Calais, Gerald J. Fuzzy Cognitive Math Theory

FOCUS On Colleges, Universities, and Schools
Volume 2 Number 1, 2008
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Fuzzy Cognitive Maps Theory: Implications for
Interdisciplinary Reading: National Implications
Dr. Gerald J. Calais
Associate Professor
Department of Teacher Education
Burton College of Education
McNeese State University
Lake Charles, Louisiana
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ABSTRACT
Fuzzy Cognitive Maps (FCMs) are initially shown to have evolved from Cognitive
Maps (CMs). The components and functions of FCMs are described and their
superiority over CMs is explained. A hypothetical fuzzy cognitive map, employing a
nine-step procedure and data tables, is then used to demonstrate the impact of drug
addiction in America. Conclusions are subsequently derived from these data tables,
and implications for interdisciplinary reading are provided.
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Fuzzy Cognitive Maps Theory: Implications for Interdisciplinary Reading
Robert Axelrod (1976) inaugurated the use of cognitive maps (CMs) for formally
modeling decision making processes associated with political and social systems. CMs
are directed graphs capable of modeling interrelationships or causalities existing amongst
concepts (nodes). Concept variables and causal relations constitute the two fundamental
elements that CMs employ for graphically describing systems. Concept variables are
represented by nodes, such as C1, C2, C3, and C4 in Figure 1, a basic CM having four
concept variables describing the impact of drug addiction. Causal variables always
depict concept variables at the origin of arrows; effect variables, on the other hand,
represent concept variables at the terminal points of arrows. For example, in looking at
C1 C2 in Figure 1, C1 is said to impact C2 because C1 is the causal variable, whereas C2
is the effect variable.

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Crime
C2
+ +
Drug Addiction C1 C4 Incarceration
- -
C3
Employment Opportunities
Figure 1 - A traditional cognitive map on the impact of drug addiction
According to Alexlrod (1976), causal variable C1’s total effect on effect variable
C4 is the aggregate sum of all the paths’ indirect effects from each causal variable
associated with each effect variable. A positive total effect implies that each indirect
effect is also positive; a negative total effect implies that each indirect effect is also
negative; an indeterminate effect, on the other hand, implies that some indirect effects
manifest positive effects while others manifest negative effects (Kosco, 1986).
Unfortunately, when cognitive maps contain many concepts and paths, indeterminacy
dominates. For example, in Figure 1 above, C1’s total effect on C4 is indeterminate. This
intrinsic drawback persists because cognitive maps cannot accommodate knowledge-
based building since causality itself generally tends to be fuzzy because it admits of
vague degrees [e.g., a little, some, often, much, usually, very much] (Fons, S., Achari, G.,
& Ross, T.J., 2003).
Fortunately, Kosco (1986, 1992) introduced fuzzy cognitive maps (FCM) that
augment a CM’s power by accommodating the aforementioned knowledge-base building
feature, because FCMs are capable of modeling cyclically dynamic systems, which in
turn permits feedback within a cycle. FCMs, which are typically dependent upon experts’
input, may be thought of as fuzzy-graph structures that represent the fuzzy nature of
causal reasoning by permitting vague degrees of causality between vague causal
concepts. Their graph structure, moreover, thrives on feedback and can connect various
FCMs to propagate knowledge bases.
Figure 2, a FCM describing the impact of drug addiction, associates fuzzy values
with each of the cognitive map’s concepts and uses fuzzy degrees as the metric for
designating the interrelationships between concepts. In essence, a FCM is a signed
directed graph that entails feedback and employs concepts (nodes) and weighted edges
(arcs) between concepts. Nodes of the graph designate each concept that represents a
system variable (e.g., actions, events, goals, policies, processes) whose values vacillate.

