INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL
ISSN 1841-9836, 10(4):480-491, August, 2015.
Development of a Fuzzy Logic System to Identify the Risk
of Projects Financed from Structural Funds
M.I. Boloş, D.C. Sabău-Popa, P. Filip, A. Manolescu
Marcel Ioan Boloş*, Diana-Claudia Sabău - Popa
Departament of Finance-Accounting, Faculty of Economic Sciences,
University of Oradea
Romania, 410087 Oradea, Universitatii St. 1
marcel_bolos@yahoo.com, dpopa@uoradea.ro
*Corresponding author: marcel_bolos@yahoo.com
Petru Filip
1. Dimitrie Cantemir Christian University,
Romania, 040042 Bucharest, Splaiul Unirii, 176
2. Agora University of Oradea,
Romania, 410526 Oradea, Piata Tineretului, 8
3. University of Oradea
Romania, 410610 Oradea, University Street, 1
pfilip@uoradea.ro
Adriana Manolescu
Departament of Social Sciences
Agora University of Oradea
Romania, 410526 Oradea, Piata Tineretului, 8
adrianamanolescu@univagora.ro
Abstract: The fuzzy logic system developed in this research paper seeks to identify
the financial risk of projects financed from structural funds when changes occur in
project values, in the duration of the projects and in the implementation durations.
Those two factors are known to influence the financial risk. The fuzzy system was
simulated using Matlab and the results showed its operation and the conclusion that
the financial risk of the project is dependent on the developments values and on
the implementation duration. The developed and tested fuzzy logic system provides
information on financial risk intensity organized into three categories: small, medium
and large and on the inflection point of transition from low risk to high risk. This is
considered an early warning system for the management staff with responsibilities in
structural funds.
Keywords: Fuzzy Logic System (FLS), artificial intelligence, financial risk, struc-
tural funds, centroid method.
1 Introduction
The fuzzy logic systems (FLS) are used as a tool for decisions making, for the projects
financed from structural funds, for the early identification of risks that affect the performance of
the allocation of funds for EU member countries, through various financial instruments known as
operational programs. The risk of the projects financed from structural funds has various forms,
but the most important remains the financial aspect, that generates losses for the budget of the
member states. Although there are now used statistical methods for risk measurement, the most
common being the standard deviation (σ2), it should be noted that they have a major drawback
since they reflect the risk at the project level. Moreover, the classical statistical indicators
provide insight into project financial risk without taking into account the influence factors or
Copyright © 2006-2015 by CCC Publications
Development of a Fuzzy Logic System to Identify the Risk
of Projects Financed from Structural Funds 481
correlations that exist between the various projects [3]. FLS have the advantage of being able
to identify the financial risk for the entire portfolio of projects contained by the operational
program and to contribute to the decision of management to avoid or eliminate the financial
risk. The FLS input variables of this model are set according to the project particularities, on
which ultimately depend the financial risk of the project, or project value (VP) and the duration
of their implementation (DI). The output variable is the financial risk of the project (RF). The
assessment of the financial risk of the project (as an output variable of FLS) was structured by
verbal expressions (specific to fuzzy logic): high financial risk, medium financial risk and low
financial risk, depending on the seriousness of the risk but also to highlight the intensity of the
losses from the budget allocated to EU member states as a result of the manifestation of the
financial risk event [6]. The FLS developed to identify the financial risk of the projects financed
from structural funds becomes a novelty in literature but also a management tool for decision
makers. With the help of FLS they can measure the financial risk for all the projects entering
in the structure of the operational program. Based on these ways of measuring the financial
risk, identified using FLS, corrective action can be taken for the efficient and fair presentation
of structural funds for member states of the EU budget.
