Despite of increasing interest of researchers to issues related to maturity and specially the role of organizational maturity and its impact on OPM3 there is not enough studies about maturity level measurement. The purpose of this research is maturity assessment of OPM3 of organizations by an intelligent system. Here, a Fuzzy Expert System has been designed with considering main effective variables on maturity assessment as Inputs variables and level of maturity as output. Then, the system rules have been extracted from some experts and the system has been developed with the use of FIS tool of MATLAB software. Finally, the presented steps have been run in an IT company as empirical study.

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ACEEE Int. J. on Information Technology, Vol. 3, No. 2, June 2013
A Fuzzy Expert System for Maturity Assessment based
on OPM3
Ahmad Nadali*1, Saeede Vakhshoori2, Mahdieh Khalilinezhad3 , Shima Khalilinezhad4
2
Department of Information Technology Management, Science and Research Branch, Islamic Azad University, Tehran, Iran
* Corresponding Author Email: Nadali.ahmad@gmail.com
1
Department of Business Management, North Tehran Branch, Islamic Azad University,
Tehran, Iran
Email: Saeedevakhshoori@yahoo.com
3
Department of Computer Engineering, University of Qom, Qom, Iran
Email: A.khalilinezhad@gmail.com
4
Department of IT Management, University of Sistan and Baluchestan, Zahedan, Iran
Email: Shimakh2000@gmail.com
Abstract— Despite of increasing interest of researchers to
issues related to maturity and specially the role of
organizational maturity and its impact on OPM3 there is not
enough studies about maturity level measurement. The
purpose of this research is maturity assessment of OPM3 of
organizations by an intelligent system. Here, a Fuzzy Expert
System has been designed with considering main effective
variables on maturity assessment as Inputs variables and level
of maturity as output. Then, the system rules have been
extracted from some experts and the system has been
developed with the use of FIS tool of MATLAB software.
Finally, the presented steps have been run in an IT company
as empirical study.
Index Terms - Maturity Assessment, Fuzzy Expert System,
OPM3.
I. INTRODUCTION
Project Management can be described as “a general purpose management tool that can bring projects to successful
completion and to the satisfaction of the project stakeholders, given the traditional constraints, of defined scope, desired quality, budgeted cost, and a schedule deadline. Hence,
project management is applicable to any organization with
the core objectives of scope, quality, schedule and cost” [1,
2]. The need for project Management and the benefits that
are possible from implementing project management methodologies are well documented and in many industries project
management has already become both a central activity and
the third element of organizational management systems that
is bringing balance, harmony, and success in global organizations [1, 2]. Project management provides a special and
distinct role, due to the organizational form of traditional structures, which is highly bureaucratic and cannot respond rapidly enough to a changing environment [1, 3]. Maturity models are seen as models that reflect certain aspects of reality,
often called capabilities, and define qualitative attributes
which are used to classify a competence object into one of
several clearly defined areas. These classes are typically
brought into a sequential order [4]. Maturity models in areas
involving process and high-performance delivery are proving to be useful because they allow individuals and organi
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DOI: 01.IJIT.3.2.1142
zations to self-assess the maturity of various aspects of their
processes against benchmarks. Many scholars have put forward the evaluation index system of project management
capability. Rad, Parviz F. Levin, and Ginger divided the project
management capacity into four areas: enterprise management,
material management, people management and technical content management [5, 6]. Jian Lirong and Liu Sifeng applied
the ideas of systems engineering to analyze the system of
project management capabilities, and divided project management capabilities into four levels: capability to develop
project management strategic planning, ability to choose the
project management organization, systems engineering capabilities of project management, project management team
ability [5,7].At present, many studies of the project management maturity focused on empirical research, examined the
stage of enterprise project management, and determined the
enterprise project management in which a certain stage of
maturity model. James J. Jiang et al. investigated software
enterprise management maturity, noted the high failure rate
in the software design, and insisted that CMM can improve
the success rate of software production [5,8]. E.S. Anderson
and S.A. Jessen investigated the status of the project maturity in organization, pointed out that the maturity of the organization primarily composed of three steps: the project management, program management, and document management,
and put forward that the attitudes and knowledge is more
important than the action for an organization in terms of maturity management [5,9]. Pekka Berg proposed the Quality
Maturity Model (QMM) to determine the management level
of R&D projects [5, 10]. Mohammad Khoshgoftar and Omar
Osman compared recent maturity models in terms of selected
variables, and concluded that OPM3 is a more suitable model
than others [5,11]As it was previously mentioned, there are
some models that can measure level of maturity and OPM3 is
one of the most applicable. If you are a project manager and
you are concerned if the software of assessment of organizational project management maturity model (opm3) is not available, or you anxious to achieve to the intuition without using
the particular software, what can you do to convince senior
management of the benefits of adopting a different model?

