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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Computational Intelligence for Project Scope</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Joseph M. McQuighan</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Robert J. Hammell II</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Towson University 8000</institution>
          <addr-line>York Road Towson, Maryland 21252</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
      </contrib-group>
      <abstract>
        <p> Managing scope is a critical process in information technology (IT) project management. Reporting the status of scope requires both an understanding of the status of individual activities and the aggregation into an overall status for the project. Unlike cost and schedule which have the objective measures of currency spent or days passed, scope is subjective. Understanding the status of scope as a project moves forward is critical to success; however, many times IT projects fail due to mismanagement of scope constraints. Recent research has confirmed status reporting and analysis as a major problem in IT projects. Other research has looked at how computational intelligence (CI) techniques might be applied to the domain of project management for cost and time constraints. This study looks at scope, a third constraint of project management. Since scope has properties of imprecision and vagueness, fuzzy logic would be an appropriate tool from Computational Intelligence. This study focuses on using the recently proposed Z-mouse for the collection of status information, and then using fuzzy logic for the reporting of project status for the scope constraint.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>Introduction</title>
      <p>
        Project managers collect data on the performance of their
projects in order to be able to report the status and to
forecast future performance. The Standish Group recently
surveyed 400 organizations and reported that only 32% of
information technology projects were successful, with
close to a quarter of the projects reported as failures
        <xref ref-type="bibr" rid="ref12 ref13 ref14">(Levinson 2009a)</xref>
        . Articles in CIO magazine point out that
poor requirements and scope management contributes to
these failures
        <xref ref-type="bibr" rid="ref12 ref13 ref14">(Levinson 2009b, Levinson 2009c)</xref>
        . Much
has been written about how to manage scope, from
improving business cases by establishing clear objectives,
to ensuring requirements specify an acceptance criteria, to
change management processes. The measuring of scope
status has largely been ignored because of the difficulty of
measuring requirements. This research looks at the fuzzy
nature of the inputs to status reports for the scope constraint
to answer two questions:
• Can fuzzy systems offer a tool that can capture the status
of the scope of an individual activity in an IT project?
• Can the scope status for activities be aggregated into a
meaningful project scope status?
It is anticipated that from the first question it might be
possible to determine if there is a common or generally
accepted understanding amongst project managers as to
how to report status when the inputs are vague or imprecise
for an activity. The Z-mouse tool proposed by Lotfi Zadeh,
which is an extension of Zadeh's work on fuzzy set theory
        <xref ref-type="bibr" rid="ref24">(Zadeh 1973)</xref>
        , is a leading edge data collection mechanism
that will be used as the data collection tool in this study.
      </p>
    </sec>
    <sec id="sec-2">
      <title>Project Status</title>
      <p>
        Weill and Broadbent have stated that information
technology (IT) is "very strongly project based"
        <xref ref-type="bibr" rid="ref23">(Weill
1998)</xref>
        . Understanding the status of a project is important to
project managers, upper management, and executive
sponsors of a project. There are many stakeholders outside
of a project's organizational structure also interested in the
status of a project
        <xref ref-type="bibr" rid="ref16">(PMBOK Guide 2008)</xref>
        . The overall
project status many times is seen as an aggregation of the
status of the three traditional project constraints: cost,
schedule, and scope. Depending on the project, the fourth
constraint of quality could also be present
        <xref ref-type="bibr" rid="ref16">(PMBOK Guide
2008)</xref>
        . Further, the overall status of each specific
constraint is an aggregation of the status of each activity
status considering that constraint. For example, each
activity is examined to judge how it is meeting the cost
constraint; the project status related to cost is an
amalgamation of all the individual activity cost-related
statuses. The project status for schedule is similarly
determined by first considering each how each activity is
performing with respect to that constraint. Finally, the
overall project status is established by combining the
individual constraint statuses. Thus, for the entire project,
the constraints are dimensions that are evaluated
independently and then later aggregated.
      </p>
    </sec>
    <sec id="sec-3">
      <title>The Problem</title>
      <p>
        As mentioned, the overall project status should be
determined by aggregating the individual activity statuses.
