Journal of Natural Disaster Science, Volume 32, Number 2, 2011, pp63-77

Systems methodologies in Vitae Systems of Systems

Keith W. HIPEL*
D. Marc KILGOUR*,**
Liping FANG*,****Conßict Analysis Group
Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada**Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada***Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto,
Ontario, M5B 2K3, Canada(Received December 17, 2010 Accepted March 15, 2011)
ABSTRACT
Systems methodologies constitute an implementation science to address complex environmental problems from a Vitae Systems of Systems perspective. The aim of Implementation
Science is to obtain sustainable, fair and responsible solutions that satisfy as much as possible the value systems of stakeholders while upholding the Vitae principles of survivability, viability and conviviality. To represent the environmental and other societal problems
under investigation, the insightful concept of a system of systems is adopted. For example,
the Vitae viewpoint on solutions to global warming problems at the regional, national orinternational level is captured in the interactions of societal systems, such as industrial andservice systems, with atmospheric, oceanic and land systems. To tackle the strategic aspectsof complex systems of systems problems, there is a rich variety of systems engineering decision tools that can handle multiple stakeholders with multiple objectives; these tools are
explained and compared according to their inherent capabilities.
To demonstrate how systems tools can implement a Vitae Systems of Systems philosophy,
three different techniques are applied to complex large-scale environmental and water resources management problems. The Graph Model for Conflict Resolution is used to address
the large-scale environmental problem that arose over a massive irrigation project proposed
for the US state of North Dakota í the infamous Garrison Diversion Unit. Next, a largescale optimization model, integrating concepts from hydrology, economics and cooperative
game theory, is employed to identify fair and feasible allocations of water resources amongusers in the South Saskatchewan River Basin located in southern Alberta, Canada. Finally,
Multiple Criteria Decision Analysis techniques are used to assess different strategies to satisfy future water demand from multiple stakeholders within the Regional Municipality ofWaterloo situated in southern Ontario, Canada.
Keyword: environmental systems management; graph model for conflict resolution; implementation science; multiple criteria decision analysis; resource allocation; risk
assessment; systems engineering; system of systems; vitae systems; water resources management.
63

KEITH W. HIPEL, D. MARC KILGOUR, LIPING FANG

ceptual framework for integrated disaster risk management, as an organizing framework to minimize thevulnerability to disasters of a complex social system.
The three Vitae System principles are• Survivability: Aim for resilience, defined as
the ability to withstand shocks with (1) the least
possible probability of damage or (2) the least
severe damage. Make sure you survive in the
short term.
• Viability: Promote good health and provide a
range of useful and fulfilling activities. Encourage each individual to be resourceful and tolead a full and healthy life.
• Conviviality: Emphasize communication andcooperation within a community and amongcommunities. Aim for positive, reinforcing
group interactions.
By implementing these three principles, a community
has the best chance of minimizing the impact of disasters, or of avoiding them altogether.
The aim of this paper is to show how the Vitae
System can be incorporated into a systems of systems
paradigm. This integration is particularly beneficial
because it brings a broad range of proven tools andtechniques to the practical implementation of theVitae System. Figure 2 presents a Vitae Systems of
Systems framework. This structure therefore enables
practitioners, planners, and decision-makers to implement policies and practices for risk management andsustainable development. These policies and practices
must not only be technically, environmentally, financially, and economically feasible, but also be sociallyand politically viable. Thus, SoS decision methodologies can constitute an Implementation Science, under

1 Systems thinking for Vitae Systems of Systems
Systems of systems (SoS), involving multiple participants with multiple objectives, can be classified into
the four main types, environmental, societal, intelligent, and integrated, shown in Figure 1 (Hipel andFang, 2005; Hipel et al., 2007). The set of all natural
systems of systems, within which the other three types
can be found, is referred to as environmental systemsof systems, and includes hydrological, atmospheric,and ecological systems of systems. The wide rangeof activities executed by human beings for achieving objectives of individuals and groups constitutesocietal systems of systems, such as economical, political, infrastructure, and urban systems of systems.
For achieving human objectives, intelligent systemsof systems, like robotic and mechatronic systems ofsystems, are designed, implemented, and maintainedby humans and organizations within societal systemsof systems. Combinations of societal and intelligent
systems of systems form integrated systems, such as
humans and software agents bidding for products on
eBay through the Internet.
A number of overlapping definitions for a systemof systems have been proposed. For example, Sage
and Biemer (2007) define a system of systems as “alarge-scale, complex system, involving a combinationof technologies, humans, and organizations, and consisting of components which are systems themselves,achieving a unique end-state by providing synergistic
capability from its component systems”. Based uponearlier research by Maier (1998), Sage and Cuppan(2001), and others, Sage and Biemer (2007) put forward the following key characteristics that a systemof systems should possess:• operational independence of the individual system,• managerial independence of the individual system,• geographical distribution,• emergent behavior,• evolutionary development,• self-organization, and• adaptation.
Additionally, another important characteristic of asystem of systems is the presence of multiple participants along with each participant’s value systems assuggested by Hipel and Fang (2005) and Hipel et al.
(2007, 2008b, 2009, 2010).
Okada (2002) proposed the Vitae System, a con-Environmental
Systems of
Systems

Societal
Systems of
Systems

Multiple ParticipantMultiple Objective
Systems of Systems
Intelligent
Systems of
Systems

Integrated
Systems of
Systems

Figure 1 Types of multiple participant-multiple objective systems of systems
64

SYSTEMS METHODOLOGIES IN VITAE SYSTEMS OF SYSTEMS

operational aspects of radar systems (Blackett, 1962;
Waddington, 1973; Hipel et al., 2008a). Although its
origins can be traced back to WW II, Systems Engineering (Sage, 1992; Sage and Rouse, 2008) became
firmly established as a discipline at NASA (National
Aeronautics and Space Administration) in the US in
the 1960s and 1970s. In fact, these “systems science”
fields provide a broad range of approaches to decision making which constitute a valuable componentof Implementation Science because they have been
operationalized for actual application to complex realworld problems.
A systems thinking approach to decision making is both an art and a craft. The art consists of ageneral approach to solve a given complex decision
making problem in which one must take into accountthe technical, environmental, financial, economic andpolitical aspects of the challenging Vitae Systems of
Systems problems being investigated. The craft component refers to the rich variety of mathematicallybased decision tools which have been specificallydesigned for solving real problems in the design,
management, maintenance and operation of systemsof systems. Figure 3 depicts how formal decision
making methods can be categorized according to thefactors of the number of decision makers (DMs) andthe number of objectives. As can be seen, most techniques reflect the viewpoint of one DM having one
objective. For instance, linear programming can be
employed as an optimization tool by an organization
to minimize its costs. Team theory is an example of atechnique for modeling a situation in which there are
two or more team members, such that each member ispursuing the single objective of winning. Multiple criteria decision analysis (MCDA) methods are designed
for finding the more preferred alternative solutions to
a problem when the discrete alternatives are evaluatedagainst criteria ranging from cost (a quantitative criterion) to aesthetics (a qualitative criterion) (see booksby authors such as Belton and Stewart (2002), Hobbs
and Meier (2000), and Hammond et al. (1999) forgood descriptions of MCDA techniques). The evaluations of the criteria for each alternative reflect theobjectives or preferences of the DM. As indicated in
the bottom right cell in Figure 3, game theory methods are designed for handling a decision problem inwhich there are multiple DMs, participants, players or
stakeholders, each of whom has multiple objectives.