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ACEEE Int. J. on Information Technology, Vol. 3, No. 2, June 2013
development levels including Initial Repeatable, Defined,
Managed and Optimizing to assess the maturity of software
processes .Most maturity models are two-dimensional which
keep in closer relationship with project management than
CMM. PMS-PMMM is a matrix model. The first dimension
reflects five maturity levels based on the SEI CMM. The
second dimension depicts the key areas of project management concerned and adopts the Structure of nine PMI knowledge areas.[18] In November 2003, the U.S. Project Management Institute (PMI) launched the Organizational Project
Management Maturity Model (OPM3), and promoted as the
industry standard [5,21].At present, many studies of the
project management maturity focused on empirical research,
examined the stage of enterprise project management, and
determined the enterprise project management in which a
certain stage of maturity model.[14].OPM3 differs from other
models in that it is three dimensional, so it is possible to
determine the maturity of an organization from different perspectives in different ways on the basis of OPM3[18]. In a
word, superior to any other management maturity model,
OPM3 gives consideration to project management, program
management and portfolio management, focuses on the continuous improvement of organizational project management,
and creatively develops continuous structure by means of
logic relevance. In addition, compared with CMM,
PMSPMMM and P3M3 (P2MM), OPM3 enjoys some advanced features. The opm3 proposed by PMI provides a
framework and guideline to assess the organizational project
management capability [18].
Can you trust your own intuition and experience? Where can
you look for evidence that there is a better way of approaching the maturity of project management across an organization? [12] This paper presents the results of an investigation
into the using a different way to foresight levels of maturity
of project management based on the OPM3.
This article mainly focuses on the evaluation of “OPM3”
in an IT organization. The aim of this study is to design an
Expert System which evaluating the maturity level of an IT
company as Output based on major factors as Input variables.
The factors consist of four main variables. Some project
managers as the research experts identify the innovation
culture level according to linguistic variables based on
different situations of these four main factors. Since the
experts’ judgment is explained with linguistic variables, using
fuzzy functions and Fuzzy Inference system can be
advantageous to build a basic knowledge system for
assessing maturity situation in organization.
The remainder of this paper is structured as follows: in
the next section, the literature review about Project
management maturity models and OPM3 are represented, in
section 3 the concept of fuzzy expert systems is outlined, in
section 4 the proposed system & empirical study process of
this research is presented as a case study, In Section 5 the
results and discussion are presented. Finally the article
conclusions are drawn in Section 6.
II. THE LITERATURE REVIEW
A. Project Management Maturity ModelsThe Literature
A project is a temporary endeavor undertaken to create a
unique product, service, or result [13]. Project management
maturity models, as a subset of strategic planning for project
management provide a means of identifying key steps, the
tasks that need to accomplish, and the sequence of events
needed to realize meaningful and measurable results.
Basically, the purpose of the maturity model is to provide a
framework for improving an organization’s business result
by assessing the organization’s project management
strengths and Weaknesses, enabling comparisons with
similar organizations, and a measure of the correlation
between an organization’s project management level and
actual project performance [14, 15,16,17] A large numbers of
complex and systematic projects are being established each
year.[18] The concept of process maturity was born in the
Total Quality Management (TQM) movement, where the
application of statistical process control (SPC) techniques
showed that improving the maturity of any technical process
leads to two things: a reduction in the variability inherent in
the process, and an improvement in the mean performance of
the process [12,19]. Project management maturity models are
important assessment tools for the profession. Maturity
models identify organizational strengths and weakness in
addition to providing benchmarking information [14,20].