2 The concept of financial risk of projects financed from struc-
tural funds
The financial risk of the projects financed from structural funds is a fairly new concept both in
literature and in practice. In essence the financial risk of the projects should answer the following
question: "What is the financial size of the potential loss that a member state is expected to suffer,
due to the implementation of projects financed from structural funds?" The project financial risk
depends on a number of factors determined by the main project implementation cycle. In this
category are included factors that are measured through the implementation period, resulting the
physical progress of projects or the requests repayment duration. In practice, the most important
factor that influences the financial risk of the project remains the physical progress [11]. The
physical progress, although it seems a technical term, is most often defined as the ratio between
the duration of implementation of a project under implementation cycle (Dic ) and the duration
of implementation actually achieved (Dr ) according to a relation of the form:
Pf =
Dr
Dic
×100 (1)
The achieved physical progress can record higher values than those set, for a project suitable
for the implementation cycle, situation in which the financial risk of the project is small or can
record lower values, where the financial risk of the project increases. The financial dimension
of a project risk therefore depends on the value of the project (Vp), on the physical progress
established under implementation cycle (pfc) and on the actual physical progress achieved (pr)
after a relationship of the form:
Rf = Vp(pfc −pfr) (2)
or
Rf = Vp × (
Dct
Dip
−
Dr
Dip
) (3)
The higher is the difference between the physical progress of the project under implementation
cycle (pfc) and the actual physical progress achieved (Pfr), the higher is the risk of losing a larger
482 M.I. Boloş, D.C. Sabău-Popa, P. Filip, A. Manolescu
amount of the budget allocated to a project. In practice, the most common form of financial risk
measurement remain in the project’s value (Vp) and the deviation of the achieved implementation
duration of the project Dr towards the set one based on implementation cycle (Dci), after a
relationship of the form:
Pf = Vp ×
Dci −Dr
Dci
×100 (4)
There are projects with high financial risk, for which the difference between the two periods
(according to implementation cycle and the one actually achieved) is far from average, or projects
with low financial risk for which the same difference is close to average. The average difference
between the two periods is determined for all projects that are part of the operational program.
To appreciate the intensity of the financial risk of a project it can be used the standard deviation
or variance [13], characterizing the removal from the average financial risk of a project after a
relationship of the form:
Rf =
√
1
N
n∑
i=1
Rfi −Rf (5)
Depending on the value of this statistical indicator, the intensity of the financial risk is
estimated. The higher is the percentage value of this indicator, the higher is the financial risk of
lossing the budget allocated to projects. The indicator, thus, doesn’t provide a complete picture
of risk, as it is determined based on historical values recorded in previous periods of time [2].
In FLS , the financial risk of the projects will be divided into three categories (large, medium
and small), considered as an output of the system. In essence, the financial risk of a project,
regardless its quantification and intensity, depends on a number of factors that will transform
the input for FLS, as follows [10]:
1. The value of projects, that influences the size of the financial risk: The rule is simple: The
higher is the project value and the deviation from the implementation period, the higher
is the financial risk
2. The project implementation duration, which is determined according to the intensity of
risk: The implementation period is known in the literature as the duration necessary
to implement a project, so that it can be achieved its project objectives and outcome
indicators. The further the implementation period of this project removes from the one set
according to the implementation period, the higher is the risk that a part of the budget will
be lost.The project value and its implementation duration, as influencing factors underlying
the financial risk will be considered for FLS as input variables.
