APPLICATION OF THE ROUGH SET METHOD

FOR EVALUATION OF STRUCTURAL FUNDS PROJECTS

Tadeusz A. Grzeszczyk

Institute of Production Systems Organization, Warsaw University of Technology, ul. Narbutta 85, 02-524 Warsaw, Poland

Keywords: Structural funds, project proposals, evaluation, rough set theory.

Abstract: Main subject of the present paper is presentation of the concept for application of rough set theory in

evaluation of structural funds projects. Author presents scheme of classification algorithms based on rough

set approach. This algorithm can be used for the problem of project proposals classification.

1 INTRODUCTION

Structural funds of European Union are considered

as a great chance for economical development of the

entire Community. However, as results from

practical experience, their absorption is still

considered as a source of significant methodical

difficulties for the beneficiaries as well as for

institutions which hold management of these funds.

One of the key aspects in management of these

funds are the procedures of monitoring and

evaluation of the project proposals. In this

connection, the problem of effective evaluation of

the projects to be co-financed by all the EU funds –

including structural funds – is particularly important

for solution of aforementioned methodical

difficulties.

In order to support the process of EU funds

absorption, special information systems are created.

All the institutions dealing with management of EU

funds as well as final beneficiaries make use of the

above systems. The main tasks of a. m. systems are

as follows (www.mf.gov.pl;

www1.ukie.gov.pl/www/en.nsf):

− ensuring effective and transparent management of

EU funds within the range of programs to be

financially supported by EU,

− monitoring and management of projects

beginning at the moment of preparing and sending

application forms through all the stages of their

realization, up to their final stage,

− monitoring and evaluation of financial indicators

and effects of tasks carried out within the range of

Community Support Framework and Operational

Programmes,

− ensuring required reporting to European

Commission, referred to implementation of EU

structural funds and Cohesion Fund in Poland.

In the second point of the present paper, basic

concepts useful for determining classification

algorithm are presented. Rough set theory allows

processing the experimentally obtained data. This

theory and Case-Based Reasoning Technology are

the fastest growing areas in the field of knowledge-

based systems (Aamodt, 1994; Cao, Shiu, Wang,

2001; Kruse, Schwecke, Heinsohn, 1991). Rough

sets are not yet as popular as fuzzy sets theory

(Zadeh, 1965; Zadeh, 1994) which is in a sense

complementary to the first one. Algorithm presented

in point 3. can be applied at implementation of rules-

based knowledge base for realization of evaluation

system referred to EU financed project proposals.

Slowinski and Zopoundis were the first to apply

rough set approach in the evaluation of corporate

failure risk (Slowinski, Zopounidis, 1995). This

method attempts to describe a set of enterprises by a

set of multi-valued attributes. Grzeszczyk discusses

the layout of conception referred to the use of

artificial intelligence methods (neural networks) for

prior appraisal of project proposals to be submitted

by Polish enterprises to European Union in order to

get financial assistance for investments from the EU

structural funds and the state budget (Grzeszczyk,

2004). Main subject of the present paper is

presentation of the concept for application of rough

set theory in evaluation of structural funds projects.

202

A. Grzeszczyk T. (2006).

APPLICATION OF THE ROUGH SET METHOD FOR EVALUATION OF STRUCTURAL FUNDS PROJECTS.

In Proceedings of the Eighth International Conference on Enterprise Information Systems - AIDSS, pages 202-207

DOI: 10.5220/0002495702020207

 SciTePress

The research connected with structural fund

projects evaluation system for qualitative analysis

was set in motion by the author in order to define the

procedure of creating an information system (set of

basic definitions is quoted in point 2.). At this stage

of research it was defined what conditional attributes

were as well as so-called universe. In this point of

paper many definitions are presented (connected

with rough set theory) being indispensable for

further research works. Next step is announcing a

way of creating decision table that includes a set of

values of decision attribute, responding to given

condition attributes. Preparation the classification

algorithm finishes the works connected with creating

the conception of qualitative analysis. In accordance

with conception assumed by the author, determining

of the values that decision attribute accepts, is

possible in stage of tests and exploitation of

evaluation system. Then an already created rules-

based knowledge base (consisting of decision rules)

is used. The following proceeding stages are

assumed.