There are many maturity models developed for organizations. CMM, as the first maturity model, can be regarded as a
one-dimensional framework. The model defines five maturity
© 2013 ACEEE
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B. OPM3
The Organizational Project Management Maturity Model
(OPM3) falls naturally within the sequence of Standards
published by the Project Management Institute (PMI).
Organizational Project Management Maturity Model (OPM3)
is to formulate such a standard, applicable to different sizes
and forms, different industries and cultural organizations, to
guide the organization to cultivate and enhance project
management capabilities, namely, to achieve the
organizational strategic goals by the success of the project
[5]. OPM3 is comprised of three general elements: knowledge,
presenting the contents of the Standard; Assessment,
providing a Method for comparison with the Standard; and,
improvement setting the Stage for possible organizational
changes [22]. There are three basic elements to applying
OPM3 in an organization:
1) The Knowledge element describes organizational
project management and organizational project management
maturity, explains why they are important, and how project
management maturity can be recognized. 2) The Assessment
element presents methods, processes and procedures that
an organization can use to self-assess its maturity. 3) The
Improvement element provides a process for moving from its
current Maturity to increased maturity. The Improvement element is what clearly differentiates OPM3 from other products in the marketplace [22] a “maturity model” is a conceptual framework, with constituent parts, that defines maturity
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III. FUZZY EXPERT SYSTEM METHODOLOGY
in the area of interest—in this case, organizational project
management. In some cases, such as with OPM3, a maturity
model may also describe a process whereby an organization
can develop or achieve something desirable, such as a set of
Capabilities or practices. This process can result in a more
highly evolved organizational state; in other words, a more
mature organization. In OPM3, this is reflected by the combination of Best Practices achieved within the Project, Program, and Portfolio domains [23]. A Best Practice is an optimal way currently recognized by industry to achieve a stated
goal or objective. For organizational project management,
this includes the ability to deliver projects predictably, consistently, and successfully to implement organizational strategies. Furthermore, Best Practices are dynamic because they
evolve over time as new and better approaches are developed to achieve their stated goal. Using Best Practices increases the probability that the stated goal or objective will
be achieved. OPM3 is a maturity model describing the incremental Capabilities that aggregate to Best Practices, and which
are prerequisite to effective organizational project management. The progression of increasing maturity designed into
OPM3 consists of several dimensions, or different ways of
looking at an organization’s maturity. One dimension involves
viewing Best Practices in terms of their association with the
progressive stages of process improvement—from standardization to measurement to control and, ultimately, to continuous improvement. Another dimension involves the progression of Best Practices associated with each of the domains
first addressing Project Management, then Program Management, and finally, Portfolio Management. Each of these
progressions is a continuum along which most organizations
aspire to advance. Also, within these two dimensions is the
progression of incremental Capabilities leading to each Best
Practice. Taken as a whole, these three dimensions constitute valuable reference points when an organization assesses
its maturity in organizational project management and considers possible plans for improvement. OPM3 was intentionally designed without an overall system of “levels” of maturity. Establishing specific maturity levels can be relatively
straightforward if the progression of maturity is one-dimensional. For example, as just discussed, there is a progression
of four stages of process maturity from process standardization through continuous process improvement. OPM3, however, is multidimensional. In addition to the three dimensions
described above, OPM3 also categorizes the Capabilities in
terms of their association with the five project management
process groups (Initiating, Planning, Executing, Controlling,
and Closing), permitting evaluation of a fourth dimension of
maturity. Multiple perspectives for assessing maturity allow
flexibility in applying the model to the unique needs of an
organization. This approach also produces a more robust
body of information than is possible with a simpler, linear
system of levels, giving the organization greater detail in
support of decisions and plans for improvement [23].