Instead, it is often reported as the opinion of the project
manager, which is subjective. Recent postings on the
LinkedIn internet site for professional project managers
requesting help on project status met with a wide variety of
rapid responses indicating the high interest level of
practicing project management professionals. Since
executive managers tend to focus on problem areas, this
translates to projects in trouble and as a result, there is a
tendency to under report status. Snow and Keil
investigated variance between the true status of a software
project from the reported status and found that accuracy
was a major problem. "The intangible nature of software
makes it difficult to obtain accurate estimates of the
proportion of work completed, which may promote
misperceptions regarding project status"
        <xref ref-type="bibr" rid="ref20">(Snow 2001)</xref>
        .
      </p>
      <p>
        Snow and Keil found that in addition to misperceptions
in the status of a software project, project managers might
also censor the status reports of poorly performing
projects. They cited an example of a project that lost $125
million over 3 years, yet senior management did not have
any insights into the problems. "The combined effects of
project manager misperceptions (errors) and bias in
reporting leads to what we call “distortion” in the project
status information received by senior executives"
        <xref ref-type="bibr" rid="ref20">(Snow
2001)</xref>
        . Snow identified the need for better tools for
understanding project status, and the necessity to automate
the reporting of status to avoid project manager bias and
reporting errors. With other research projects focused on
schedule and cost constraints, this study investigates scope.
      </p>
    </sec>
    <sec id="sec-4">
      <title>Project Status Background</title>
      <p>Projects by definition are unique, and "because of the
unique nature of projects, there may be uncertainties... The
project team must be able to assess the situation and
balance the demands in order to deliver a successful
project" (PMBOK 2008). Assessments are the feedback
during the execution of a project so that the project can be
guided to a successful completion. As projects move
forward, project managers are constantly gathering data on
the status, converting that data into useful information to
be reported, and then acting upon the information. Often
the data is vague, or needs interpretation. An example of
vague data is that it is difficult to determine to what extent
the scope is being met. To label project scope as 67.35%
met is recognized as impractical precision. The
imprecision in the data is the subject of this study, and
rather than using traditional methods to attempt to quantify
scope, computational intelligence offers new tools and
techniques for capturing vagueness. Computational
intelligence tools can "identify semantically ambiguous
concepts and convert them to fuzzy sets" (Cox, 1999)
which can then be resolved into solutions that can be
handled by project managers.</p>
      <p>With over 300,000 members, the Project Management
Institute (PMI) is recognized worldwide as an authority on
project processes. Their Project Management Book of
Knowledge (PMBOK) does not spell out the format of
status reports, nor does it tell project managers specifically
how to write a status report. Instead the PMBOK identifies
processes, defines inputs, tools and techniques, and the data
flows that tie the processes together (PMBOK 2008). The
PMBOK, as stated in section 1.1, is an assembly of good
practices that has the consensus and general agreement of
project management professionals. The PMBOK "is a
guide rather than a methodology. One can use different
methodologies and tools to implement the framework"
(PMBOK 2008). This gives practitioners the flexibility to
choose techniques that work for their given situation.</p>
      <p>The Project Management Institute's PMBOK identifies
the performance reporting process as part of their
Monitoring and Controlling process group (PMBOK 2008).