1) Qualification of basic concepts connected with

analysis of information system (indispensable for

further works on the use of rough sets theory at

discovering decision rules):

− qualification of universe,

− information system and knowledge base (def. 1.-

2.),

− indiscernibility relation and its properties (def.

3.),

− lower and upper approximations of set (def. 4.),

− concept of reduct and core set of attributes (def.

5.-6.).

2) Concepts used in analysis of decision system:

− decision table (def. 7.),

− dependence between attributes (def. 8.),

− dependence coefficient between sets of attributes

(def. 9.).

3) Presentation of classification algorithm.

Mathematical tools (using the rough set theory)

applied by author for analysis of decision table, on

basis of which it is possible to define the decision

rules, are presented in the next point of the present

paper. The definitions are facilitating presentation of

conception related to use of approximate reasoning

in process of determining the value of decision

attribute. Presenting of classification algorithm (see

point 3. as well as fig. 1.) finishes this part of

research connected with rough set method for

evaluation in the process of structural funds projects

preparation.

2 ANALYSIS OF ROUGH SET

A crucial role in understanding the rough set theory

is played by a clear-cut defining of way for

representation of knowledge. Information is kept in

form of table, which unambiguously defines the

studied information system. Lines of this table are

making up the aforementioned objects, while

columns make up next conditional attributes.

Now it is necessary to define the basic concepts

to be useful in further considerations, definitions

quoted after: (Damasio, Maluszynski, Vitoria, 2003;

Pawlak, 1982; Pawlak, 1991).

Definition 1. Information system

Information system is a pair K = (U, A), where:

− U is a non-empty finite set of objects called a

universe,

− A is a non-empty finite set of conditional

attributes, where every attribute

Aa ∈

is a function

VUa →:

, where Va is a domain of attribute a.

− Every subset

UX ⊆

is called a concept in U.

Tools, which use approximate approach, are well

useful to create a suitable knowledge representation,

which is often called the ability of classification of a

definite reality. Knowledge then, can be equivalent

to the skill of conducting the process of

classification (of divisions) within a given universe.

Second definition describes knowledge base from

the point of view of rough sets theory.

Definition 2. Knowledge base

If U is a universe and R means set (or a family)

of equivalence relation then W=<U,R> is called

knowledge base about U.

Another important concept is an indiscernibility

relation. It is significant while solving the problem

of reduction of knowledge.

Definition 3. Indiscernibility relation

If K=(U, A) is an information system and

AB ⊆

, then in the universe set, the following

binary indiscernibility relation can be defined,

occurring between objects in system K:

)}.()(::),{()( yaxaBaUUyxBIND =∈

∀

∈

Recapitulating, any two objects x, y (belonging

to universe) fulfil the indiscernibility relation, if they

have identical attribute „a” values, for the set of

attributes under analysis.

Checking indiscernibility of objects is one of

many basic actions that should be done while

creating decision rules. The above mentioned

definition is used, among others, at the stage of

dividing universe into elementary concepts, that is

sets of objects which are undistinguishable in respect

APPLICATION OF THE ROUGH SET METHOD FOR EVALUATION OF STRUCTURAL FUNDS PROJECTS

203

of given attributes. A special case is division into

decision classes (that is: sets of elements which are

undistinguishable in respect of conditional

attributes).

Approximation of sets is a basic activity in the

rough sets theory. In this connection, one should

qualify two approximations of set. The following

definition serves to it.

