C# method for all Types of Nodes in Fuzzy GERT

Abstract

The advancement of human communities depends on the quality of research. Research projects are usually cost as well as time consuming. Project scheduling is one of the integral parts of project management. Results achievement in short period is considered as an important factor. This paper presents new methodology to solve Fuzzy GERT networks for all kind of nodes. In this method the GERT network is simulated and scheduled by combination of C# and Matlab which leads to solve functions and equations faster than previous manually methods.

Full text

57
International Journal of Artificial Intelligence and Neural Networks– IJAINN
Volume 5 : Issue 1 [ISSN : 2250-3749]
Publication Date: 30 April, 2015
C# method for all Types of Nodes in Fuzzy GERT
[Roland Lachmayer, Mahtab Afsari, Rashid Hassani]
Abstract—The advancement of human communities depends
on the quality of research. Research projects are usually cost as
well as time consuming. Project scheduling is one of the integral
parts of project management. Results achievement in short
period is considered as an important factor. This paper presents
new methodology to solve Fuzzy GERT networks for all kind of
nodes. In this method the GERT network is simulated and
scheduled by combination of C# and Matlab which leads to solve
functions and equations faster than previous manually methods.
Keywords— Research Projects, Fuzzy GERT, α-cuts,
Scheduling, C#
I. Introduction
The history of using fuzzy logic in project control dates
back to the 70s decade. Chanas and Kamburowski [18]
introduced a new method titled FPERT. This method estimates
the duration of activities and project completion time using
fuzzy logic. Kaufman and Gupta [19] presented a method
based on taking the uncertainty provision for activity timing
into account and considering the conditions in which experts
extensively disagree. In this method, the fuzzy CPM has been
solved once using optimistic data and once using pessimistic
data. To find the fuzzy path, fuzzy subtraction is used.
Kufmann et al. and Alfered et al. [22]. Margaret Shipley et al.
[19] presented an algorithm named BIFPET which computed
the expected time using optimistic, most likely and pessimistic
times. Chang [5], [6] in his first article introduced the fuzzy
GERT method for solving the reliability problem for series
systems. In his second article, he presented the capability of
repairable systems using fuzzy GERT method. The Chang
method has investigated the issue using the Exclusive-OR and
cannot be used in research projects which include different
types of node. The Itakura and Nishikawa[7] method has also
some deficiencies as follows: Time is considered as discrete
fuzzy numbers which is impossible in reality.
Roland Lachmayer, Mahtab Afsari
Leibniz University of Hannover
Germany
Rashid Hassani
University of Rostock
Germany
Algorithm is determined based on parts, paths and loops
which is very difficult in extended networks. Other
deficiencies include:
• In this method, the possibility of occurrence has been
considered the same for all the loops which does not happen in
reality.
• Activities on the loop have been assumed certain in
recursions which is not always possible in reality.
• Only fuzzy has been used in the GERT network. It is
better to use a combination of fuzzy and probability.
• The membership degree of activity branch or the
occurrence possibility of branch has been expressed as a
certain number. In their method, the number of activities
outside each node belongs to a fuzzy network [22], [7]. The
solution is alike probabilistic GERT method except that min,
max functions have been used for fuzzy networks [4]. Karimi
Gavareshki et al. presented new Fuzzy GERT method [1], [2].
In this method they used Fuzzy Triangular numbers to show
time of activities. They compared 3 methods of Fuzzy GERT,
GERT and CPM to show application and suitability of Fuzzy
GERT for scheduling research projects [1], [16], [21].
A. Research project
Research projects are usually cost and time consuming and
do not end in result in short term. Project scheduling is one of
the integral parts of project management. Project Management
includes management of costs, time, quality, resources and
materials procurement. Research projects have some
particularities including [1],[2],[9]:
• Uncertainty in defining the activities
• Ambiguous and uncertain results of researches
• Uncertainty in periods of activities
• Non-repetitiveness of project activities
• Loops and recurrences.