The PMBOK lists three outputs from the performance
reporting process: 1) Performance reports, 2)
Organizational process assets updates, and 3) change
requests. The purpose of the reports is to act as feedback
into the processes that "track, review, and regulate the
progress and performance of the project; identify any areas
in which changes to the plan are required; and initiate the
corresponding changes" (PMBOK 2008). To this extent,
data is converted into actionable information guiding the
project to completion. This process of reporting
performance is crucial to initiating corrective actions and
preventive actions, and becomes part of the organization's
lessons learned historical database.</p>
      <p>
        When reporting the status of projects, Dow and Taylor
have found that project dashboards are often used by senior
managers
        <xref ref-type="bibr" rid="ref7">(Dow 2008)</xref>
        . Dashboards are a graphical
summary of the status of a project, many having a drill
down capability. The purpose is to give a quick, high level
overview of a project to upper management whose role is
to prioritize, review, and make funding decisions
        <xref ref-type="bibr" rid="ref3">(Benson
2004)</xref>
        . Dow and Taylor state that two constraints of project
management, cost and schedule, are evaluated
independently and summarized. It is interesting to note
that they make no mention of scope. They also found that
to assist with quick problem identification sometimes a
stoplight report is produced where each area is assigned a
color to represent the status of that constraint. Typically
the stoplight colors of red, yellow, and green are used to
represent the status of each constraint
        <xref ref-type="bibr" rid="ref7">(Dow 2008)</xref>
        . These
constraint statuses will be aggregated into a cumulative
status for the project (Barnes 2009). Green-Yellow-Red
traffic light status reporting is widely used because of its
simplicity, and the quickness with which people can
identify if there is a problem that needs addressing. This
traffic light technique is in common use many projects, and
especially popular in status reports to stakeholders who
might have little time or inclination to understand the
project details. Performance reports are essential inputs
necessary to monitor and control a project (PMBOK
2008), but the dashboards get the attention of the
executives.
      </p>
      <p>It would seem that numerical inputs into reports and
dashboards should yield an objective status for reporting
purposes. The ideal ought to be that for a given activity,
the fixed numerical data goes in and a Green, Yellow, or
Red project status comes out. The next stage in the
process would be that the individual activities are then
mechanically aggregated into an overall project status.
The reality is that there are many factors that influence the
decision to label a project status with a particular status
value for a singular activity, and that the aggregation of
those statuses for multiple activities of the critical
constraints is open to interpretation as well.</p>
      <p>When the project status is not a clear green or red,
Barnes and Hammell found that "ambiguity is present in
the scenario where the expert had to decide that the status
of a project is Yellow" (Barnes 2009). Looking at the case
of rating just one of the activities in a project, it is simple
for status green. Most managers would look at a truly
green activity and agree that the status is okay, or green.
Beyond green status, it becomes questionable. Barnes has
shown that yellow status can be misinterpreted or
communicated as green.</p>
      <p>
        The problem is much worse when the project is in
serious trouble. Snow and Keil found that IT project status
of red is frequently misreported
        <xref ref-type="bibr" rid="ref21">(Snow 2002)</xref>
        . Projects
that are failing need the most attention from the executive
management team; yet, without the knowledge that the
status is red, the proper level of actions are not taken to
bring a red project into compliance which often leads to
financial disasters. The magnitude of project failures is
alarming. For example, barely ten years ago The San
Francisco Chronicle reported that the state of California
wasted over $1 billion on failed computer automation
projects (Lucas 1999).
      </p>
      <p>The second stage in reporting status, aggregation of the
constraints into an overall project status, has been studied
by a number of authors. But there are complexities that
make the automatic summarization difficult. For example,
a project that is ahead of schedule might also be
significantly over cost at that point in time. What is the
true status of that project? Just looking at the raw data
might yield a green status on schedule, but a red status for
cost. However, the costs might reflect that fact that the
project is ahead of schedule, so it might be the case that the
project will finish ahead of schedule, and ultimately within
cost constraints. Ahead of schedule, and meeting cost
constraints when completed would seem to mean the
project is "green", in spite of a "red" cost. This implies
that making status a simple mechanical output of numeric
inputs can produce status errors. Human intervention is
required to interpret the data into meaningful information.</p>
    </sec>
    <sec id="sec-5">
      <title>Measuring the Constraints</title>
      <p>The cost and schedule constraints of project management
have numerical quantities that can be measured. The
numbers have an element of objectivity which can be used
in forecasts. Econometric methods such as regression
analysis and autoregressive moving averages, or time series
methods such as linear prediction, trend estimation, and
moving averages have been used by practitioners of project
management (PMBOK 2008). Currencies are tracked and
reported using time series methods such as earned value
(PMBOK 2008). Calendar dates and/or labor hours can be
tracked for the time constraint. Depending on the project,
quality might also be measurable and reportable.</p>
      <p>
        Scope, however, is much more difficult to measure, and
at the same time is the critical element from which the time
and cost are derived. Richardson and Butler stated that
"the concept of project scope is a foundation idea. It
establishes the base for much of the subsequent
management activities"
        <xref ref-type="bibr" rid="ref17">(Richardson 2006)</xref>
        . At a high level
overview of the project management processes defined by
the PMI, scope is derived from the project charter and
requirements, the scope baseline then feeds into the Work
Breakdown Structure (WBS). The WBS is the input to
time management, which was an output of the scope
definition being decomposed into activities. "Activities
provide a basis for estimating, scheduling, executing, and
monitoring and controlling the project work" (PMBOK
2008).