Figure 2 Vitae Systems of Systems

the umbrella of the Vitae Systems of Systems philosophy. Some of these SoS decision methodologies
are described in the next section, and illustrated using
three specific examples in Section 3: strategic analysis of an international environmental conflict (Section3.1), fair water allocation among competing uses in alarge-scale river basin (Section 3.2), and selection ofa regional water supply system according to a rangeof criteria (Section 3.3).
2 Systems tools for Vitae Systems of Systems
Systems tools and methodologies for formallymodeling and analyzing decision making processes
that could arise in Vitae Systems of Systems havebeen developed within a range of systems-related
disciplines, such as Operational Research, Systems
Engineering, Industrial Engineering and Project Management. All of these disciplines were launched justbefore, during or after World War II. For example,
Operational or Operations Research (OR) was initiated in July 1938 when the British High Commandordered that research be executed with respect to the65

KEITH W. HIPEL, D. MARC KILGOUR, LIPING FANG

Finally, as pointed out by authors such as Hatfieldand Hipel (2002) and Haimes (2009), risk assessment
forms an integral part of strategic decision making
involving multiple DMs and objectives. A comprehensive set of risk assessment tools is needed for taking a Vitae System of Systems approach for tackling
tough systems problems, such as preserving resiliencein societal systems, which constitutes a systems property that is of great import in proactively planning foreffective responses to natural disasters. For instance,
reliable and adaptable systems plans were in place topermit the Japanese people to respond as effectively
as possible to the massive earthquake and accompanying devastating tsunami that occurred suddenly on
March 11, 2011 in northeast Japan near Sendai.
Multiple participant-multiple objective decision
making is in reality the most general type of decision
making and it is certainly an inherent characteristicof Vitae Systems of Systems. An informative way
in which to classify a game theoretic method is according to the DMs’ type of preference information.
A given DM’s preferences reflect his or her beliefs,
value systems, priorities and objectives. Therefore, tocalibrate a conflict model, one must elicit each DM’s
preferences over the feasible outcomes or states ina particular conflict. The methods listed in the left
column in Figure 4 are usually categorized as being
non-quantitative approaches, since they only assume relative preference information. Hence, it is notnecessary to know exactly the degree to which one
prefers one state over another. Moreover, Metagame
Analysis (Howard, 1971), Drama Theory (Howard,
1999; Bryant, 2003), Conflict Analysis (Fraser and
Hipel, 1979, 1984), and the Graph Model for Conflict
Resolution (Kilgour et al., 1987; Fang et al., 1993)
can handle both transitive and intransitive preferences. Techniques falling within the right branch in
Figure 4 generally require cardinal preference information expressed by von Neumann and Morgenstern(1953) utility functions. Accordingly, these techniques
are usually labeled as being quantitative. One should
keep in mind that all of the procedures given in boththe left and right parts of Figure 4 constitute formal
mathematical models.
Significant research advances in the developmentof decision techniques that concentrate on multiple

OBJECTIVESDECISION
MAKERSOne

Two or MoreOne

Most Models

Multiple Criteria
Decision Analysis

Two orMoreTeam Theory

Game Theory

Figure 3 Classification of decision making methods

Figure 4 Genealogy of formal conflict models
66

SYSTEMS METHODOLOGIES IN VITAE SYSTEMS OF SYSTEMS

stakeholders having multiple objectives have been
made, in conjunction with insightful water resources,
environmental management and other kinds of applications, by members of the Conflict Analysis Groupat the University of Waterloo. For instance, important
methodological extensions to the Graph Model for
Conflict Resolution (Kilgour et al., 1987; Fang et al.,
1993; Hipel et al., 1993; Hipel, 2009a,b) include its
capability to model coalitions (Kilgour et al., 2001;
Inohara and Hipel, 2008a,b), uncertain preference (Liet al., 2004a, 2005a), strength of preference (Hamouda
et al., 2004, 2006; Xu et al., 2009b), fuzzy preferences (Al-Mutairi et al., 2008; Hipel et al., 2011), emotions (Obeidi et al., 2005, 2006, 2009a,b), attitudes(Inohara et al., 2007; Walker et al., 2009), policies(Zeng et al., 2007), large conflicts (Xu et al., 2009a,c)and the evolution of a conflict to a final outcome (Liet al., 2004b, 2005a,b). To permit the Graph Model
methodology to be applied in practice, a flexible decision support system has been constructed (Fang et al.,2003a,b; Hipel et al., 1997, 2001).
Other contributions to the creation, refinement
and application of decision-making techniques include initiatives in multiple criteria decision analysis(MCDA) methods (such as Rajabi et al. (1998, 1999)
and Chen et al. (2006, 2007, 2008)), enforcement
techniques for environmental regulations (Kilgour
et al., 1992; Hipel and Fang, 1994; Fang et al.,1997), fair resource allocation (Wang et al., 2007a,b,
2008a,b) and decision making under uncertainty (see,for example, Hipel and Ben-Haim (1999) and Hipeland McLeod (1994)). Professor Norio Okada and his
research team in Japan, first at Tottori University andlater within the Disaster Prevention Research Instituteat Kyoto University, have completed high quality
research on challenging topics such as regional planning, environmental and water resources management, allocation of costs and benefits, mitigation ofnatural disasters and risk assessment. Collaborative
research projects between Canadian and Japanese researchers produced publications on subjects including
conflicts with misperceptions (Okada et al., 1985),
conflict analysis (Okada et al., 1988), regulation ofpollutant discharges into lakes (Kilgour et al., 1988),
compliance to environmental regulations (Fukuyama
et al., 1994, 2000) and participatory infrastructure
management (Okada et al., 2006).