© 2013 ACEEE
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Fuzzy expert systems use fuzzy data, fuzzy rules and fuzzy
inference, in addition to the standard ones implemented in
the ordinary expert systems [24]. Fuzzy inference systems
can express human expert knowledge and experience by using
fuzzy inference rules represented in “if-then” statements. The
fuzzy inference process has five steps: Fuzzify inputs, apply
fuzzy operator, apply implication method, aggregate all
outputs and Defuzzify. In order to obtain a good FIS it is
necessary that the researchers possess domain knowledge;
the knowledge has to be represented in a symbolic form, be
complete, correct and consistent [25].
Following the fuzzy inference mechanism, the output can
be a fuzzy set or a precise set of certain features. Fuzzy
inference infers the results from the existing knowledge base.
1) Fuzzy concept base: This contains the terminology and
relevant predicate of a linguistic expression. Terminology is
in the domain of the fuzzy set, possesses many pre-defined
dismemberment values denoted by predicates. 2) Fuzzy
proposition base: Membership functions accrue to the fuzzy
proposition, which was induced from fuzzy concept base.
There are numerous types of membership functions, such as
S-shape, Z-shape, and P-shape, all easily definable with
equations and parameters.
There are different types of fuzzy systems are introduced.
Mamdani fuzzy systems and TSK fuzzy systems are two types
of fuzzy systems commonly used in literature that has different
ways of knowledge representation. TSK (Takagi-SugenoKang) fuzzy system was proposed in an effort to develop a
systematic approach to generate fuzzy rules from a given
input–output data set. Numeric analysis approach of fuzzy
system was first presented by Takagi and Sugeno and then a
lot of studies have been made [26].
A basic Takagi–Sugeno fuzzy inference system is an
inference scheme in which the conclusion of a fuzzy rule is
constituted by a weighted linear combination of the crisp
inputs rather than a fuzzy set and the rules have the following
Structure:
If x is A1 and y is B1, then
(1)
z1 = p1x + q1y + r1 .
Where p1, q1, and r1 are linear parameters.
TSK Takagi–Sugeno Kang fuzzy controller usually needs
a smaller number of rules, because their output is already a
linear function of the inputs rather than a constant fuzzy set
[27,28].
Mamdani fuzzy system was proposed as the first attempt
to control a steam engine and boiler combination by a set of
linguistic control rules obtained from experienced human
operators. Rules in Mamdani fuzzy systems are like these:
If x1 is A1 AND/OR x2 is A2 Then y is B1
(2)
Where A1, A2 and B1 are fuzzy sets. The fuzzy set
acquired from aggregation of rules’ results will be defuzzified
using defuzzification methods like centroid (center of gravity),
max membership, mean-max, and weighted average. The
centroid method is very popular, in which the ‘‘center of mass’’
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ACEEE Int. J. on Information Technology, Vol. 3, No. 2, June 2013
of the result provides the crisp value. In this method, the
defuzzified value of fuzzy set A, d (A), is calculated by the
formula (3)
(3)
where is the membership function of fuzzy set A .Regarding
our problem in which various possible conditions of parameters are stated in form of fuzzy sets, the Mamdani fuzzy
systems will be utilized due to the fact that the fuzzy rules
representing the expert knowledge in Mamdani fuzzy systems, take advantage of fuzzy sets in their consequences,
while in TSK fuzzy systems, the consequences are expressed
in form of a crisp function [29, 30].
Fig.1. Three Gaussian Membership function for Standardize
IV. THE PROPOSED SYSTEM AND EMPIRICAL STUDY
In this section we try to evaluate the maturity level of
opm3 in organization, considering the level of each other of
major effected variables on it .This expert system is designed
for assessing the maturity degree of organizations based on
PMI criteria. As it was mentioned in the Second section,
OPM3 dimensions are included: Standardize (stan), Measure
(meas), Control (cont), Continuous improve (Impr), Organizational Enabler (OE) [8].
Here the purpose is assessment of Maturity Level (ML)
as output factor in an Iranian IT company according to the
situation of these five dimensions as main input factors. Since
the obtained ideas by the experts, managers and IT consultants, about the relation between the maturity level and each
criterion, are not precise and have ambiguity, evaluation is
done by linguistic variables.