      </p>
      <p>
        In a similar manner, scope and the WBS feed into cost
estimates and cost management. This means that if the
scope is wrong, the time and cost estimates will be wrong,
or if the scope changes then time and cost can be severely
impacted. Time and cost estimates are calculated by
activity, but the list of activities comes from the scope
definitions and WBS that were completed early in the life
cycle of a project
        <xref ref-type="bibr" rid="ref8">(Gido 2009)</xref>
        . This implies that scope and
requirements errors early in a project can carry over into
constraints that are perceived to be more objective, such as
cost.
      </p>
      <p>
        Schwalbe states that managing scope is especially
difficulty on IT projects. Scope can be relatively undefined
at the beginning, can grow out of control due to creep, and
suffer from an inability to verify
        <xref ref-type="bibr" rid="ref18">(Schwalbe 2010)</xref>
        .
Textbooks on project management will point to cases such
as the bankruptcy of FoxMeyer Drug in 1996 due to an IT
project that had scope problems
        <xref ref-type="bibr" rid="ref10 ref19">(James 1997 and Scott
1996)</xref>
        . McDougall cites a $170 million project failure by
McDonalds Restaurants in 2001 due to scope problems
(McDougall 2006).
      </p>
      <p>
        Weill and Broadbent have stated that projects are late
sometimes due to specification changes, or new business
needs that occur during the project
        <xref ref-type="bibr" rid="ref23">(Weill 1998)</xref>
        . This
event, called scope creep, impacts the other areas that
management tracks for status reporting. The criteria that
are more readily measured by objective criteria (time, cost,
and resources) are directly impacted by scope creep
(PMBOK 2008). The uncontrolled changes of scope
creep add costs of which a customer might not approve,
delay schedules, and reroute critical resources.
      </p>
      <p>
        The IT industry is full of examples of scope creep. A
Google search of the term "project scope creep" produced
over 4 million hits. A quick review of just a fraction of
these web sites demonstrates a common assumption: that a
project manager knows exactly and precisely the scope,
and that the problem is that the scope changes or grows.
This is a questionable assumption. Fleming and
Koppelman, major advocates of the deterministic Earned
Value model, admit that "earned value accurately measures
project performance, but must assume that scope definition
is adequate"
        <xref ref-type="bibr" rid="ref6">(Fleming 2010)</xref>
        . Many sites are devoted to
advice about managing scope through a change control
process, a respected technique, but this assumes that the
scope is well defined, and that the changes are recognized.
In reporting project status the ascertaining and reporting of
scope status is critical, and yet lacks a clear and
measureable standard. Stakeholders and executives have
difficulty making decisions based on vague, subjective,
and imprecise inputs. To put it simply, scope is fuzzy.
Scope and the corresponding set of requirements are a
collection of words describing an end product, and whether
or not the deliverable meets the requirements can be open
to interpretation.
      </p>
    </sec>
    <sec id="sec-6">
      <title>Computational Intelligence Background</title>
      <p>Computational intelligence (CI), implemented in a variety
of soft computing techniques, has allowed the automation
of the handling of vague and imprecise data.
Computational intelligence offers a revolutionary set of
tools capable of responding to fuzzy, inaccurate inputs.