3 Systems practice
The overall objective of this section is to demonstrate how various systems tools in Figure 4 can be
employed in an Implementation Science fashion foraddressing complex Vitae Systems of Systems problems. In particular, the Graph Model for Conflict Resolution (given in the left branch of Figure 4), cooperative game theory procedures (right branch in Figure 4)
in combination with other appropriate methods, andMCDA techniques (top right cell in Figure 3) are applied to practical realworld problems in environmental conflict resolution, fair allocation of water amongusers in a river basin, and selection of future reliable
water supplies in Sections 3.1 to 3.3, respectively.
The three upcoming applications deal with examples of effectively handling strategic problems which
well-functioning societies must address in order tohave secure and robust societal systems of systems
that interact in responsible ways among and withinthemselves as well as their supporting environmental
system of systems. Having prosperous, fair, and accountable societies means that these societies are in amuch stronger and more stable position to be able toact in a proactive, integrative and adaptive fashion tocrises, such as natural disasters, from a Vitae System
of Systems perspective. Hence, when a disaster does
strike, such as the March 2011 Sendai earthquake
and accompanying tsunami, lives can be saved, property damage minimized and recovery time kept to areasonable time period when rebuilding private andpublic property and infrastructure in order to restore
system resilience and other key system characteristics. This kind of Vitae System of Systems philosophy
can only grow in importance as increasingly complex
societal, technological and natural systems interact
in largely unknown ways to produce emergent behaviour, like irreversible climate changes and serious
food crises (Hipel et al., 2010), which societies will
ultimately have to confront. Now is clearly the time
to positively change the attitudes of decision makers
in government, industry and non-governmental organizations towards more responsible and realistic ways
to govern via systems thinking.
3.1 Conflict resolution in an international
environmental conflict
Conflict is an innate characteristic of Vitae Sys67

KEITH W. HIPEL, D. MARC KILGOUR, LIPING FANG

tems of Systems as people and organizations compete and cooperate within societal and technologicalsystems of systems (Hipel and Fang, 2005; Hipel etal., 2007, 2008b, 2009, 2010). Accordingly, conflict
resolution methodologies constitute a key type of
Implementation Science for fairly resolving disputes
in an attempt to reach win/win settlements among
disputants. Consider, now how the Graph Model for
Conflict Resolution can be employed for systematically investigating the strategic aspects of a complex
international environmental controversy.
The Garrison Diversion Unit (GDU) is a partially constructed multipurpose water resources projectin the United States of America (US) that involves
the transfer of water from the Missouri River Basin toplanned irrigation areas in central and eastern North
Dakota, most of which are located within the Hudson
Bay Drainage Basin. Because the resulting runoff
from the planned irrigated fields would flow via the
Red and Souris Rivers into the Canadian provinceof Manitoba, Canada could become seriously polluted. In particular, adverse environmental effects
from the GDU include high pollution levels of theirrigation waters, increased chances of flooding of
the Souris River, and the possibility of catastrophic
environmental damage caused by foreign biota from
the Missouri River Basin destroying indigenous biota
such as certain fish species in the Hudson Bay Drainage Basin. Previously, the GDU dispute was formallystudied using metagame analysis (Hipel and Fraser,1980), conflict analysis (Fraser and Hipel, 1984, Ch.

2) and the Graph Model for Conflict Resolution (Fanget al., 1993, Ch. 6). Here, the decision support systems GMCR II is employed to study the conflict as itexisted in April 1976. The Graph Model for Conflict
Resolution has also been used to model the conflict as
it existed in early December 1984, just before a final
resolution was reached (Fang et al., 1993, Seciton 6.6).
Figure 5 lists the DMs and the options under eachDM’s control for the GDU conflict and with the status
quo state existing in April 1976, the point in time forwhich the modeling and analysis is done. As can beseen, the dispute is modeled as a conflict among four
DMs: US Support (for the project), US Opposition (agroup composed mainly of environmentalists), Canadian Opposition (mainly the governments of Manitoba
and Canada), and the IJC (International Joint Commission), the boundary waters advisory council, with equal
representation from Canada and the US, which had
recently been requested by the US and Canada to carryout a study in order to make recommendations to bothgovernments on how to handle the problem. The status
quo state, consisting of a column of Ys and Ns, is thesituation existing at the start of the dispute in April 1976.
When defining a state using the option notation, theDM controlling a given option decides whether or not
to choose it: a “Y” means “yes”, while an “N” indicates“no”, and the option is not taken. To form the status quo
state in Figure 5, which is written horizontally in text as(YNN N N NNNN), the US Support, US Opposition,
Canadian Opposition, and the IJC have chosen the strategies (YNN), (N), (N), and (NNNN), respectively.

Figure 5 Decision makers and options for the GDU conflict as of 1976
68

SYSTEMS METHODOLOGIES IN VITAE SYSTEMS OF SYSTEMS

Besides determining the DMs, each DM’s options and the possible feasible states, one must also
ascertain the relative preferences among the states
for each DM before carrying out an indepth stability
analysis. In general, a state is stable for a given DM
according to a particular solution concept describing
human behaviour under conflict, if it is not advantageous for the DM to move from that state. A state
which is stable for all DMs with respect to a specificsolution concept is called an equilibrium. Based upon
the results of an exhaustive stability analysis, Figure
6 portrays how the conflict evolved from status quo
state 1, through the transitional states 26 and 28, tothe equilibrium state 34, which actually took place in
1976. The arrows in Figure 6 indicate which option
selections a DM changes in order to cause the conflict
to move from one state to another. Specifically, the
IJC unilaterally causes the conflict to move from state
1 to state 26 by changing its strategy selection fromnot making a recommendation (strategy NNNN) to
recommending the Lonetree Reservoir option (strategy NNYN), which is referred to as an allowablestate transition. The US Support then moves the conflict from state 26 to 28 by proceeding to construct a
modified GDU project to appease the US Opposition.
In response, the Canadian Opposition threatens to go
to court under the Boundary Waters Treaty of 1909,
and hence causes the conflict to progress from state
28 to 34. Because state 34 is a strong equilibrium,
as indicated in Figure 6, no DM has an incentive tounilaterally move from it. Accordingly, this was theequilibrium reached in 1976.