3 The development of the FLS to identify financial risk of a
project
Each fuzzy logic system supposes four distinct phases [14] as follows: setting the input
variables and their associated fuzzy sets, the fuzzy rule base identification, the establishment
of fuzzy inference operators and defuzzification. In the first stage of development of the fuzzy
logic system were established the input variables mentioned above, namely: the project value
(PV) and the duration of implementation (DI), while the output variable (result) is the financial
risk of the project. The input variables are structured according to the size of their impact
on financial risk. The project value (VP) is divided into three categories, namely: high value
Development of a Fuzzy Logic System to Identify the Risk
of Projects Financed from Structural Funds 483
projects (HVP), the average project value V Pm, and the small projects value V Pm. At the same
time, the duration of project implementation is structured according to the exceeding of the
project implementation duration to that established in the implementation cycle as follows: high
exceeding (between 180 days and 360 days) (DIM), average exceeding (between 90 days and 180
days) DIm and low exceeding DIm under 90 days. The financial risk of the project, as the output
variable of the system, is determined by the fuzzy base rules, the fuzzy inference operators as
well as by the expert assessments, that are divided into three categories namely: high financial
risk (RFM), average financial risk RFm and low financial risk RFm. In order to completely define
the fuzzy set, for the input variables were established the following membership functions [3]:
1. The trapezoidal membership function, for the value of projects (VP) defined according to
the value types of projects
2. The triangular membership function, for the exceeding duration of the project implemen-
tation (DI) which was also structured in: high, medium and low exceeding;
Figure 1: The trapezoidal membership function for the input variables
The fuzzy sets allow the partial membership of elements, the fuzzy membership degree being
able to take any value from 0 (not belonging) to 1 (full membership). For example, the trapezoidal
membership’s function for V P ∈ [V Pn−2,V Pn+2], and for project with medium values will be
expressed as:
µV PM(V P) =
0 if V Pn−2 < V P and V P > V Pn+2
V P−V Pn−2
V Pn−1−V Pn−2 if V Pn−2 ≤ V P ≤ V Pn−1
1 if V Pn−1 ≤ V P ≤ V Pn+1
V Pn+2−V P
V Pn+2−V Pn+1 if V Pn+2 ≤ V P ≤ V Pn+1
Similarly, the trapezoidal membership function for the interval V P ∈ [V Pn−k,V Pn−1], which
corresponds to the values of small projects, which will be expressed as follows:
484 M.I. Boloş, D.C. Sabău-Popa, P. Filip, A. Manolescu
µV Pm(V P) =
0 if V P < V Pn−k and V P > V Pn−1
V Pn−1−V P
V Pn−1−V Pn−2 if V Pn−2 ≤ V P ≤ V Pn−1
1 if V Pn−k ≤ V P ≤ V Pn−2
The triangular membership function for the input variable, the exceeding of the duration of
implementation (DI) of the project is represented in figure no.2. The triangular membership
function can be expressed, for example, for the low exceeding of the duration of implementation
by the relationship, (DI ∈ [DIn−k,DIn−1]):
µDIm(DI) =
0 if DIn−k < DI and DI > DIn−1
DI−DIn−k
DIn−2−DIn−k
if DIn−k ≤ DI ≤ DIn−2
DIn−1−DI
DIn−1−DIn−2 if DIn−2 ≤ DI ≤ DIn−1
Similarly, the triangular membership function for the input variable, the duration of the
implementation of the project on the interval [DIn−2,DIn+2]], can be expressed as:
µDIm(DI) =
0 if DIn−2 < DI and DI > DIn+2
DI−DIn−2
ḊIn−2−DIn−2
if DIn−2 ≤ DI ≤ ḊIn−2
DIn+2−DI
DIn+2−ḊIn−2
if ḊIn−2 ≤ DI ≤ DIn+2
Figure 2: The triangular membership function for input variable of the system - The duration
of implementation (DI)
For the FLS were identified the input variables of the system and their membership functions
according to fuzzy rules, to which a fuzzy set is completely determined by the set of ordered
pairs [7, 8]:
A = {(x,µA(x))/x ∈ X} (6)
In the second stage of the FLS are set the fuzzy rules base. The specific of these rules is that
based on two conditions, namely "if" and ‘"then", are established with the help of experts the
Development of a Fuzzy Logic System to Identify the Risk
of Projects Financed from Structural Funds 485
influence factors of the financial risk. The number of fuzzy rules base will be equal to 32 = 9
and the financial risk will be divided into three risk classes. The fuzzy rules base for financial
risk related to projects financed from structural funds will have the following form:
Rule 1: If the project value is large (VPM) and the exceeding of the duration of the imple-
mentation is high (DIM), then the project financial risk is high (RFM);
Rule 2: If the project value is average V Pm and the exceeding the implementation is high
(DIM), the financial risk is high (RFM);
Rule 3: If the project value is small V Pm and the exceeding of the duration of the imple-