Definition 4. Lower and upper approximation

Let K=(U, A),

ABUX ⊆⊆ ,

B-lower approximation of X, then:

})(:{ XxIUxXB

⊆∈=

B-upper approximation of X, then:

})(:{ ∅≠∩∈= XxIUxXB

B-borderline region of X, then:

XBXBXBN

−=)(

There are additional remarks connected with the

above presented definition 4:

− in relation to B-borderline region it is possible to

apply the following, equivalent record

BXXBXBN

\)( =

− it is possible to qualify B-positive region of X

(equal to lower approximation):

XBXPOS

=)(

− in analogy to previous point, it is possible to

record B-negative region) of X, as:

XBUXNEG

−=)(

, or

XBUXNEG

\)( =

− concept X is B-definable for

∅== )(, XBNXBXB

− lower B-approximation of concept X is the

maximum B-definable subset of universe U

contained in X, and upper B-approximation is B-

definable minimum subset of universe U

containing X:

XBXXB ⊆⊆

Next notion, of which applying is indispensable

in case of conducting reduction of attributes, is

reduct. It is a minimum subset of initial set of

attributes, which guarantees the same set of

elementary concepts as the initial set. It means that

in case of reduct we have smaller number of

arguments, and the same knowledge, characterizing

the fragment of reality (universe) we are interested

in.

Definition 5. Reduct of set of B attributes

Let K=(U, A) mean information system, set of

attributes

AB ⊆

. Another subset of attributes

marked as

BR ⊆

, is a reduct of a set of attributes B,

if: set R is independent and IND(R)=IND(B).

Family of all reducts of set of attributes B is

marked with symbol RED(B).

The next defined concept is a core. It defines

these attributes, which cannot be removed in any

case. The core is a set of attributes contained in

every reduct. Attributes of the core define the

division of universe into elementary concepts,

carrying in themselves desirable knowledge.

Definition 6. Core of set of B attributes

Let K=(U, A) mean information system, set of

attributes

AB ⊆

The core of set of attributes B, in information

system K, marked with symbol CORE(B) is called

the set of all indispensable attributes of this set.

It is obvious, that in every reduct there is a core.

Sometimes, it can happen, that all conditional

attributes are indispensable. In such case the reduct

is equal to the core.

Information system added to one column,

including record of three different values of decision

attribute, can be called a decision table. Its formal

definition is shown below.

Definition 7. Decision table (Kryszkiewicz,

1996)

Decision table is an information system

}){,( dAU ∪

, where:

− U is a universe,

− A is a set of conditional attributes,

−

∉

is a decision attribute.

The decision table presents dependence between

conditional attributes and decision attribute. So it

can be helpful at investigation of dependence in

bases of knowledge. Interesting are e.g.

dependencies occurring between sets of attributes.

Knowledge represented by certain set of attributes

can be mutually combined or result from knowledge

characterising the other set. It seems to be

indispensable to define in this place a dependence

between sets of attributes: both total as well as

partial ones.

Definition 8. Dependence between attributes

Let K=(U, A) mean information system,

ACAB ⊆⊆ ,

CB ⇒

, which we read, set of attributes C

depends on set of attributes B, when the following

record is fulfilled:

)()( CINDBIND ⊆

Here it is necessary to define partial dependence,

which can occur between sets of attributes.

Definition 9. Partial dependence between sets of

attributes

Let K=(U, A) mean information system,

ACAB ⊆⊆ ,

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204

Set of attributes C depends on set of attributes B

(in other words, knowledge contained in C depends

on knowledge in B) in degree k, which can be

written in symbols:

⇒

when:

CPOS

)(

)( ==

Coefficient “k” accepts values from interval

10 ≤≤ k

, it is defined as dependence coefficient

between sets of attributes. k=1 means, that total

dependence exists, marked as

CB ⇒

. In this

situation every object of universe belongs to positive

region (i.e. lower approximation). There are no

objects which would possess identical conditional

attributes, and different decision attributes. In such

case there is not contradictory information. On the

other hand, for k=0 there is not any dependence

between sets of attributes.

Above author gives only the basic concepts

indispensable for further works on the usage of

rough sets theory at discovering of decision rules.

They are applicable for determining algorithm of

creating decision rules. Detailed description of rough

set theory can be found in: (Damasio, Maluszynski,

Vitoria, 2003; Pawlak, 1982; Pawlak, 1991).

3 CLASSIFICATION

ALGORITHM BASED ON

ROUGH SET

In fig. 1. classification algorithm can be seen, which

leads to formulating decision rules and to dealing

with problem of resolving conflicts between

decision rules classifying a new project to different

classes and predicted decision value for new object

(project). Its basic task is reduction of redundant

objects and conditional attributes (total and local).