3.2 Fairness and cooperation for water
allocation in a large-scale river basin
Fair allocation of resources within the multiple
participant decision making context is crucial for the
implementation of Vitae Systems of Systems in society. Consider the problem of equitably allocating water among the competing users or stakeholders overan entire river basin. Because a unit of water can produce different economic benefits for different users,
water allocations based on water rights alone does not
usually produce an economically efficient plan for thewhole river basin. On the other hand, particular water
users will usually consider economically efficientwater allocation plans to be inequitable, and unfair
plans are often difficult or impossible to implement.
Moreover, allocation plans have implications forsustainability – environmental requirements (stream
flow and reservoir storage), water quality constraints,
conservation of water, and sharing of water shortages,
must also be considered. Predicted radical climate behaviour caused by global warming, such as more extreme droughts and floods, only increases the demand
for the utilization of responsible and fair resource
allocation techniques to help maintain the principles
of Vitae Systems of Systems shown in the top right of
Figure 2.
A comprehensive Cooperative Water Allocation
Model (CWAM) has been developed to find equitable, efficient and sustainable water allocations among
competing users or stakeholders in a river basin (Wanget al., 2007a,b, 2008a,b). The CWAM framework
integrates concepts from hydrology, economics andFigure 6 Transition from the status quo to the equilibrium state
69

KEITH W. HIPEL, D. MARC KILGOUR, LIPING FANG
Red Deer River
IN1

D1 G1 I1

R1
S1

Bow River
IN2
H1

R2 Kananaskis River
IN3

J1

D2 G2 I2

A1

A3

Outlet to O1
Saskatchewan

I3
R7

R5

H2

R3

J4
J3

S2

Little Bow RiverR4

D4 G4 I4

R6
Elbow River

IN4

A2
Oldman
River
IN6

J5

IN7

S4

G3

D3

A4

R10

R9
R8

J9

J8

J7

S3

A5

A6

A7

A8

A9

R13 R14

R15

R16

R17

R12
R11
J10
IN8
IN9
Waterton Belly
River River
Inflow

IN10
St. MaryRiver

Junction

Reservoir

Municipal and Industrial Demand

Hydropower plant

Stream flow demand

Agricultural DemandOutletLink

Figure 7 Network of the South Saskatchewan River Basin in southern Alberta
cooperative game theory within an overall large-scale
optimization structure. Based on a network representation of the river basin, CWAM allocates water in
two steps: (1) initial allocation founded on existing
legal rights or agreements; and (2) reallocation ofwater and net benefits to achieve efficient utilizationof water and equitable redistribution of net benefits.
The effect of the application of cooperative gametheoretic approaches is to promote cooperation among
all users in the river basin. The CWAM methodology
has been applied on a large scale to the water allocation problem in the South Saskatchewan River Basin(SSRB) located in the southern part of the Province ofAlberta, Canada (Wang et al., 2008a,b). The network
representation of SSRB is shown in Figure 7.

Canada is a good example. The Regional Municipality of Waterloo, located in the Great Lakes basin,comprises the three cities of Kitchener, Waterloo,
and Cambridge, plus adjacent rural municipalities.
In 1990, Waterloo decided to develop a Long Term
Water Strategy to the year 2041. This extensive study,
which took ten years to complete, highlights many
issues associated with vitae systems, and illustrates
many features that can be expected to arise in the associated decision problems.
In 1990, the Regional Municipality of Waterloo
was the largest community in Canada to depend on
groundwater for most (over 90%) of its water supply.
(Waterloo Regional Council, 2000) The population
was almost 500,000, and daily water consumption
was about 45 million gallons per day (MGD). Driven
mainly by increasing population, water consumption
was predicted to increase steadily to 67 MGD in 2041.
Almost every year, seasonal droughts led to water
restrictions, resulting in the perception that reliabilityof water supply was a major problem for the Region.
Water quality was also a rising issue, as health-related

3.3 Group decision using multiple criteria
decision analysis for regional water supply
Water resource development can provide an excellent illustration of the Vitae Systems of Systems
philosophy in action. The selection of projects toensure the future water supply of Waterloo, Ontario,
70

SYSTEMS METHODOLOGIES IN VITAE SYSTEMS OF SYSTEMS

concerns forced the temporary closure of some wellsin Kitchener and Waterloo, which also further exacerbated supply problems. In 1990, it was discoveredthat a carcinogen, probably of industrial origin, had
contaminated the entire aquifer under Elmira (Kilgour
et al., 2001); consequent arrangements to supply water to Elmira from elsewhere in the region are still inplace. Finally, unusual weather conditions sometimes
combined with difficulties in operating dams along
the Grand River to produce flooding, the worst instance of which occurred in 1974.
The Region of Waterloo hired Associated Engineering as primary technical consultant for its Long
Term Water Strategy project. Meetings of consulting
and city engineers, politicians, major water users, andcitizens began in 1991. Eventually, the twelve water sources shown in Table 1, along with their likely
long-term capacities, were identified as feasible.
The meetings of experts, citizens, and interested
parties focused on the discussion of criteria for evaluating the choice of water source. Initially, the primarygoals for the project were determined to be:
Respect and Maintain Tradition by minimizingchanges to existing systems and infrastructure, and by
minimizing environmental impacts, negative social
impacts, and costs.
Achieve Water Security by minimizing the risk of
disruption due to poor water quality or sudden decreases in water supply.
Ensure Water Supply by reducing or eliminating
shortfalls, relative to predicted water needs, insofar as

possible.
Later these goals were refined into seven measurable
criteria, as follows: investment cost (INVEST); operating cost (OPER); water quality (QUAL); infrastructure impact (INFRA); environmental impact (ENVIR);
risk (RISK); and supply capability (SUPPLY). Twocriteria, SUPPLY and QUAL, are positive criteria(increasing values are preferred), while the remainder
are negative (decreasing values are preferred).
A preliminary evaluation of the twelve alternatives according to the seven criteria was carried out
by consultants to the Region; the results are shown in
Table 2. Note that consequence measures (numbersin the body of the Table) are given in natural units as
selected by the consultants; no attempt has been madeto scale them according to criteria weights.
MCDA techniques are designed to assist asingle decision-maker faced with a complex decision
problem. The use of such techniques might be questioned in a multiple decision-maker context such as
the Waterloo water supply problem. But in this case,the cities of Kitchener, Waterloo, and Cambridge
were facing essentially the same problem, and had along history of cooperation on water-related issues.
Moreover, procedures for allocating costs were wellestablished. Because there was little conflict among
the major decision-makers, MCDA techniques arequite appropriate to this problem.
However, the Waterloo water supply problem
has two special features that may well characterizedecision problems originating in vitae systems, inter-

Table 1 Feasible water sources and capacities for Waterloo Region

Groundwater
Aquifer Recharge
Grand River
Low Flow
Augmentation
High-Pressure Pipeline