This research envisions that these tools and techniques can
be effectively applied to project status assessment. This
study concentrates on Information Technology (IT)
projects, in particular the scope constraint, because of the
inherent lack of a measure for scope. The IEEE
Computational Intelligence Society defines CI as a number
of core technologies, among them fuzzy systems, neural
networks, evolutionary programming, and genetic
algorithms (IEEE 2011). These technologies build
intelligent systems to help with complex problems in
which the information and data are vague, approximate,
and uncertain. For this research computational intelligence
will focus on fuzzy logic as applied to project status. In
order to put a reasonable boundary around the subject,
only project scope status will be evaluated.</p>
      <p>
        Lotfi Zadeh proposed the concept of fuzzy variables that
are linguistic in the 1960's. For project cost these
linguistic variables might be (costs = {over, on cost,
under})
        <xref ref-type="bibr" rid="ref15">(Li 2006)</xref>
        . Fuzzy systems can replicate human
decision making by handling vague data, to the point of
coping with noisy and/or missing data (Yen 1999).
McNeill in his text Fuzzy Logic explained the difference
between fuzzy logic and probability by asserting that with
fuzzy logic “you have all the information you need. The
situation itself makes either Yes or No inappropriate. …
Fuzzy answers…handle the actual ambiguity in
descriptions or presentations of reality" (McNeill 1994).
To this McNeill adds three characteristics of fuzziness:
(McNeill 1994)
 Word based, not number based.
      </p>
      <p>Example: "hot", not 85 degrees
 Nonlinear and changeable
 Analog (ambiguous), not digital (yes/no)</p>
      <p>
        Zimmermann expanded upon Zadeh's description of
fuzziness as that of possibility, with the idea of a possibility
distribution. Zimmermann’s example is that a fuzzy set
F~ = { (1,1), (2,1), (3,0.8) } has a possibility
distribution such that 0.8 is the possibility that X is 3
        <xref ref-type="bibr" rid="ref25">(Zimmermann 1996)</xref>
        . The possibility distribution thus
allows for something to be both “true” and “fairly false” at
the same time. This concept is the basic question that will
be asked of the experienced project managers in this
research: is it possible that the measurement of scope is
inherently fuzzy, and therefore does it make more sense to
use tools and techniques that can capture the fuzziness
associated with scope status.
      </p>
    </sec>
    <sec id="sec-7">
      <title>Application of CI to Project Status</title>
      <p>
        Some authors have suggested that in spite of objective and
measureable numbers in cost and time constraints, there
can be fuzziness in the interpretation of those numbers. Li,
Moselhi, and Alkas proposed a forecasting method for cost
and schedule constraints using Fuzzy Logic to compensate
for the variability found on construction projects. They
looked at four different, generalized methods to forecast
project status
        <xref ref-type="bibr" rid="ref15">(Li 2006)</xref>
        . The first were stochastic methods
that assumed each unit of work has a mean and standard
deviation, but according to Li, et al, these methods are
weakened by variability in costs per reporting period. The
second methods were deterministic, such as earned value.
The third method that they looked at was social judgment
theory based, using human judgment in lieu of mathematic
methods. The last method was their proposed use of fuzzy
logic for project forecasting and status (Li 2008).
      </p>
      <p>Other researchers have applied computational
intelligence tools to project management for schedule and
time control. Jin-Hsien Wang and Jongyun Hao proposed a
Fuzzy Linguistic PERT (Program Evaluation &amp; Review
Technique) to replace stochastic methods that use means
and standard deviations. They assert that too much data
may be needed to obtain the random variable distribution,
so fuzzy methods are more applicable (Wand 2007).
Wang and Hao expanded PERT/CPM (Critical Path
Method) by storing each activity duration as a fuzzy set.</p>
      <p>Klakegg, et al, have already analyzed what should be
measured in projects, and at the same time they
acknowledge that warning signs of problems are "often
unclear and imprecise" (Klakegg 2010). They describe
what, but not how to measure the subjective constraints.