To do this, a Mamdani’s Fuzzy Expert system has been
designed. This system is designed based on a set of obtained rules from experts regarding the relation between input variables and output. Some of the selected rules are shown
in Table 1.
TABLE I. T HE SELECTED RULES
FOR FUZZY EXPERT SYSTEM
Stan
1
2
3
4
5
6
7
8
9
10
11
12
Fig.2. Three Gbell Membership function for Measure
Meas
Cont
Impr
OE
M
H
M
L
M
L
M
M
H
H
L
H
H
M
L
M
H
M
L
M
H
H
L
L
M
H
M
L
H
L
H
M
M
M
M
M
L
H
L
L
M
L
M
L
L
M
L
H
H
M
VL
M
VH
L
M
H
H
VH
M
VL
Maturity
Level
(ML)
M
H
VL
L
H
VL
L
M
H
VH
VL
M
Fig.3. Three Gaussian2 Membership function for Control
After specifying, input and output variables, a membership function is defined for each of them. These membership
functions are illustrated in Figures 1 to 6.
In the next step, the discussed fuzzy expert system is
designed by MATLAB software according to the obtained
© 2013 ACEEE
DOI: 01.IJIT.3.2.1142
Fig.4. Three Gbell Membership function for Continuous improve
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ACEEE Int. J. on Information Technology, Vol. 3, No. 2, June 2013
Fig.5. Five Gbell Membership function for Organizational Enabler
Fig.7.Assessed Maturity level of Plan by designed system
Fig.6. Five Gaussian Membership function for Maturity Level
rules from the organization experts about the relation between
Input variables and Output which are shown in table I.
To create a Fuzzy Inference System (FIS), MATLAB fuzzy
logic toolbox provides a user friendly interface in which they
can choose the intended specification from drop-down
menus.
>>fis = readfis (‘OPM3’)
name: ‘OPM3’
type: ‘mamdani’
and Method: ‘min’
orMethod: ‘max’
defuzzs Method: ‘centroid’
imp Method: ‘min’
agg Method:’max’
input: [1*5 struct]
output: [1*1 struct]
rule: [1*12struct]
Variables Range: [0 1]
Fig.8.Assessed Maturity level of Project by designed system
VI. RESULTS AND DISCUSSION
This system is able to determine the innovation culture
measure of organization based on the effective criteria. Regarding to the proposed fuzzy expert system, we have evaluated the maturity level in IT Co. for “Project”, “Plan” and
“Portfolio” as Fig 7 to Fig 9.
According to the experts’ opinions as the inputs, the
following results have been identified:
As a result, Maturity Level (ML) of IT Company for Plan
© 2013 ACEEE
DOI: 01.IJIT.3.2.1142
Fig.9.Assessed Maturity level of Portfolio by designed system
would be 0.524 out of 1 and Maturity Level of IT Company
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for Project would be 0.28 out of 1 and finally Maturity Level
of IT Company for Portfolio would be 0.485 out of 1.
We can determine the Maturity Level of company by
simple averaging of 3 Maturity Levels: (0.524+0.28+0.485)/
3=0.43 Therefore Maturity Level of IT Company is 0.43 out of
1.
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[14] Khoshgoftar, Mohammad & Osman, Omar, “Comparison of
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CONCLUSIONS
Assessing the maturity level of OPM3 based on effective
criteria is the major fundamental in this paper. To reach this
goal, a Mamdani’s Fuzzy expert system has been designed
with considering the situation of four main effective factors
on maturity in the organization as the Inputs and the maturity level as the output and Membership functions have been
defined for the variables. Then, according to the rules which
have been obtained from consultants and managers as the
experts, the fuzzy expert system has been designed. This
system has the ability to determine the organization OPM3
level based on criteria levels as an evaluator system. The
most important advantage for this Fuzzy Expert system is
predicting the degree of plan, project and portfolio. Finally,
managers will be able to plan for the future works with considering the obtained results of the proposed system to improve their maturity current measure.
ACKNOWLEDGMENT
Here, we appreciate from the WBB Team & Experts of the
IT Company who have given their knowledge to the
researchers and supported this research.
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