GW1
GW2
AQ1
AQ 2
GR
LF1
L F2
L F3
PL1
PL2
PL3
P L4

Develop sources in Kitchener andWaterloo
Develop sources in other areas
Recharge and recovery site 1
Recharge and recovery site 2
Increase Grand River extraction
West Montrose dam
L o w- p re s s u re Geo r gia n B ay pi peli n e
Lo w- p re s s u r e L ak e Hu r o n p i peli ne
Pipeline from Lake Ontario
Pipeline from Lake Erie
Pi pe li n e f r om Lak e H u ro n
(Goderich)
P i p e l i n e f r o m Ge o r g i a n B a y(Thornbury)
71

MGD
20
20
40
40
5
50
80
80
80
80
80
80

KEITH W. HIPEL, D. MARC KILGOUR, LIPING FANG

dependency and timing. Some of the actions (thosesourcing water from the Great Lakes) provided sufficient capacity in themselves to meet long-term waterneeds, but could not be implemented quickly, necessitating the choice of some other action(s) as a temporary measure. Moreover, actions not sourcing waterfrom the Great Lakes were unlikely to meet needs
over the long term, so a Great Lakes source was probably inevitable. In other words, this was not a conventional MCDA problem, since the issue was not tochoose an action but to choose a schedule of actions.
In particular, actions not sourcing water from theGreat Lakes could delay the expensive but inevitablepipeline, and expenditure delayed is money saved. Insum, the timing of choices is at least as important as
the choices themselves.
It is important to note that the evaluation of asubset of actions according to a criterion may notbear any simple relation to the evaluations of the individual actions by the same criterion. The whole may
be greater than, equal to, or less than the sum of theparts. Rajabi et al. (1998, 1999) developed a methodof measuring the interdependence of actions which
can be applied to this problem. For example, any GW
action and any PL action have synergy –0.2 on RISK
(because total risk is reduced when there are two different sources) but synergy +0.1 on INFRA (because
the required infrastructures are more expensive tobuild in parallel).
In the MCDA context, Rajabi et al. (1999) developed a theory of optimal subset selection, and applied
it to a simplified model of the Waterloo Water Supply
Problem. Later, Chen et al. (2008) showed that the
problem can be solved, at least approximately, using
screening methods, which do not take direct accountof synergies and may therefore be computationallyvery efficient.
On May 10, 2000, the Waterloo Regional Coun-cil approved a long-term water strategy for Waterloo
Region consisting of three alternatives on different
construction schedules. Specifically, the plan was toimplement AQ1 to a capacity of 5 MGD immediately,with a further 5 MGD of AQ1 in 2007, then GW2 to alevel of 3 MGD in 2018, followed by PL2 or PL3 by
2035. Implementation is in progress at this time. Figure 8 shows that the average capacity of the system
will remain well ahead of expected needs.
The solution of the Waterloo Water Resources
Problem provides an excellent illustration of the vitae
principles of survivability, viability and conviviality.
The water supply to the region will be adequate forits health and economic development, and the risks
to the supply will be minimal. At the same time, environmental and social values have been affirmed,
and costs – capital, infrastructure, and operating –have been minimized, ensuring that social resources
are available to meet other needs as may be requiredin the future. Moreover, a community or region’s
economic future is constrained by the availability ofadequate amounts of clean freshwater. The pollutionof an aquifer, such as the one underlying the Town
of Elmira in Ontario, Canada (Kilgour et al., 2001),
means that the community’s economic vitality andsustainability have been seriously diminished throughthe loss of its local water supply.
4 The road ahead
As exemplified in Section 3 by three large-scalecase studies, society is currently facing many challenging problems and, as emphasized by Hipel etal. (2007), both expected and unforeseen difficulties
will arise in the future. Although the three applications deal with tough systems of systems problems
that have occurred or continue to evolve in the North
American continent, they reflect general types of situ-

Table 2 Future water supply for Waterloo Region as an MCDA problem

GW1 GW2 AQ1 AQ2 GR LF1 LF2 LF3 PL1 PL2 PL3 PL4INVEST 100 61 8.6 17 5 112 123.6111.3 120.4 126 181 222
OPER
4 2.4 5.9 8.8 2 6.2 6.6 6.7 4.2 3.4 2.3 2.5
INFRA
30 30 40 50 30 60 60 60 60 65 60 60
ENVIR
60 60 45 45 40 50 40 90 80 80 80 80
80 80 50 50 80 60 70 70 30 30 30 30
RISK
SUPPLY 20 20 40 40 5 50 80 80 80 80 80 80
QUAL
50 50 70 70 30 60 60 60 70 70 80 70
72

SYSTEMS METHODOLOGIES IN VITAE SYSTEMS OF SYSTEMS

100

90

PL2/PL3

M GD

80

GW2(3)70

AQ1(5)

60

Forecast Demand

50

40
1991

96

01

06

11

16

21

26

31

36

2041

Figure 8 Strategic Plan for future Waterloo water supply (Source: Waterloo Regional Council, 2000)

ations taking place around the globe. For instance,
a common feature underlying all three case studies
is the decreasing supply of fresh water, along withassociated degradation of water quality, in the faceof increasing water demand by a rapidly expanding
population. Consider water shortages associated with
the infamous Aral Sea debacle (see Nandalal and Hipel (2007)) along with associated references) as wellas drastic water shortages now taking place in regions
such as Australia, North Africa, the Western andSouthwestern United States, as well as many parts ofChina and India. Moreover, most of these problems
are interconnected as a result of global warming happening around the world. For instance, global warming is currently causing the glaciers of the Rocky
Mountains in Western Canada to retreat which in turnmeans that summer flows of the Saskatchewan Riverand its tributaries will certainly decrease in the futuresince the summer flows are largely generated by these
crucial glaciers. Because the rivers flowing from west
to east across the provinces of Alberta and Saskatchewan eventually reach Lake Winnipeg in the provinceof Manitoba, this will cause Lake Winnipeg and othernearby lakes to greatly decrease in size. In fact, Lake
Winnipeg has the potential to become the “Aral Sea”
of North America. As noted earlier, resilient and secure societies are needed to be able to proactively
confront known potential disasters, such as earthquakes and tornadoes, as well as unknown unknowns.
Clearly, systems thinking methodologies, suchas those outlined in Section 2 and applied to practicalproblems in Section 3, are sorely needed as an Implementation Science for executing, in practice, a Vitae
Systems of Systems philosophy discussed in Section
1 and Figure 2. The development of a sound theoretical basis to this new idea of the Vitae Systems of Systems approach will require the talents, attention anddedication of researchers around the globe. Moreover,as is also pointed out by Hipel et al. (2007), there is agreat need to develop a solid theoretical foundation to
the field of Systems Engineering along with an arrayof systems tools for handling many types of complex
systems of systems problems. As exemplified by theunexpected tsunami of December 26, 2004, whichravaged nations adjoining the Indian Ocean, society
may not even be aware of sudden disasters that could
take place in the future. Hence, these systems tools
must be comprehensive and integrated and be capableof handling vast amounts of information such that key
decisions can be made in real time to mitigate the array of complex risks associated with any large-scaledisaster.
Acknowledgments
The authors would like to sincerely congratulate
Professor Norio Okada on the occasion of his 60thbirthday, and to join in the celebration of his many
academic accomplishments and his remarkable career.
Hence, they are thankful for being afforded the opportunity to participate in the “International Conference on Vitae Systems – New Paradigm for Systems
73

