incorporates probabilistic decision rules. This is an

important extension, since as noted by Kattan and Cooper

[30, p. 468], when discussing computer based decision tech-

niques in a corporate failure setting, ‘In real world decision

making, the patterns of classes often overlap, suggesting

that predictor information may be incomplete... This lack of

information results in probabilistic decision making, where

perfect prediction accuracy is not expected’.

An et al. [27] applied VPRS (which they termed

‘Enhanced RST’) to generating probabilistic rules to pre-

dict the demand for water. Relative to the traditional rough

set approach, VPRS has the additional desirable property of

allowing for partial classication compared to the complete

classication required by RST. More specically, when

an object is classied using RST it is assumed that there

is complete certainty that it is a correct classication. In

contrast, VPRS facilitates a degree of condence in clas-

sication, invoking a more informed analysis of the data,

which is achieved through the use of a majority inclusion

relation [29].

This paper extends previous work by providing an em-

pirical exposition of VPRS, where we present the results of

an experiment which applies VPRS rules to the corporate

failure decision. In addition, we mitigate the impact of us-

ing the subjective views of an expert (as employed in previ-

ous studies) to discretise the data, by utilising the sophisti-

cated FUSINTER discretisation technique which is applied

to a selection of attributes (variables) relating to companies’

nancial and non-nancial characteristics. The discretised

data, in conjunction with other nominal attributes, are then

used in this new VPRS framework to identify rules to clas-

sify companies in a failure setting.

To facilitate a comparison of our experimental VPRS re-

sults with those of existing techniques, we present the pre-

dictive ability of classical statistical methods—logit anal-

ysis and MDA—together with two more closely related

non-parametric decision-tree methods, RPA and the Elysee

method, which utilises ordinal discriminant analysis (see

[15,31], for an exposition of these methods). However in

the spirit of previous experimental research—and more par-

ticularly the previous failure prediction study of Frydman

et al. [15, p. 239], who concluded that ‘we feel that the at-

tributes of new techniques like RPA can be presented and

evaluated in a rigorous framework without the necessity of

proving its absolute superiority over existing procedures’—

the comparative classication results are not meant to be

denitive, but rather to illustrate the potential of VPRS. In

this context, research on the criteria to select the most e-

cacious and parsimonious set of VPRS rules (for predictive

purposes) is still in its infancy [27].

The remainder of the paper is organised as follows: The

next section gives a brief exposition of the VPRS method

and a discussion of the FUSINTER discretisation method.

The results of the empirical experiments are then reported,

including a discussion of the predictive ability of VPRS

relative to other existing parametric and non-parametric

methods.

M.J. Beynon, M.J. Peel / Omega 29 (2001) 561–576 563

Table 1

Example of a decision table

Condition attributes (C) Decision

attribute (D)

Objects c

101101 L

100000 L

001000 L

101101 H

000011 H

101101 H

000010 H

2. An overview of VPRS

VPRS (as with RST) operates on what may be described

as a decision table or information system. As is illustrated

in Table 1, a set of objects U (o

;:::;o

) are contained in

the rows of the table. The columns denote condition at-

tributes C (c

;:::;c

) of these objects and a related decision

attribute D (d). A value denoting the nature of an attribute

to an object is called a descriptor. As noted above, a VPRS

data requirement is that it must be in discrete or categori-

cal form. Table 1 shows that, with this particular example,

the condition attribute descriptors comprise 0’s and 1’s (for

example, denoting yes and no answers), and the decision at-

tribute values are L and H (for example, denoting low and

high). The table shows that the objects have been classied

into one of these decision values, which are also referred to

as concepts.

For the condition attributes in this example, all of the

objects (U) can be placed in ve groups: X

= {o

};

= {o

}; X

= {o

}; X

= {o

} and X

= {o

}. The ob-

jects within a group are indiscernible to each other so

that, objects o

and o

in X

have the same descriptor

values for each of the condition attributes. These groups

of objects are referred to as equivalence classes or condi-

tional classes, for the specic attributes. The equivalence

classes for the decision attribute are: Y

= {o

} and

= {o

}. The abbreviation of the set of equiva-

lence classes for the conditional attributes C, is denoted by

E(C)={X

; X

} and for the decision attribute,

it is dened E(D)={Y

; Y

VPRS measurement is based on ratios of elements con-

tained in various sets. A case in point is the conditional

probability of a concept given a particular set of objects (a

condition class). For example:

Pr(Y

) = Pr({o

}|{o

})

|{o

}∩{o

|{o

=0:333:

It follows that this measures the accuracy of the allocation

of the conditional class X

to the decision class Y

[29].