Due to such problems, specific techniques are required
for scheduling research projects. Certain techniques do not
have the capability in modeling uncertain activities and
duration of activities and nodes [10]. So, it is obvious that
employing these techniques will increase the error percentage
in scheduling research projects.
GERT networks are widely used in solving existence and
reliability problems [23]. In GERT networks, two parameters
are related to activity branches, namely activity period and
occurrence probabilities are expressed in terms of probable
distribution. it seems that fuzzy GERT networks are the same
as probable GERT networks, but fuzzy parameters have been

58
International Journal of Artificial Intelligence and Neural Networks– IJAINN
Volume 5 : Issue 1 [ISSN : 2250-3749]
Publication Date: 30 April, 2015
replaced by probable parameters [9], [12].There are 6 type
nodes in GERT networks that includes 3 inputs and 2 outputs.
These nodes are shown in Table I.
TABLE I. combining 3 input and 2 output relations
B. Why we create this tool?
There is not any tool to draw GERT networks, except a
simulator that is produce in 1970. This simulator developed
through FORTRAN language [9]. There is not any newer tool
for GERT analysis, simulation and draw. So we decide to
create a tool to draw GERT diagram as first step. We have
tried to produce a user friendly tool that is developed through
C#.
As you know today, more researches we need to do since
1970. These research activities are time and cost consuming.
Using computer program help us to control and manage
research teams better. We feel this requirement and develop
software in this direction.
II. Application software
A. C#
In June 2000, Microsoft introduced the C# programming
language (pronounced ―C-sharp‖). It was designed to improve
upon the C++ language developed in the early 1980s at AT&T
Labs [13]. Because it is a totally new language, it has no
backward compatibility issues, as C++ had with its
predecessor, the C language. C# also shares many features
with Java, a programming language released in 1996 by Sun
Microsystems. It is impossible to discuss C# without
discussing the Microsoft .NET Framework that supports C#
and many other programming languages. The .NET
Framework is essentially a giant collection of tools for
software development. It was designed to allow traditional
text-based applications, GUI applications, and Web-based
programs to all be built with equal ease. Currently, over 60
languages are supported by the .NET Framework. That means
applications written in any of these languages have access to
the tools provided within the .NET Framework. Applications
can even be written that mix and match modules in various
languages. In April 2003, only three years after the first
release of C# and .NET, C# and the CLI (Common Language
Infrastructure—a significant subset of the .NET tools) were
adopted as ISO (International Organization for
Standardization) standards. C# continues to grow in popularity
[14], [15].
For the first 30 to 35 years of software development, text
was virtually the only method of displaying results in human-
readable form, and in those early days it was quite common
for programs to produce huge stacks of alphanumeric output
[15]. These days an alternative form of output— graphics—
has become much more widely used. With graphics, we are no
longer limited to 100 or so printable characters; instead,
programmers are free to construct whatever shapes and images
they desire. C# is an elegant and type-safe object-oriented
language that enables developers to build a variety of secure
and robust applications that run on the .NET Framework. You
can use C# to create traditional windows client applications,
XML Web services, distributed components, client-server
applications, database applications, and much, much more. We
used C# in our algorithm to solve fuzzy GERT because it was
easy in graphically part and for drawing GERT networks that
have complexity in structure, it is better to use C# for solving
the GERT networks.
B. Graphic software
In my developed software, a user must enter node
information such as fuzzy time, loops start and end nodes,
paths and multiple inputs node. Location of each node in the
computer display is another problem for a user. In this
software tried, a user draw nodes and paths and relationships
of them easily. After doing changes through user to the GERT
network, it is a complete model of a project. It means you can
change nodes information, location and relationships. At last
you can save this GERT network in a file in your computer. If
a model was large with many nodes and paths and loop, you
can enter this model in many days. Each time you can enter
some parts of model and save it, and then in another time you
can enter other parts to complete your model.