KEITH W. HIPEL, D. MARC KILGOUR, LIPING FANG

in multiple criteria decision analysis’, Decision Sup-

Science: Survivability, Vitality and Conviviality inSociety”, which was held in the Clock Tower Building at Kyoto University, Kyoto, Japan, on December
first and second in 2007. The original version ofthis paper was presented as a keynote address at thishighly successful conference. The authors are especially appreciative of the collegiality and friendshipthat Professor Okada has shared with them, as withhis many students and other colleagues, over the past
three decades, and look forward to many more yearsof cooperation and comradeship. They are also grateful to his colleagues and former students for having
so ably organized and carried out such an excellent
international conference in his honour. Finally, theauthors would like to thank Professor Okada, as wellas many other Japanese and international colleagues,
for the key roles they have played in educating both
Japanese and Canadian students to have a systems
perspective in their careers and lives, as demonstrated
by the highly successful student exchange programs
that Professor Okada helped to establish between
Tottori and Kyoto Universities, and the University ofWaterloo (Hipel et al., 2003; Fukuyama et al., 2005).

port Systems, Vol. 45, pp. 278-290.
Fang, L., Hipel, K.W. and Kilgour, D.M. (1993) Interactive
Decision Making: The Graph Model for Conflict Resolution, (New York: Wiley).
Fang, L., Hipel, K.W., Kilgour, D.M. and Peng, X. (2003a)‘A decision support system for interactive decision
making, Part 1: Model formulation’, IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, Vol. 33, No. 1, pp. 42-55.
Fang, L., Hipel, K.W., Kilgour, D.M. and Peng, X. (2003b)‘A decision support system for interactive decision
making, Part 2: Analysis and output interpretation’,IEEE Transactions on Systems, Man, and Cybernetics,
Part C: Applications and Reviews, Vol. 33, No. 1, pp.
56-66.
Fang, L., Kilgour, D.M. and Hipel, K.W. (1997) ‘How penalty affects enforcement of environmental regulations’,
Applied Mathematics and Computation, Vol. 83, Nos.
2 & 3, pp. 281-301.
Fraser, N.M. and Hipel, K.W. (1979) ‘Solving complex
conflicts’, IEEE Transactions on Systems, Man, andCybernetics, Vol. 9, No. 12, pp. 805-816.
Fraser, N.M. and Hipel, K.W. (1984) Conflict Analysis:
Models and Resolutions, (New York: NorthHolland).

References

Fukuyama, K., Kilgour, D.M. and Hipel, K.W. (1994) ‘SysAl-Mutairi, M.S., Hipel, K.W. and Kamel, M.S. (2008)

tematic policy development to ensure compliance to‘Fuzzy preferences in conflicts’, Journal of Systems

environmental regulations’, IEEE Transactions on Sys-

Science and Systems Engineering, Vol. 17, No. 3, pp.

tems, Man and Cybernetics, Vol. 24, No. 9, pp. 1289-

257-276.

1305.
Fukuyama, K., Kilgour, D.M. and Hipel, K.W. (2000) ‘Self-

Belton, V. and Stewart, T.J. (2002) Multiple Criteria Decision Analysis: An Integrated Approach, (Dordrecht:

reporting systems for environmental compliance’,

Kluwer).

Journal of Water Resources Planning and Management, Vol. 126, No. 1, pp.3-12.

Blackett, P.M.S. (1962) Studies of War, (Edinburgh: Oliver

Fukuyama, K., Okada, N. and Hipel, K.W. (2005) ‘Inter-and Boyd).
Bryant, J. (2003) The Six Dilemmas of Collaboration: Inter-nationalization of engineering education through ex-organisational Relationships as Drama, (Chichester:change programs’, Journal of the Japanese Society forEngineering Education, Vol. 53, No. 2, pp. 36-42.

John Wiley & Sons).
Chen, Y., Hipel, K.W. and Kilgour, D.M. (2007) ‘Multiple

Haimes, Y.Y. (2009) Risk Modeling, Assessment, and Man-

criteria sorting using case-based distance models withagement, 3rd Edition, (Hoboken, New Jersey: WileyInterscience).

an application in water resources management’, IEEE

Hammond, J.S., Keeney, R.L. and Raiffa, H. (1999) Smart

Transactions on Systems, Man, and Cybernetics, Part

Choices: A Practical Guide to Making Better Deci-

A: Systems and Humans, Vol. 37, No. 5, pp. 680-691.
Chen, Y., Kilgour, D.M. and Hipel, K.W. (2006) ‘Multiple

sions, (Boston: Harvard Business School Publishing).

criteria classification with an application in water

Hamouda, L., Kilgour, D.M. and Hipel, K.W. (2004)

resources planning’, Computers and Operations Re-‘Strength of preference in the graph model for conflictsearch, Vol. 33, No. 11, pp. 3301-3323.

resolution’, Group Decision and Negotiation, Vol. 13,
pp. 449-462.

Chen, Y., Kilgour, D.M. and Hipel, K.W. (2008) ‘Screening

74

SYSTEMS METHODOLOGIES IN VITAE SYSTEMS OF SYSTEMS

fessor Lotfi Zadeh, to appear.

Hamouda, L., Kilgour, D.M. and Hipel, K.W. (2006)‘Strength of preference in graph models for multiple

Hipel, K.W., Kilgour, D.M., Fang, L. and Peng, X. (1997)

decision-maker conflicts’, Applied Mathematics and‘The decision support system GMCR II in environ-

Computation, Vol. 179, pp. 314-327.

mental conflict management’, Applied Mathematics
and Computation, Vol. 83, No. 2/3, pp. 117-152.

Hatfield, A.J. and Hipel, K.W. (2002) ‘Risk and systems

Hipel, K.W., Kilgour, D.M., Fang, L. and Peng, X. (2001)

theory’, Risk Analysis: An International Journal, Vol.

‘Strategic decision support for the services industry’,22, No. 6, pp. 1043-1057.

IEEE Transactions on Engineering Management, Vol.

Hipel, K.W. (Ed.) (2009a) Conflict Resolution, Volume 1,

48, No. 3, pp. 358-369.