mentation is high (DIM), then the financial risk is medium RFm;
Rule 4: If the project value is large (VPM) and the exceeding of the duration of the imple-
mentation is average DIm, then the financial risk is high (RFM);
Rule 5: If the project value is average V Pm and the exceeding of the duration of the imple-
mentation is average DIm, then the financial risk is medium RFm;
Rule 6: If the project value is small V Pm and the exceeding of the duration of the imple-
mentation is average DIm, then the financial risk is small RFm;
Rule 7: If the project value is large (VPM) and the exceeding of the duration of the imple-
mentation is small DIm, then the financial risk is medium RFm;
Rule 8: If the project value is average V Pm and the exceeding of the duration of the imple-
mentation is small DIm, then the financial risk is medium RFm;
Rule 9: If the project value is small V Pm and and the exceeding of the duration of the
implementation is small DIm, then the financial risk of the project is small RFm;
The fuzzy rules base for FLS that targets the projects financial risk, aim to capture the best
way in which financial risk occurs when there is a change in the value of projects and concomitant
a change in terms of exceeding the project implementation duration. Depending on the intensity
of these changes, the risk of project budget loss may be, as mentioned above: large, medium or
small. On the third stage were applied the fuzzy inference operators on the rules basis generated
in the second stage [4]. As shown, the fuzzy rules base is connected by "AND" which means
that the operator inference for the rules base is minimum. For each of the previous defined fuzzy
rules, is established the degree of membership of the output variable (RF). Therefore will result:
For rule 1: µRFM,1 = min[µV PM(V P),µDIM(DI)]
For rule 2: µRFM,2 = min[µV Pm(V P),µDIM(DI)]
For rule 3: µRFm,3 = min[µV Pm(V P),µDIM(DI)]
For rule 4: µRFM,4 = min[µV PM(V P),µDIm(DI)]
For rule 5: µRFm,5 = min[µV Pm(V P),µDIm(DI)]
For rule 6: µRFm,6 = min[µV Pm(V P),µDIm(DI)]
For rule 7: µRFm,7 = min[µV PM(V P),µDIM(DI)]
For rule 8: µRFm,8 = min[µV Pm(V P),µDIm(DI)]
For rule 9: µRFm,9 = min[µV Pm(V P),µDIm(DI)]
From the rules analysis is shown that the affiliation of the system financial risk in a fuzzy set
can be from one or more fuzzy rules which are likely to result in different degrees of belonging
to the same fuzzy set. But it takes a single degree of belonging and in order to establish it,
is applied a fuzzy controller MAX corresponding to the reunion of the fuzzy sets. Under these
conditions will result [9]:
µRFM = max[µRFM,1,µRFM,2,µRFM,4]
µRFm = max[µRFm,5,µRFm,7,µRFm,8]
µRFm = max[µRFm,3,µRFm,6,µRFm,9]
In this stage are obtained the solutions of the fuzzy rules, without a certain amount of input
variables in the system (V Pi,DIi) to be determined the intensity of the financial risk by applying
all rules of financial risk in the fuzzy base. It is therefore necessary to identify these solutions at
486 M.I. Boloş, D.C. Sabău-Popa, P. Filip, A. Manolescu
the last stage of FLS, namely defuzzification. In the last stage of defuzzification is extracted a
deterministic scalar value, from the fuzzy information which is associated to the output variable,
the essence of which is to provide more explicit the best value of the output variable [1]. Each of
the result in the third stage of the FLS will be used to determine the surface area (Si) bounded by
the parallel to the horizontal axis, taken through the point that determines the size of the output
variable, the horizontal axis (Ox) and the graphic of the function associated to output variables.
For a given value of the project (V Pi) and some exceeding of the project implementation duration
(DPi ) would result that from the original surface (Si) only a certain percentage (p) is the result
that will be taken into account to determine the final amount of financial risk [5]. The conversion
of the fuzzy result in a real number value is done by determining the center of gravity of the
surface obtained by aggregating the proportion (p) of the initial areas for each graphical input
variables as follows:
Z =
∑9
i=1 µV P,DI(V Pi,DPi)×V Pi/DPi∑9
i=1 µV P,DI(V Pi,DIi)
(7)
The result (S) of equation 7 undergo a conversion from area into a real value through the
centroid method, which consists in determining the numerical value (z) through which the per-
pendicular traced to the horizontal axis divides the S area into two equal parts by a relationship
of the form:
S =
9∪
i=1
%pSi (8)
The obtained numerical Z value represents the size of the financial risk of a project that has
a certain value and a certain level recorded for the (exceeding) implementation duration of the
project. The higher this value is, the higher is the probability of losing a part of the project
budget.