Hence for a given probability value , the -positive region

corresponding to a concept is delineated as the set of objects

with conditional probabilities of allocation at least equal to

. More formally:

-positive region of the set Z ⊆ U : POS



(Z)



Pr(Z|X

)¿

∈ E(P)} with P ⊆ C:

Following An et al. [27],  is dened to lie between

0.5 and one. Hence for the current example, the condition

equivalence class X

= {o

} have a majority inclusion

(with at least 60% majority needed, i.e.  =0:6) in Y

,in

that most objects (2 out of 3) in X

belong in Y

. Hence X

in POS

0:6

). It follows POS

0:6

)={o

Corresponding expressions for the -boundary and

-negative regions are given by Ziarko [29], as follows:

-boundary region of the set Z ⊆ U : BND



(Z)



1−¡Pr(Z|X

)¡

∈ E(P)} with P ⊆ C;

-negative region of the set Z ⊆ U : NEG



(Z)



Pr(Z|X

)61−

∈ E(P)} with P ⊆ C:

Using P and Z from the previous example, with  =

0:6, then BND

0:6

)=∅ (empty set) and NEG

0:6

}. Similarly for the decision class Y

it follows

POS

0:6

)={o

}, BND

0:6

)=∅ and NEG

0:6

VPRS applies these concepts by rstly seeking subsets of

the attributes, which are capable (via construction of deci-

sion rules) of explaining allocations given by the whole set

of condition attributes. These subsets of attributes are termed

-reducts or approximate reducts. Ziarko [29] states that a

-reduct, a subset P of the set of conditional attributes C

with respect to a set of decision attributes D, must satisfy the

following conditions: (i) that the subset P oers the same

quality of classication (subject to the same  value) as

the whole set of condition attributes C; and (ii) that no at-

tribute can be eliminated from the subset P without aecting

the quality of the classication (subject to the same  value).

The quality of the classication is dened as the propor-

tion of the objects made up of the union of the -positive

regions of all the decision equivalence classes based on the

condition equivalence classes for a subset P of the condition

attributes C. Associated with each conditional class is an

upper bound on the  value above which there is no oppor-

tunity for majority inclusion and hence not in a -positive

region—in the previous example Pr(Y

)=0:333 and

Pr(Y

)=0:667, hence if  =0:7 then X

is not in the

associated -positive region, since the upper bound on 

(for majority inclusion) is 0.667. The lowest of these upper

bounds (amongst the condition classes) on the  values is

dened 

min

and relates to the overall level of condence in

剩余15页未读，继续阅读

评论收藏

内容反馈

sinbba

粉丝: 0
资源: 13

Variable precision rough set theory and data discretisation an a...

最新资源

Variable precision rough set theory and data discretisation an a...

Variable Precision Rough Set and a Fuzzy Measure

Attribute Reduction in the Bayesian Version of Variable Precision Rough Set Model

变精度粗糙集Variable Precision Rough Set Model

Reducts within the variable precision rough sets model A further investigation

Novel algorithms of attribute reduction with variable precision rough set model

Research of reduct features in the variable precision rough set model

Precision parameter in the variable precision rough sets model an applicatio

A hybrid model based on rough sets theory and genetic algorithms for stock price

rough set

Fuzzy rough regression with application to wind speed prediction

rosetta rough set tool

rough set 的FuzzyGen

Rough set 软件：RSES

An Improved Decision Tree Algorithm Using Rough Set Theory in Clinical Decision Support System

基于模糊推理的模糊粗糙集相似度计算及其在句子相似度计算中的应用_Computing Fuzzy Rough Set based

python大作业 含爬虫、数据可视化、地图、报告、及源码（整和为一个文件）（2014-2020全国各地区原油加工量）.rar

仿真电路以及操作方法

【纯干货啊】华为IPD流程管理(完整版).pptx

信号与系统——保研复习资料.pdf

可编程语言标准IEC61131-3中文版.pdf

OFDM完整仿真过程与教程.zip

Landsat_WRS2.zip

最全的Visio形状/图形库

数字信号处理——保研复习资料.pdf

最新资源

python大作业含爬虫、数据可视化、地图、报告、及源码（整和为一个文件）（2014-2020全国各地区原油加工量）.rar