To control the setting and clearing of pixels, programmers
use a collection of functions that are part of a special software
package called a graphics library. Virtually all modern
programming languages, including C#, come with an
extensive and powerful graphics library for creating different
shapes and images. Typically, an ―industrial strength‖
graphics library includes hundreds of functions for everything
from drawing simple geometric shapes like lines and circles,
to creating and selecting colors, to more complex operations
such as displaying scrolling windows, pull-down menus, and
buttons. We restrict our discussion to a modest set of
functions. Although the set is unrealistically small, it will still
give you a good idea of what visual programming is like, and
enable you to produce some interesting, nontrivial images on
the screen. Graphical drawing in the C# and .NET
environment is supported by a framework called GDI. GDI
stands for Graphical Device Interface. To be able to draw on
the screen, it is necessary to set up a ―window‖ to hold the
drawing canvas [14], [15], [11], [3], [17].
III. Methodology
We need to develop two softwares. One to draw a GERT
network and save network data in a file and another to
evaluate nodes, paths, loops then generate outputs and results.
We use C# for developing first software. Matlab is used to
develop the second part of our software. Generated outputs
and results of first software which is C# software are inputs of
second software which is Matlab software. In both parts of our

59
International Journal of Artificial Intelligence and Neural Networks– IJAINN
Volume 5 : Issue 1 [ISSN : 2250-3749]
Publication Date: 30 April, 2015
software we must consider the following assumptions
[16],[21].
 Duration time of activities is represented by
triangular Fuzzy numbers.
 Repetitions number of loops is represented by
triangular fuzzy numbers.
 Membership degree of activities and loops is a
number between 0,1.
 Occurrence possibility of loops for different
repetitions is equal.
We used fuzzy relations in our calculations. Followings are
some used fuzzy equations and variables [1],[2]:
IV. Algorithm of Fuzzy GERT for
nodes
1) For start node set
2) For each node from start to end compute average
time of node (
i
MT
)
Figure 1. Exclusive-OR node
2.a) Computing ending time and membership degree of
precedence activities (for input activities to node):
2b) Computing initial release time of node
 
iTS~
Initial release time of node is calculated based on kind of
input side.
A) Exclusive-OR node
Normalization of membership degree:
B) Inclusive- OR node
C) AND node
3) Computing average time of node (
i
TM~
)
4) Computing project completion time with evaluating
network nodes from first node to end node, project network
is scheduled and project completion time is obtained that is
equal with average time of end node of project network.
V. Creating and running C#
program
Creating and running a C# program is basically a three-
step process.
The first step is to type the program into a text editor.
When you are finished, you save the file, giving it a name with
the extension .cs.
On the second step, the program must be compiled using a
C# compiler for your computer, and the resulting object code
linked with any C# library object code.
The third step loads and executes the program file; you
may have to type operating system commands for the last two
steps. The instructions in C#, or indeed in any high-level
language, are designed as components for algorithmic problem
solving, rather than as one-to-one translations of the
underlying machine language instruction set of the computer.
Thus they allow the programmer to work at a higher level of
abstraction.

60
International Journal of Artificial Intelligence and Neural Networks– IJAINN
Volume 5 : Issue 1 [ISSN : 2250-3749]
Publication Date: 30 April, 2015
We used MS-Visual Studio 2012 integrated development
environment (IDE) to type and edit my codes, compile and run
my program. It is suitable tool to create and run C# program.
VI. Description of defined
methodology
In our software there are many command buttons as you
can see in figure 2 which is the screen shot of software.
Figure 2. Example screenshot of this software
We have tried to describe each command button action:
1. ―Add Node‖ button action
Before click on ―Add Node‖ button you must enter node
number into a textbox, node position on the screen (X and Y)
which you can see in the node visual properties section of
screenshot, then select node type through combo box.
By pressing or clicking on ―Add Node‖ this operation starts.