4 The FLS simulation for the financial risk of projects financed
from structural funds
The developed fuzzy logic system was simulated using MATLAB programming language,
taking into account the following assumptions, namely:
1. The input variable - the value of projects was divided into three classes: small projects
(between 0 and 350 million UM), average project (between 250 million and 750 million
U.M.) and large projects ( between 650 million UM and 1,000 mil);
2. The input variable - the exceeding of the project implementation duration was also divided
into three classes, namely: low exceeding (between 0 and 90 days), average exceeding
(between 60 to 180 days) and high exceeding (between 150 days and 270 days).
In the first FLS stage, were established the input variables and their membership functions.
Thus, for the input variable, the project value (PV), was stated the following fuzzy set (trape-
zoidal membership function) as depicted in Figure 3.
For the input variable, the exceeding of the project implementation duration (DI), resulted
the following fuzzy sets (using the trapezoidal membership function) as depicted in Figure 7.
For the output variable, the financial risk of the projects, were established three risk classes,
using the triangular membership function as follows: low financial risk for values between 0 and
Development of a Fuzzy Logic System to Identify the Risk
of Projects Financed from Structural Funds 487
Figure 3: The fuzzy set for the input variable - The project value
Figure 4: The fuzzy set for the input variable - The implementation duration
488 M.I. Boloş, D.C. Sabău-Popa, P. Filip, A. Manolescu
3, average financial risk for values between 2 and 6 and greater financial risk for values between
5 and 10. The resulted fuzzy set for the output variable is represented in Figure 5.
Figure 5: The fuzzy set for the output variable - The financial risk of the projects
After continuing the simulation of FLS, for the financial risk of the projects, were established
9 fuzzy rules base according to the developed and were introduced in the program shown in
Figure 6.
Figure 6: The fuzzy rules base for the financial risk in Matlab
Subsequently were applied the inference operators on fuzzy rules base and the results were
presented in Figure 7.
The obtained results are for a project with a value of 500 million U.M., 135-days exceeding
duration of the project implementation and a financial risk value of 4.33. The FLS simulation
for the financial risk was further carried out for different values of input variables in order
Development of a Fuzzy Logic System to Identify the Risk
of Projects Financed from Structural Funds 489
Figure 7: Results obtained by applying the inference operators on fuzzy rules base
to identify the developments that the financial risk has when changes occur in values and in
exceeding duration of the project implementation. The results were obtained in Figure 8.
Figure 8: The evolution of financial risk for projects based on input variables
The simulation results are:
1. For project values between 0 and 600 million and an exceeding duration of the project
implementation of 55 days, the financial risk tends to zero;
2. For project values between 600 million and 800 million and an exceeding duration of the
project implementation between 55 and 100 days, the financial risk is increased from 0 to
about 4.5 (and is considered a medium risk);
3. For project values between 800 million and 1,000 million and an exceeding duration of the
project implementation between 100 and 270 days, the financial risk is increased from 4.5
to the maximum 9 (being considered a high risk);
490 M.I. Boloş, D.C. Sabău-Popa, P. Filip, A. Manolescu
5 Conclusion
The computational intelligence is an area of great interest for both specialists in computer sci-
ence and finance. This is because often are abandoned the statistical concepts and methods that
didn’t characterize the phenomena and economic processes and are used specific computational
intelligence methods that adapt quite well the dynamics of the phenomena studied. The fuzzy
logic system developed in this paper, as part of computational intelligence, studies the behavior
of financial risk of the projects financed from structural funds when there is a change in the value
of projects or in the durations of implementation. This financial risk was defined as the risk of
losing a part of the project budget, when there are exceedings in the duration of implementation,
based on their implementation cycles. The rules of the fuzzy base were defined according to the
impact that the system input variables have on financial risk. The fuzzy inference operators were
applied on the basis rules to determine the membership in fuzzy output variable. With the help
of defuzzification was ensured the convertion of the fuzzy values in numeric values to determine
the size of financial risk for different values of the input variables. Following the simulation for
the output variable (the financial risk of projects), were reached the following conclusions:
1. There are situations where the financial risk is zero, or almost zero, for different values of
input variables in the system;
2. The financial risk of projects increases as changes occur in the value of projects and in
the duration of implementation. This increase in financial risk value becomes in time
proportional to changes in the input variables in the system;
3. The financial risk is maximum, when the input variables in the system approach the max-
imum values that they may register;
The developed fuzzy logic system is a management tool for decision making in the structural
funds, under which can be taken measures to avoid or reduce the financial risk, especially for
the early identification of the emerging financial risk in the portfolio of projects falling within
the structure of the operational program. This early identification of financial risk can be very
useful in structural funds management, for taking the necessary actions to avoid this category of
risk [12].