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Drug Addiction
+ +
Always Very Much
Health Problems Crime
- +
Much - Very much
Always
Employment Incarceration
Opportunities
- +
Some Much
Recidivism
Figure 2 - A fuzzy cognitive map on the impact of drug addiction over time
Signed and weighted edges, on the other hand, express the causal relationships existing
between any two concepts. In addition, a directed edge may connect any concept not
only to any other concept but also to itself, signifying that a concept’s current value
determines its future value. In fact, all of a FCM’s values are fuzzy. Accordingly, each
concept’s value is influenced by its previous value and the connected concepts’ values
accompanied with their appropriate weights. Hence, it is a FCM’s memory capabilities
that enable it to demonstrate how a change in one concept’s value affects the entire FCM
by keeping track of the concept’s old and new values following each of the FCM’s new
cycling, runtime, or simulation. For example, in using a unipolar threshold function,
weighted values for concepts or nodes traditionally range from 0 to 1, with 0 indicating
maximum negative representation, 0.5 representing ambivalence, and +1 indicating
maximum positive representation. Connecting edges, which indicate the degree of
causality between any two concepts, traditionally employ a bipolar threshold function
ranging from -1 to +1, with -1 reflecting a strong negative impact, through 0 reflecting no
impact, to +1 reflecting a strong positive impact (Brubaker, 1996).
In Figure 2, word weights like “some” and “always” denote the causal
relationships between concepts, and the symbols “+” and “-” denote the type of
relationship between concepts. A fuzzy rule, causal link, or connection is defined by
each arrow in the same figure: A plus (+) represents causal increase, and a negative (-)
represents casual decrease. According to the plus rule, for example, if drug addiction
increases, then health problems increase to some degree, too; if drug addiction decreases,
however, health problems decrease to some degree, too. The minus rule, in contrast,
implies that if health problems increase, then employment opportunities decrease to some
degree. Hence, the plus rule and the minus rule exhibit a directly proportional and
inversely proportional relationship, respectively.

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A typical runtime operation, or simulation, of a FCM entails the following general
procedures: First, drawing an FCM via an expert’s (or experts’) experience and expertise
regarding a system’s operation is arguably the most pivotal step. The expert (or experts)
identifies the appropriate concepts most crucial in modeling the system, determines each
concept’s negative or positive effect on other concepts, and assigns fuzzy values for all
events or interconnections. Second, with the successful construction of the FCM, it is
now possible to model and simulate the system’s behavior. At this juncture, the FCM is
ready to be initialized. This means that the expert(s) assigns each concept an activation
level having an initial value ranging in the interval [0,1]. Third, the concepts are then free
to interact, resulting in the concepts’ values changing during each step of the cycling
process or runtime operation. Fourth, contingent upon the quantity of concepts and the
quantity and complexity of events or interconnections, the system normally necessitates
several steps or cycles before it reaches equilibrium, i.e., when a system ceases to change.
It is, however, quite possible that the system may not even reach equilibrium. When this
happens, it does so because a FCM’s feedback paths render the FCM oscillatory, which
may occur either predictably or chaotically, or the paths render the FCM unstable.
As previously stated, FCMs are significantly more flexible, valuable, and efficient
than are CMs for analyzing a system’s major components and the causal connections that
exist amongst them, due primarily to their knowledge-base building capacities and
feedback. FCMs, in fact, are now used extensively for planning and decision-making in
numerous fields, especially in the physical and social sciences (Stylios, C.D.,
Georgopoulos, V.C., & Groumpos, P.P., n.d.). In the next section, a practical problem
will be employed to demonstrate how a FCM functions.
Implementation of a FCM on Drug Addiction
In this section, the problem of drug addiction, with its national and international
implications, will be modeled to obtain a feel regarding how a FCM typically works.
Drug addiction, fortunately, possesses three intrinsic characteristics that make it ideal for
analysis via fuzzy cognitive maps: First, it is a problem having many factors that
contribute to its complexity; second, modeling it mathematically is impossible because it
cannot simply be reduced to equations; and third, the problem is subject to various
interpretations because it can be perceived from different perspectives. In order to
demonstrate drug addiction’s ideal choice for analysis via FCMs, this manuscript will
focus next on the preparation of a hypothetical fuzzy cognitive map, whose topic is based
in part on Kosko’s (1993) work, for problems associated with drug addiction. Results of
hypothetical simulations for the fuzzy cognitive map are provided, and hypothetical
conclusions are drawn from them.