Node information is read and checked so that the information
is not wrong and is in the limits. After checking the input
information, if there are not mistakes or deficiencies, this
information is added to the output array then a message is
shown to the user to be informed that the information is
inserted. Otherwise, the error message relevant to the
deficiency is shown to the user.
2. ―Save New Path Info‖ button action
On the left part of the form there is a place for inserting
information of each path (See Screen Shot). Information such
as number of path, number of the start and finish node, µ, and
t1, t2, t3 are given by the user. Then information is checked to
be complete and µ be in the limits. If there is any error, an
error message suitable with the user's mistake is shown
otherwise the path information is saved in an array and a
positive correct message is sent to the user.
3. ―Add Loop‖ button action
In the central part of the form and page designed by C# (See
Screen Shot), there is a place to insert input information of
each loop. Information such as destination node number of the
loop, µ of the loop and t1, t2, t3 of the loop that is entered by
the user. If the information is wrong or is not in the limits, it is
checked and an error message relevant to the mistake is sent.
Otherwise, the message of saving the information is shown
and the information of the loop or loops of each path is saved.
Here, you may have several loops for a path and the loops are
inserted one by one from the most internal to the most
external. This means that information of each loop is inserted
separately.
4. Draw GRET diagram in the form method
By pressing ―Draw Path‖ button the GRET starts to draw in
the bottom of the form. Showing GRET may start before final
saving of the information inserted in the model to ensure the
correctness of the input model. To draw GRET, information of
each path and loops of them is read one by one. According to
the type of start and finish nodes, appropriate shape of and
is drawn on the place of showing GRET in the determined
coordinate for this node. Then, the connecting line of these
two nodes is drawn. After that information of the loops is
analyzed and loop lines are drawn. The array of the
information of the paths is checked. If there is no path
remained, this algorithm is finished and otherwise, we do the
same set operations to fulfill the process.
5. ―Save To File‖ button action
By pressing ―Save To File‖ button, this operation starts. A
file opens to save the information. For the first path, (0, 0, 0,
0) is saved in this file. After arrangement of the information of
each path, a path and the first path is read and its information
and its loops are saved on the file. If all the loops of the path
are saved, it moves to the next path. If there is a path, the
process explained above starts and is repeated and if no path is
remained, a message is sent to the user that says saving the
information is finished and the desired file has been closed
successfully.
VII. Some flowcharts of this
software
We used C# to draw GERT networks. You can see the
following flowcharts that we used to write program in C#.
Figure 3. Draw GERT diagram in the form (splitContainer1_Panel2_Paint)

61
International Journal of Artificial Intelligence and Neural Networks– IJAINN
Volume 5 : Issue 1 [ISSN : 2250-3749]
Publication Date: 30 April, 2015
Figure 4. List Box Flowchart
Figure 5. Search Button
We made image list for adding type nodes. In this image list
we put shapes of GERT nodes in it.
For solving the GERT network with C# we should enter some
inputs. These inputs are:
 Node numbers
 X, Y pixels in quarter coordinator
 Number of node that loop enter to it
 Membership degree of nodes
 Membership degree of loops
 Triangular number for fuzzy time of activities
After entering inputs and saving them, we will have data as
output that will save in Debug that will be numbers
Figure 6. Undo Button
These numbers have the following meaning:
Path number, from node, type node (from node), to node,
type node(to node), times, mu, loop ( from node), loop (to
node) , repeat of loops, mu of loop, loop (from node) , loop (to
node) , repeat of loops , mu of loop.
VIII. Example of screenshot of this
software
To better explanation, we put an example screen shot of this
software as shown in figure 2. As you can see, you must enter
nodes information first. Then enter each path information and
loops of this path. Then after entering each path you can draw
the GERT network to confirm or undo this path. If your GERT
network is large, you can search for a node. Also you can
zoom in or zoom out to visit your model better. Finally you
can save your model information into a file. This file is
comma separated file, which you can save each path and its
loop information in a line. The information is separated from
each other via comma. You can save large model in many
times. This output file acts as input file for node evaluation
and program analysis for Matlab application.