The financial dimension of risk can be determined by calculating the financial risk using the
formula 4 for each project, where FLS indicates values above the minimum for the financial
risk. The value obtained is the value of projects that may be at risk of losing resources that are
allocated from the Structural Funds through operational programs. The fuzzy logic can be also
developed on classes of projects, through clustering technique to identify financial risk for each
class of projects which will be useful in the future because each operational program includes an
amount of projects.
Bibliography
[1] A. Altrock, Fuzzy logic and Neuro Fuzzy Logic Applications Explained (1995); Prentice
Hall, Englewood Cliffsm.
[2] I.A. Bradea, C. Delcea, R.M. Paun (2014); Managing and Controlling the KRIs in Hospi-
tals Proceedings of 24rd IBIMA Conference: Crafting Global Competitive Economies: 2020
Vision Strategic Planning & Smart Implementation, Italy, ISBN: 978-0-9860419-3-8, 1824-
1830.
Development of a Fuzzy Logic System to Identify the Risk
of Projects Financed from Structural Funds 491
[3] I.A. Bradea (2014); Risks in Hospitals. Assessment and Management The Romanian Eco-
nomic Journal, ISSN: 2286-2056, 54(XVII): 25-37.
[4] R. Fuller (2000); Introduction to Neurofuzzy Systems, Advances an Inteligent and Soft
Computing, vol 2, ISBN 978-3-7908-1256-5.
[5] C. Kahraman, I. Kaya (2010); A Fuzzy Multicriteria Methodology for selection Among
Energy Alternatives, IExpert Systems with Applications, 37(9): 6270-6281.
[6] S.M. Mousave, F. Joloi, R. Tavakkoli-Moghaddam (2013); A Fuzzy Stochastic Multi-
Attribute Group Decision-Making Approach for Selection Problems, Group Decision and
Negotiation, 22(2): 207-233.
[7] S. Nadaban (2015); Fuzzy Euclidean Normed Spaces for Data Mining Applications, Inter-
national Journal of Computers Communications & Control, 10(1): 70-77.
[8] S. Nadaban, I. Dzitac (2014); Atomic Decompositions of Fuzzy Normed Linear Spaces for
Wavelet Applications, Informatica, http://dx.doi.org/10.15388/Informatica.2014.33, 25(4):
643-662.
[9] A. Nieto-Morote, F. Ruz-Vila (2011); A Fuzzy Approach to Construction project Risk As-
sessement, International Journal of Project Management, 29(2): 220-231.
[10] E. Scarlat, N. Chiriţă, I.A. Bradea (2012); Indicators and Metrics Used in the Enterprise
Risk Management (ERM), Economic Computation and Economic Cybernetics Studies and
Research Journal, 4(46):5-18.
[11] M.L. Tseng (2010); Implementation and Performance Evaluation Using the Fuzzy network
Balanced Scorecard, Computers & Education, 55(1): 188-201.
[12] Y.L. Xu, J.F.Y. Yeung, A.P.C. Chan, D.W.N. Chan, S.Q. Wang, Y.L. Ke (2010); Develop-
ing a Risk Assessement Model for PPP project in China - A Fuzzy Synthetic Evaluation,
Automation in Construction, 19(7): 9293-943.
[13] L.A. Zadeh (1992); Fuzzy logic and the calculus of fuzzy if-then rules, Proceedings of the
22nd Intl. Symp. on Multiple-Valued Logic, Los Alamitos, CA: IEEE Computer Society
Press, 530-561.
[14] L.A. Zadeh (1996); Fuzzy logic - computing with words, IEEE Trans. Fuzzy Systems,
4(2):103-111.