(Oxford, UK: Eolss Publishers).

Hipel, K.W., Kilgour, D.M., Rajabi, S., and Chen, Y. (2008a)

Hipel, K.W. (Ed.) (2009b) Conflict Resolution, Volume 2,‘Chapter 27 - Operations Research and Refinement of(Oxford, UK: Eolss Publishers).
Hipel, K.W. and Ben-Haim, Y. (1999) ‘Decision making

Courses of Action’, In Handbook of Systems Engineer-in an uncertain world: information – gap modeling ining and Management, edited by A.P. Sage and W.B.

water resources management’, IEEE Transactions on

Rouse, Second edition, (New York: Wiley).
Hipel, K.W. and McLeod, A.I. (1994) Time Series Model-

Systems, Man and Cybernetics, Part C: Applications

ling of Water Resources and Environmental Systems,

and Reviews, Vol. 29, No. 4, pp. 506-517.

(Amsterdam: Elsevier).

Hipel, K.W. and Fang, L. (Eds.) (1994) Effective Environ-

Hipel, K.W., Obeidi, A., Fang, L. and Kilgour, D.M. (2008b),

mental Management for Sustainable Development,‘Adaptive systems thinking in integrated water re-(Dordrecht, The Netherlands: Kluwer).

sources management with insights into conflicts over

Hipel, K.W. and Fang, L. (2005) ‘Multiple participant decision making in societal and technological systems’, inwater exports’, INFOR, Vol. 46, No. 1, pp. 51-69.

T. Arai, S. Yamamoto, and K. Makino, (Eds.), Systems

Hipel, K.W., Obeidi, A., Fang, L. and Kilgour, D.M. (2009),

and Human Science—For Safety, Security, and De-‘Sustainable environmental management from a sys-

pendability. Selected Papers of the 1st Internationaltem of systems perspective’, In System of Systems En-

Symposium, SSR2003, Osaka, Japan, Published bygineering: Innovations for the 21st Century, edited by

Elsevier, Amsterdam, The Netherlands, Chapter 1, pp.

M. Jamshidi, Wiley, New York, Chapter 18, pp. 443-

3-31, 2005.

481.

Hipel, K.W., Fang, L. and Heng, M. (2010) ‘System of sys-

Hipel, K.W., Okada, N., and Fukuyama, K. (2003) ‘The

tems approach to policy development for global foodinternationalization of engineering education: a tale ofsecurity’, Journal of Systems Science and Systems En-

two countries’, IEEE Transactions on Systems, Mangineering’, Vol. 19, No. 1, pp. 1-21.

and Cybernetics, Part C: Applications and Reviews,
Vol. 33, No. 1, pp. 137-148.

Hipel, K.W., Fang, L. and Kilgour, D.M. (1993) ‘Game
theoretic models in engineering decision making’,

Hobbs, B.F. and Meier, P. (2000) Energy Decisions andJournal of Infrastructure Planning and Management,

the Environment: A Guide to the Use of Multicriteria
Methods, (Massachusetts: Kluwer).

Japan Society of Civil Engineers, No.470/IV-20, pp.1-

Howard, N. (1971) Paradoxes of Rationality: Theory of

16.

Metagames and Political Behaviour, (Cambridge,

Hipel, K.W. and Fraser, N.M. (1980) ‘Metagame analysis of
the Garrison conflict’, Water Resources Research, Vol.

Massachusetts: MIT Press).

16, No. 4, pp. 629-637.

Howard, N. (1999) Confrontation Analysis: How to Win

Hipel, K.W., Jamshidi, M.M., Tien, J.J., and White III, C.C.

Operations Other Than War, (Pentagon, Washington,(2007) ‘The future of systems, man and cybernetics:

DC: CCRP Publications).

application domains and research methods’, IEEE

Inohara, T. and Hipel, K.W. (2008a) ‘Coalition analysis inTransactions on Systems, Man, and Cybernetics, Part

the graph model for conflict resolution’, Systems Engi-

C: Applications and Reviews, Vol. 37, No. 5, pp. 726-

neering, Vol. 11, No. 4, pp. 343-359.

743.

Inohara, T. and Hipel, K.W. (2008b) ‘Interrelationships

Hipel, K.W., Kilgour, D.M., and Bashar, M.A. (2011) ‘Fuzzyamong noncooperative and coalition stability con-preferences in multiple participant decision making’,

cepts’, Journal of Systems Science and Systems Engi-

Scientia Iranica, special publication in honour of Pro-

neering, Vol. 17, No. 1, pp. 1-29.

75

KEITH W. HIPEL, D. MARC KILGOUR, LIPING FANG

pp. 481-500.

Inohara, T., Hipel, K.W., and Walker, S. (2007) ‘Conflict
analysis approaches for investigating attitudes andObeidi, A., Hipel, K.W. and Kilgour, D.M. (2006) ‘Tur-

misperceptions in the war of 1812’, Journal of Systems

bulence in Miramichi Bay: the Burnt Church conflict

Science and Systems Engineering, Vol. 16, No. 2, pp.

over native fishing rights’, Journal of the American

181-201.

Water Resources Association, Vol. 42, No. 12, pp.
1629-1645.

Kilgour, D.M., Fang, L. and Hipel, K.W. (1992) ‘Gametheoretic analyses of enforcement of environmental

Obeidi, A., Kilgour, D.M., and Hipel, K.W.(2009a) ‘Percep-

laws and regulations’, Water Resources Bulletin, Vol.

tual stability analysis of a graph model system’, IEEE
Transactions on Systems, Man, and Cybernetics, Part

28, No. 1, pp. 141-153.
Kilgour, D.M., Hipel, K.W. and Fang, L. (1987) ‘The graph

A, Systems and Humans, Vol. 39, No. 5, pp. 993-1006.

model for conflicts’, Automatica, Vol. 23, No.1, pp.

Obeidi, A., Kilgour, D.M., and Hipel, K.W. (2009b) ‘Perceptual graph model systems’, Group Decision and41-55.

Negotiation, Vol. 18, No. 3, pp. 261-277.