IX. Conclusion
Fuzzy GERT networks are the same as probable GERT
networks in which fuzzy parameters have been replaced for
probable parameters. These networks provide several features
such as high capabilities to model research projects using
logical nodes, fuzzy branches and cycles as well as
simplifying the calculations and expressing uncertainty in the
projects. Therefore, fuzzy GERT networks are suitable means

62
International Journal of Artificial Intelligence and Neural Networks– IJAINN
Volume 5 : Issue 1 [ISSN : 2250-3749]
Publication Date: 30 April, 2015
for research project scheduling. So far, three different methods
have been presented for fuzzy GERT networks.
In reality, estimating a single number for a possibility is
difficult. The results from the three methods (fuzzy GERT,
fuzzy CPM and certain CPM) indicate that the method of
fuzzy GERT and Fuzzy CPM is closer to reality. In
conclusion, it is recommended that in higher levels, the fuzzy
GERT networks to be used because it considers loops and
uncertainties that may be unimportant for project managers.
In this article, we presented new method of fuzzy GERT
networks by using C# software to solve functions and
equations faster than manually method. We have seen how the
using of a high-level language overcomes many of the
disadvantages of assembly language programming, creating a
more comfortable and useful environment for the programmer.
In a high-level language, the programmer need not manage the
storage or movement of data values in memory. The
programmer can think about the problem at a higher level, can
use program instructions that are both more powerful and
more natural language–like, and can write a program that is
much more portable among various hardware platforms.
As a future work, we suggest the program that can solve all
kinds of nodes in Matlab and C# .we suggest also methods that
can show fuzzy inference systems in Matlab for all types of
nodes in GERT networks. C# is not the only high-level
language. You might be interested in looking at the other
online modules for languages similar to C# (Java, Python,
C++). Still other languages take quite a different approach to
problem solving. We used C# to draw Graphical part of GERT
networks because it is easier than other languages in Graphical
solutions
References
[1] Karimi. G and M. H,‖ New Fuzzy GERT Method for research project
scheduling’ IEEE International Engineering Management Conference,
pp. 820-824, ISBN: 0-7803-8519-5, Singapore, 2004.
[2] Karimi. G, M.H,‖New Technique in Fuzzy GERT for research project
scheduling‖, M.S. thesis, Dept. Electron. Eng, Iran Science and
Technology Univ., Iran, 2001.
[3] Rashid Hassani, Amirreza Fazely, Riaz Choudhury and Peter Luksch,
―Analysis of Sparse Matrix-Vector Multiplication Using Iterative
Method in CUDA‖, IEEE NAS 2013, IEEE computer society, ISBN:
978-0-7695-5034-3/13, pp. 262-266, DOI: 10.1109/NAS.2013.41, July
2013, Xiamen, China.
[4] Juite. A, ‖Fuzzy project scheduling approach to minimize schedule risk
for product development‖, Journal of Fuzzy Sets and Systems, Special
issue: Optimization and decision support systems. 2002.
[5] Chang, C. H, ‖Fuzzy repairable reliability based on Fuzzy GERT
Microelectronic reliability‖,36: NO.10 , pp. 1557-1563, 1996.
[6] Chang, C. H, ‖Fuzzy consecutive K-Out-Of-N Microelectronic
reliability‖, NO.12, pp. 1909-1922, 1994.
[7] Itakura. H and Nishikawa. Y, ―Fuzzy Network technique for technical
forecasting‖, Fuzzy set and systems, pp. 99-131, 1984.
[8] Pritsker. A, ―GERT:Graphical Evaluation and Review Technique‖, Rand
Corporation , NASA RM, pp. 44-73, 1996.
[9] Pasit Lorterapong and Osma Moslehi, ―Project Network analysis using
Fuzzy set Theory‖, Journal of Construction Engineering and
Management, pp. 308-318, DOI: 10.1061/ASCE0733-9364122:4308,
1996.