While other researchers have proposed how fuzzy set
theory can be integrated into project management across
the time and schedule constraints, this work focuses on the
scope constraint. Additionally, we will use a CI tool to
capture scope status directly from experts in a more
realistic, human friendly form. Once the status is captured,
it can then be aggregated into an overall scope status for a
project. Without an objective criterion such as currency
spent or elapsed time, scope is difficult to measure. Fuzzy
systems allow the capturing of this subjective data, and
then the aggregation using recognized fuzzy set
mathematics.</p>
    </sec>
    <sec id="sec-8">
      <title>Methodology for Collecting Status</title>
      <p>This study proposes to use computational intelligence (CI)
tools, in particular alternative tools like fuzzy logic, to
understand the status of a project's scope. This use of CI is
in contrast to the more conventional bivalent logic, which
Zadeh described as working well with exact numbers,
intervals, and probabilities. Rather than the hard, crisp
nature of bivalent logic, these CI alternatives have been
sometimes labeled "soft computing."</p>
      <p>Zadeh stated that "it is a common practice to ignore
imprecision, treating what is imprecise as if it were
precise" (Zadeh 2009). The computing power available in
the 21st century allows for the implementation of the
concepts that Zadeh called computing with words (Zadeh
2009). Given the imprecise nature of project scope due to
the linguistic nature of requirements, it makes more sense
to use fuzzy intervals and fuzzy sets to capture the essence
of the status of scope.</p>
      <p>In his acceptance speech when receiving the Ben
Franklin award at Villanova University in 2009, Zadeh
provided an analogy for fuzzy logic:</p>
      <p>In bivalent logic, the writing/drawing instrument is a
ballpoint pen. In fuzzy logic, the writing/drawing
instrument is a spray pen—a miniature spray can —
with an adjustable, precisely specified spray pattern
(Zadeh 2009).</p>
      <p>Zadeh has stated that a valid application of fuzzy logic is
in the handling of imperfect information. At Villanova
Zadeh went on to say that "imperfect information is
defined as information which in one or more respects is
imprecise, uncertain, vague, incomplete, unreliable,
partially true or partially possible" (Zadeh 2009). This
leads to the core concept that membership in a fuzzy set is
a matter of degree. For project managers, when looking at
the status of a given line item's scope using fuzzy logic,
that status is allowed to be a matter of degree. In practical
terms this means that the scope of an item can be of status
mostly yellow, and at the same time that same scope item
can be of status a little red.</p>
      <p>
        This study uses a fuzzy data collection tool proposed by
Zadeh, colloquially referred to as the Z-mouse. This tool is
a spray paint web gadget that implements Zadeh’s spray
paint analogy. Jose Barranquero and Sergio Guadarrama
created the Z-mouse to gather fuzzy opinions, or
perceptions as they call it, from users
        <xref ref-type="bibr" rid="ref1">(Barranquero 2010)</xref>
        .
In their work, they give users an English language word
and ask the participant to rate that word on a scale using the
Z-mouse.
      </p>
      <p>This study builds upon their prototype by evaluating the
fitness of their Z-mouse concepts when applied to project
management. Project managers are asked to rate the scope
for a WBS activity on a scale that is words, not numbers. It
is anticipated that the non-numeric scale will be quickly
recognized and easy to use by experienced project
managers. Figure 1 illustrates the Z-mouse web gadget
using a non-numeric, linguistic scale.</p>
      <p>
        Barranquero and Guadarrama go on to state that the
Z-mouse can be easily learned by non-expert end users
        <xref ref-type="bibr" rid="ref1">(Barranquero 2010)</xref>
        . This could lead to a design where the
individuals doing the work of a WBS activity would input
their opinions on the scope status, which would be passed
on to the project manager and stakeholders. The scope
status would be seen as a measurement that is analogous to
cost and schedule measurements. Since errors in scope
lead to errors in cost and schedule, the awareness of scope
problems should contribute to early corrective actions,
increasing project success.