The author of this work suggests, that the set of rules

generated from decision tables is used to mark the

value of decision attribute, influencing the projects

proposals evaluation process.

The base of decision rules consisting of decision

rules, determined with algorithm for example

(Mrozek, 1992) – exemplifies basis for process of

approximate reasoning. The consecutive values of

Selection of rules

matching new project

Calculation of strength of

the selected rule sets for

decision class

Selection of decision class

with maximal strength of

the selected rule se

ew structural funds

project

(new ob

ect)

Predicted decision value

for new project

(new ob

ect)

Train decision table

with old projects:

accumulated knowled

Calculation of

decision rules

Decision rules

from

decision table

Figure 1: Algorithm for classification of structural funds project - source: author’s own study on the basis of (Bazan, Hung

Son Nguyen, Sinh Hoa Nguyen, Synak, Wroblewski 2000).

APPLICATION OF THE ROUGH SET METHOD FOR EVALUATION OF STRUCTURAL FUNDS PROJECTS

205

decision attribute can be determined with its use, to

decide which attribute is used to mark the value of

decision attribute for the process of new project

proposal evaluation.

4 CONCLUSION

Synthesising the presented results of research the

author presents a hypothesis about possibilities and

advisability of using the rough set theory in the

process of structural funds projects evaluation. The

main advantages of methods assisting evaluation,

based on rough set theory– in relation to traditional

statistical analyses – are first of all the features as

below.

Rough set theory is an instrument serving for

recording of experienced persons and experts

experiences in the form of decision rules based on

empirical materials as well as ensuring processing of

information relatively easy.

There occurs a relatively high certainty, that no

essential dependence between conditional attributes

affecting decision attribute (so-called decision rule)

will be omitted. However, at using traditional

methods of statistical analysis even very essential

dependencies occurring between attributes can be

omitted. Since there is a lack of instruments enabling

defining of such dependence. As an example,

multifactor analysis of correlation makes possible

qualification of numerical value of influence for

individual attributes between themselves only. It

does not create however, any possibility of defining

connections between values of individual attributes.

Methods based on applying the rough set theory

are using experts’ experience and they make

possible verification of their opinions as well as they

are assuring relative easiness in interpretation of

results. Thus the conclusions related to studied

decision attribute are received. It is also easy to

interpret their alternatively incorrect acting.

Dependences established thanks to use of rough

set theory can be ranked in accordance with the

degree of their importance. From additional

description (based on empirical materials e.g.

experts’ opinions) an opinion of significance of

decision rule as well as influence of definite

attributes onto decision results can be made. There

also exists large degree of possibility for verification

of results, because every generated rule is

accompanied with description including reference to

empirical sources.

Redundancy of attribute is easy to prove with the

use of division of decision table into elementary

concepts. The results achieved can be authenticated

by analysing a discernibility matrix.

Rough set theory makes possible carrying out

analyses for different sets of conditional attributes.

The discussed theory is well usable to investigation

of low structured processes (especially socio-

economic ones). It makes possible identification of

decision rules, difficult to intuitive defining.

There exists relative easiness of modification in

reference to decision table (by addition of new, not

considered earlier conditional attributes). This

makes possible creating different decision rules.

The SIMiK system (The Information System for

Financial Monitoring and Controlling of the

Structural Funds and the Cohesion Fund) - for

details see (www.mf.gov.pl;

www1.ukie.gov.pl/www/en.nsf) - recommended by

Ministry of Finance in Poland, is intended to

improve process of EU funds absorption. For

potential project providers the application generator

is the most important element of the system. It

serves to put in all the necessary data. The

evaluation system referred to project proposals

should in future be operated not only with SIMiK

but also with the other systems considered as the

source of knowledge and information. The

evaluation system provided with rules-base

knowledge base, described in the present paper, can

serve as one of the co-operating systems.

Preliminary research works referred to application of

classification algorithm also proved to be very

promising.

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