Kilgour, D. M., Hipel, K.W., Fang, L. and Peng, X. (2001)‘Coalition analysis in group decision support’, Group

Okada, N. (2002) ‘Developing an indicator of a communi-

Decision and Negotiation, Vol. 10, No. 2, pp. 159-175.

ty’s disaster risk awareness’, in: Risk, Reliability, Un-

Kilgour, D.M., Okada, N. and Nishikori, A. (1988) ‘Loadcertainty, and Robustness of Water Resources Systems,

control regulation of water pollution: an analysis usingeds. J. Bogardi and Z. Kundzewicz, pp. 62-69, Cambridge University Press, Cambridge, United Kingdom.

game theory’, Journal of Environmental Management,

Okada, N., Fang, L. and Hipel, K.W. (2006) ‘Perspectives

Vol. 27, pp. 179-194.
Li, K.W., Hipel, K.W., Kilgour, D.M. and Fang, L. (2004a)

in participatory infrastructure management’, Journal of‘Preference uncertainty in the graph model for conflict

Infrastructure Planning and Management, Japan Soci-

resolution’, IEEE Transactions on Systems, Man, andety of Civil Engineers, Vol. 62, No. 3, pp. 417-429.

Cybernetics, Part A: Systems and Humans, Vol. 34,

Okada, N., Hipel, K.W., Fraser N.M. and Fukushima, M.
(1988) Konfurikuto No Suuri (Mathematical Modelling

No. 4, pp. 507-520.

of Conflict Resolution) (in Japanese), (Kyoto, Japan:

Li, K.W., Hipel, K.W., Kilgour, D.M., and Noakes, D.J.

Gendai Sugakusha (Publisher)).

(2005a) ‘Integrating uncertain preferences into statusquo analysis with application to an environmental con-

Okada, N., Hipel, K.W. and Oka, Y. (1985) ‘Hypergame

flict’, Group Decision and Negotiation, Vol. 14, No. 6,

analysis of the Lake Biwa Conflict’, Water Resources
Research, Vol.21, No. 7, pp. 917-926.

pp. 461-479.
Li, K.W., Kilgour, D.M. and Hipel, K.W. (2004b) ‘Status

Rajabi, S., Hipel, K.W. and Kilgour, D.M. (1999) ‘Water

quo analysis of the Flathead River conflict’, Wa-

supply planning under interdependence of actions:ter Resources Research, Vol. 40, No. 5, W05S03,

theory and application’, Water Resources Research,doi:10.1029/2003WR002596 (9 pages).

Vol. 35, No. 7, pp. 2225-2235.

Li, K.W., Kilgour, D.M. and Hipel. K.W. (2005b) ‘Status

Rajabi, S., Kilgour, D.M. and Hipel, K.W. (1998) ‘Modellingquo analysis in the graph model for conflict resolu-

action - interdependence in multiple criteria decision

tion’, Journal of the Operational Research Society,making’, European Journal of Operational Research,

Vol. 56, No. 6, pp. 699-707.

Vol. 110, No. 3, pp. 490-508.

Maier, M. (1998) ‘Architecting principles for systems-of-Sage, A.P. (1992) Systems Engineering, (New York: Wiley).

systems’, Systems Engineering, Vol. 1, No. 4 , pp. 267-

Sage, A.P. and Biemer, S.M. (2007) ‘Processes for system284.

family architecting design, and integration’, IEEE Sys-

Nandalal, K.W.D. and Hipel, K.W. (2007) ‘Strategic deci-

tems Journal, Vol. 1, No. 1, pp. 5-16.

sion support for resolving conflict over water sharing

Sage, A.P. and Cuppan, C.D. (2001) ‘On the systems engi-

among countries along the Syr Darya River in the Aral

neering and management of systems of systems and

Sea Basin’, Journal of Water Resources Planning andfederations of systems’, Information Knowledge Sys-

Management, Vol. 133, No. 4, pp. 289-299.

tems Management, Vol. 2, No. 4, pp. 325-345.

Obeidi, A., Hipel, K.W. and Kilgour, D.M. (2005) ‘The role

Sage, A.P. and Rouse, W.B. (2008) Handbook of Systemsof emotions in envisioning outcomes in conflict analy-

Engineering and Management, second edition, (Newsis’, Group Decision and Negotiation, Vol. 14, No. 6,

York: Wiley).

76

SYSTEMS METHODOLOGIES IN VITAE SYSTEMS OF SYSTEMSVon Neumann, J. and Morgenstern, O. (1953) Theory ofhydrologic-economic modeling of coalitions of stake-

Games and Economic Behavior, third edition, (Princ-holders for water allocation in the South Saskatchewan

eton, NJ: Princeton University Press).

River Basin’, Journal of Hydrologic Engineering, Vol.
13, No. 9, pp. 781-792.

Waddington, C.H. (1973) OR in World War 2, (London:

Waterloo Regional Council (2000) ‘Waterloo’s long term

Elek Sicence).

water strategy’, Waterloo Regional Council Report,

Walker, S., Hipel, K.W. and Inohara, T. (2009) ‘Strategic

E-00-027.1, Waterloo, Ontario, Canada.

decision making for improved environmental security:
Coalitions and attitudes in the graph model for conflict

Xu, H., Hipel, K.W., and Kilgour, D.M. (2009a) ‘Matrix

resolution’, Journal of Systems Science and Systems

representation of solution concepts in multiple decision

Engineering, Vol. 18, No. 4, pp. 461-476.

maker graph models’, IEEE Transactions on Systems,
Man, and Cybernetics, Part A: Systems and Humans,

Wang, L., Fang, L. and Hipel, K.W. (2007a) ‘MathematicalVol. 39, No. 1, pp. 96-108.

programming approaches for modeling water rights

Xu, H., Hipel, K.W. and Kilgour, D.M. (2009b) ‘Multiple

allocation’, Journal of Water Resources Planning andlevels of preference in interactive strategic decisions’,

Management, Vol. 133, No. 1, pp. 50-59.
Wang, L., Fang, L. and Hipel, K.W. (2007b) ‘On achieving

Discrete Applied Mathematics, Vol. 57, pp. 3300-3313.

fairness in the allocation of scarce resources: Measur-

Xu, H, Li, K.W., Kilgour, D.M., and Hipel, K.W. (2009c) ‘A

able principles and multiple objective optimization ap-

matrix-based approach to searching colored paths in aproaches’, IEEE Systems Journal, Vol. 1, No.1, pp. 17-

weighted colored multidigraph’, Applied Mathematics

28.

and Computation, Vol. 215, No. 1, pp. 353-366.

Wang, L., Fang, L. and Hipel, K.W. (2008a) ‘Basin-wide

Zeng, D-Z., Fang, L., Hipel, K.W., and Kilgour, D.M. (2007)

cooperative water resources allocation’, European‘Policy equilibrium and generalized metarationalities

Journal of Operational Research, Vol. 190. pp. 798-

for multiple decision-maker conflicts’, IEEE Transac-

817.

tions on Systems, Man, and Cybernetics, Part A: Systems and Humans, Vol. 37, No. 4, pp. 456-463.

Wang, L., Fang, L., and Hipel, K.W. (2008b) ‘Integrated

77