      </p>
      <p>
        In contrast to fuzzy systems, social scientists have used
psychometric scales extensively in survey research. In
Likert scales the survey participants are asked to select one
number from a variety of choices. Many times these
choices are an ordered scale, forcing the user to select one
and only one value
        <xref ref-type="bibr" rid="ref22">(Trochim 2006)</xref>
        . The evaluator of a
Likert scale survey can take advantage of the bipolar nature
of this scheme, and apply conventional statistical tests,
such as variance from a mean. Likert and other systems
such as Thurstone scaling have strict rules.
      </p>
      <p>One drawback from using Likert is that it cannot handle
that people will perceive a given choice as falling into two
categories simultaneously. Those models view this human
tendency as a paradox, or a violation of the rules. A fuzzy
system allows that project managers might perceive the
status as mostly yellow, with some modest amount of red.
Having both statuses at the same time for one activity is an
acceptable possibility in fuzzy systems. Another drawback
to scaling systems is that a statistically valid number of
participants are required in order to validate the data. In
project management there might only be two or three
participants working on a WBS activity, a number not
amenable to conventional crisp probability.</p>
      <p>This study gives participants a description of an activity
and asks them to evaluate that activity for the status of the
scope. Figure 2 gives an example that is illustrative of the
types of questions in this survey.</p>
      <p>Activity 1: Web Page Design
End users have requested changes to the web pages that
should be relatively simple to accomplish. However, these
end users are known to change their minds frequently.
 Time Constraint: the project is on schedule

</p>
      <p>Cost Constraint: this activity is within the budget
Scope Constraint: use the Z-mouse to input the status
Figure 3 is an example of a potential response using the
Zmouse. The individual inputting the status would select
one of the four shades of grey from the pallet, and then
paint the status bar where they think appropriate. If they
want to indicate a lesser importance, then they would
select a lighter shade of grey. Figure 3 would be an
example of a project manager deciding that scope
constraint was mostly yellow, yet leaning towards red.
It should be pointed out that these spray paint data points
are converted to numeric values, and then evaluated using
the strict mathematical rules of fuzzy sets.</p>
    </sec>
    <sec id="sec-9">
      <title>Methodology for Aggregating Scope Status for an Entire Project</title>
      <p>
        The next step is to aggregate the individual scope statuses
for each activity into an overall status for a project. Since
the origins are the fuzzy words (green-yellow-red), the
proposed aggregation method would be an implementation
of Zadeh's computing with words. Zimmermann offers
three common methods to aggregate the individual inputs:
COA (center of area), COS (center of sums), and MOM
(mean of maxima)
        <xref ref-type="bibr" rid="ref25">(Zimmermann 1996)</xref>
        . This study will
use COS to aggregate the fuzzy sets into the crisp value
that will be reported at the overall status. Klir states that
COS is the most common method to find a value that
represents the overall conclusion. The COS calculation is
based on recognized and accepted mathematics for fuzzy
sets, which can be found in textbooks by authors such as
Klir (Klir 1997). The COS solution finds the geometric
centroid for the aggregated first moments, and then
translates the solution value into a status.
      </p>
    </sec>
    <sec id="sec-10">
      <title>Conclusion</title>
      <p>Professional project managers have objective data for the
time and cost constraints on their activities. With the
introduction of an input tool to capture the status of scope,
the measuring and reporting of subjective opinions of scope
status can be done. The next step would be that each and
every WBS activity would have a scope status that could be
aggregated into an overall project scope status. Based on
the gathering of this scope data it is expected that this
would become the third constraint in a fuzzy system such
as the one proposed by Li, Moselhi, and Alkas that only
addresses cost and schedule. Since IT projects are unique
and, thus have vague and imprecise scope requirements, it
is believed that two questions will be answered in the
positive by this study: 1) fuzzy logic can provide a tool for
measuring scope of individual activities, and 2) the fuzzy
scope can be aggregated into a meaningful project status.
IEEE Computational Intelligence Society statement of
scope: http://ieee-cis.org/about_cis/scope/</p>
    </sec>
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