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Step 1: Identification of Factors or Concepts
Based on Aspuru’s (n.d.) work, nine steps are employed in designing a cognitive
map: (1) identification of factors, (2) specification of relationships, (3) levels of all
factors, (4) intensities of causal effects, (5) changeable factors versus dependent factors,
(6) simulating the fuzzy cognitive map, (7) modifying the fuzzy cognitive map, (8)
simulating the modified fuzzy cognitive map, and (9) conclusions.
The first step when preparing a fuzzy cognitive map entails the identification of
and rationale for those requisite factors (concepts) that constitute part of it. The
following eight factors (concepts) have been selected, based on the author’s interpretation
of the current status of the impact of drug availability and drug usage in America.
Drug Usage. Drug usage is a problem that plagues many citizens in our country;
unfortunately, it is a global problem, too. The goal set for this hypothetical fuzzy
cognitive map is to determine how drug usage impacts America. Hence, it, along with
drug availability, is the most critical factor in this fuzzy cognitive map. Drug usage will
be shown to affect other factors in the FCM.
Drug Availability. As long as there are drugs, drug usage will inevitably occur
due to human nature; nonetheless, reducing the availability of drugs in its various forms,
both domestically and internationally, should help to diminish its usage. This factor,
along with drug usage, is the most critical factor in the cognitive map; it will also be
shown to impact other factors in the FCM.
American Police Interdiction. The degree to which America’s various levels of
law enforcement agencies are adequately funded determines to a great extent whether we
will succeed in reducing drug usage in our country. This dimension of enforcement will
be shown to be a pivotal factor in successfully reducing drug usage, but not sufficient,
alone. This interdiction also affects other factors in the FCM.
International Police Interdiction. Given that drug usage is a global problem, it
should come as no surprise that law enforcement at the international level is essential in
combating the flow of drugs to America as well as to other parts of the world. This
dimension of law enforcement, while central for solving drug addiction within our
borders will also be shown to be insufficient, alone. This level of interdiction also affects
other factors associated with this FCM.
Treatment Centers. As long as drugs are available and used by our citizens,
treatment centers will be needed to help rehabilitate their lives in order to become
productive citizens. Although this is but one approach for dealing with the drug issue in
this country, it is an essential one.
American Image. How America is viewed by other nations is important for our
international relations with other nations. Hence, our ability to properly and effectively
deal with drug availability and drug usage problems reflects the kind of people we are.
This factor also impacts other factors in the FCM.
Economic Productivity. Our nation’s ability to generate wealth and revenues is
highly dependent upon employees and entrepreneurs who are productive, dependable,
and reliable. Drug availability and drug usage, on the other hand, nullify these essential
attributes of economic productivity.