[10] Willy. H and Roel. L,‖project scheduling under uncertainty: survey and
research potentials‖ European journal of operational research, pp. 289-
306, 2005.
[11] Rashid Hassani, Amirreza Fazely and Peter Luksch, ―High Performance
Concurrent Multi-Path Communication for MPI‖, The 19th European
MPI conference (EuroPVM/MPI 2012), Springer LNCS 7490, pp. 285-
286, DOI: 10.1007/978-3-642-33518-1_34, Sep 2012, Vienna, Austria.
[12] Dwiri. T and Kablan. M, ‖Using fuzzy decision making for the
evaluation of the project management internal efficiency‖, Journal of
Decision Support Systems, pp. 712-726, 2006.
[13] ―Introduction to the C# Language and the .NET Framework‖, available
at ―http://msdn.microsoft.com/en-us/library/z1zx9t92.aspx‖, accessed on
10/07/2014.
[14] Online module to accompany Invitation to Computer Science, 6th
Edition, ISBN-10:1133190820, ISBN-13:9781133190820, Cengage
Learning, 2013.
[15] Lachmayer. R and Afsari. M, ―Algorithm of Converting Fuzzy GERT
into CPM for Research Project Scheduling With Case Study‖, 8th
International Conference of Project Management, 2012, Tehran, Iran.
[16] Lachmayer. R and Afsari. M, ―Fuzzy GERT method for Scheduling
Research Projects‖, 9th International Conference of Industrial
Engineering, 2013, Tehran, Iran.
[17] Rashid Hassani, Md. Aiatullah and Peter Luksch, ―Improving HPC
Application Performance in Public Cloud‖, FIE 2014, IERI Procedia by
ELSEVIER, ISSN: 2212-6678, DOI: 10.1016/j.ieri.2014.09.072, July
2014, Beijing, China.
[18] Margaret. F, and Khursheed Omer, ―A fuzzy logic approach for
determining expected values‖, Journal of the operational research
society, 1996, 47: 562-569.
[19] Kaufmann. A and Gupta. M, ―Fuzzy mathematical models in
engineering and management science‖, ISBN-10: 0444705015, 1988.
[20] Rashid Hassani, Ganesh Chavan and Peter Luksch, ―Optimization of
Communication in MPI-Based Clusters‖, CyberC 2014, IEEE computer
society, Oct 2014, Shanghai, China.
[21] Chanas. S, Zielinski. P, ―Critical path analysis in the network with fuzzy
activity times‖, Journal of Fuzzy Sets and Systems. 2001, 122: 195-204.
[22] Didier. D, Fargier. H. and Fortemps. P, Fuzzy scheduling: ―Modeling
flexible constraints‖, European Journal of Operational Research, 147:
231-252, 2003.
[23] Hong. Z, C. M.Tam and Heng. Li, ―modeling uncertain activity duration
by fuzzy number and discrete-event simulation‖, European journal of
operational research, No: 164, pp. 715-729, 2005.
About Author (s):
Prof. Dr.-Ing. Roland Lachmayer is head of the institute of
Product Development at Leibniz University of Hannover.
Mahtab Afsari has been graduated Master degree of
Industrial Engineering from Isfahan University of
Technology, Iran. She is PhD researcher in the Product
Development Institute at Leibniz University of Technology
from 2012 until now. She is working on GERT Networks in
Project Management and she is trying to make user friendly
software for GERT Networks as a computer package to
encourage project managers to use GERT Networks as the
best of networks that has appropriate benefits more that
CPM and PERT Networks.
Rashid Hassani received his BE degree in Information
Technology from VTU, India. He graduated with M.Sc.
degree in Computer System Engineering emphasized in
Embedded and Cooperating Systems from Halmstad
University, Sweden. He is currently a research assistant and
academic teacher in the department of computer science at
Rostock University, Germany. His research interests include
parallel and high performance computing, Cloud computing
and networking protocols.