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Tourism. Our nation’s ability to attract tourists is an indication of our standing in
the international community. Thus, it is imperative that we deal appropriately with drug
availability and drug usage issues. Tourism also affects other components of the FCM.
Step 2: Specification of Relationships
The second step in preparing fuzzy cognitive maps establishes the causal
relationships (positive, negative, or neutral) amongst the various factors (concepts). This
is a critical step because an articulate analysis is required to determine how and why the
values of factors or concepts change over time.
Causes of Drug Usage. The first and major cause of drug usage in America is
the availability of numerous addictive drugs, whether produced domestically or
internationally. Moreover, the causal relationship is positive (increased availability,
increased addiction; decreased availability, decreased addiction).
Causes of Drug Availability. Drug usage is the major reason for drug
availability because there is a tremendous global demand for the illicit use of drugs.
Drug usage, hence, is a positive cause of drug availability.
Causes of American Police Interdiction. Drug usage is the major cause for
American police interdiction because of the problems posed by drug users in this country.
Monies must be allocated for police forces at all levels of government in order to resolve
this major issue confronting us. Drug usage is a positive cause of American police
interdiction. Drug availability is naturally another major cause of American police
interdiction because so many drug users do drugs because they are available. Drug
availability is a positive cause of American police interdiction.
Causes of International Police Interdiction. Drug usage is a major cause of
international police interdiction because the problem exists on a global scale. Therefore,
international cooperation is imperative if the problem is to be resolved satisfactorily.
Drug usage undoubtedly is a positive cause of international police interdiction. Drug
availability is another major cause of international police interdiction because without a
source, there is no drug problem. Unfortunately, drugs are harvested and processed in
laboratories around the world. Consequently, drug availability is a positive cause of
international police interdiction.
Causes of Treatment Centers. Treatment centers are needed to rehabilitate
citizens who have fallen victim to drug usage. As a result, they can become productive
citizens again in society. Drug usage is a positive cause of treatment centers. Drug
availability is another cause of treatment centers because without drugs, such centers
would not be needed. Drug availability is a positive cause of treatment centers.
Causes of American Image. Clearly, there are many factors that contribute to a
nation’s image on the international stage. Drug usage categorically impacts the image of
the U.S.A. around the world, based especially upon how we respond to the problem.
Drug usage is a negative cause of our American image. Drug availability is another

GERALD J. CALAIS
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factor that affects our image on the international scene because it, too, reflects our ability
to respond to this problem. This factor negatively affects our American image.
Treatment centers also impact America’s image because it reflects a humane attitude
toward human failures and a desire to enable them to become more productive citizens
once again. This factor negatively affects our American image. Tourism also impacts
America’s image because, amongst other things, increased tourism reflects a desire
amongst foreigners to want to visit our country. In general, an increase in tourism tends
to reflect a favorable image of our country. Hence, this factor positively affects the
American image.
Causes of Economic Productivity. A nation’s economic productivity, to be sure,
is caused by numerous factors. For purposes of this article, only pertinent factors
associated with this FCM will be addressed. Drug usage impacts our economic
productivity; however, it does so negatively because increasing drug usage tends to
decrease employees’ productivity. Drug availability also negatively impacts economic
productivity because increasing access to drugs tends to increase drug usage, which in
turn decreases one’s productivity. Tourism is another cause of economic productivity
because tourists spend much money when they visit America, which in turn increases our
national wealth. This factor is a positive cause of tourism.
Causes of Tourism. Our American image is an important cause of tourism in our
country because our international standing will either attract or repel potential visitors to
our shore. This factor is a positive cause of tourism. Drug usage is another important
causal factor of tourism because greater usage of drugs may translate into fewer
foreigners willing to visit our shores. This is a negative casual factor. Drug availability
is also a negative causal factor of tourism because easy access to drugs may turn off
potential foreign visitors.
Factors Without Causes. In viewing the various factors associated with this
fuzzy cognitive map, none is seen as existing without any causes because each factor is
caused by one or more other factors in the fuzzy cognitive map. Naturally, this
interpretation could be challenged.
Illustration of the Fuzzy Cognitive Map. Figure 3 below represents all eight
factors or concepts of this hypothetical system’s fuzzy cognitive map.
Economic -- Drug + Treatment
Productivity Usage Centers
+
+ + + +
-- -- --
+ International Drug American --
Police + Availability + Police
Interdiction Interdiction
-- --
+ American
Tourism Image
+
Figure3: A fuzzy cognitive map on the impact of drug addiction in America

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In the next section below, the third step, the levels (ranging from 0-100) of each
factor (concept) within the system will be discussed.
Step 3: Levels of all Factors
It can be assumed that the problem of both drug usage and the availability of
drugs in the U.S.A. is essentially a constant one, rather than one that simply evolves.
Drug usage, overall, changes very little: drug users seek drugs; pushers provide the
supplies, and law enforcement agencies attempt to stem the tide. We have a major
problem within our borders and little light at the end of the tunnel.
Based on the above assumption, levels of 50 (out of 100) can be assigned to
represent the levels of each of the eight factors of the FCM, resulting in a steady state
such that none of the eight factor levels induces a change in the level of any of the
remaining factors. Verification that no evolution has occurred can be verified through
simulations on the FCM and checking after several iterations.
Allocating levels of 50 to each of the eight factors of the FCM should not be
construed as meaning, in absolute units, that equality exists amongst all factor levels.
This apparent confusion can be explained by stating that each factor actually has its own
unique level, measured in units perhaps non-applicable to the remaining factors. In other
words, having identical values representing various absolute quantities in various factors
is irrelevant because the simulation process does not employ these values to compare one
factor’s level with a different factor’s level. Rather, the values are employed for
comparing one factor’s level prior to the simulation with the same factor’s level after the
simulation run. The simulation is conducted after generating a perturbation within the
system in order to knock it out of its steady state. Any variation in one or more of the
factors’ levels constitutes a perturbation within a system.
Step 4: Intensities of Causal Effects
According to the fourth step, all causes affecting a factor vary in intensity or
degree. For example, although drug usage and tourism are causes of economic
productivity, drug usage affects economic productivity more so than does tourism.
Hence, various causes’ intensities of effect are reflections of their relative significance,
extending from 0 (no intensity) to 100 (uppermost intensity). Based on Aspuru’s (n.d.)
work, three ranges of intensities of effect are employed: high intensity (with an assigned
value of 75 out of 100), moderate intensity (with an assigned value of 50 out of 100), and
low intensity (with an assigned value of 25 out of 100). Each group’s relationships are
listed below.

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High intensity relationships:
Drug availability causes drug usage
Drug usage causes drug availability
Moderate intensity relationships:
Drug usage causes American drug interdiction
Drug usage causes international police interdiction
Drug usage causes tourism
Drug usage causes American image
Drug usage causes economic productivity
Drug availability causes American police interdiction
Drug availability causes international police interdiction
Drug availability causes tourism
Drug availability causes American image
Drug availability causes economic productivity
Low intensity relationships:
Drug usage causes treatment centers
Drug availability causes treatment centers
Tourism causes economic productivity
Tourism causes American image
American image causes tourism
Treatment centers cause American image
The above matching of intensities of effects with relationships is assuredly only
one way of matching various numeric values corresponding with the three categories of
intensity: low, moderate, and high. Furthermore, the relationships could have been
grouped differently, or a different number of groups could have been selected. In the
next section below, the fifth step, a distinction is drawn between changeable and
dependent factors.
Step 5: Changeable Factors Versus Dependent Factors
The fuzzy cognitive map’s changeable factors associated with the impact of drug
usage in America are drug usage, drug availability, American police interdiction, and
international police interdiction. The dependent factors, in contrast, are American image,
tourism, economic impact, and treatment centers.
The “agents” associated with the changeable factors have a choice of modifying
or resuming their behavior and objectives, thereby affecting the evolution of the entire
system. More specifically, the “agents” of these changeable factors are able to directly
control the systems’ factors and to modify these factor’s levels at will. However, the
“agents” are unable to directly control other factors’ levels, i.e., dependent factors. For

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example, in terms of independent factors, the drug user could have initially decided not to
do drugs by not getting involved with drugs; all parties responsible for making drugs
globally available could cease to do so; different governmental levels in the U.S. could
simply decide to use monies to have police focus on global terrorism rather than on drug
usage; and foreign countries could decide, too, to spend monies to have their police focus
on global terrorism rather than on drug usage, or they could continue to support global
drug usage without providing help for America. On the other hand, relative to dependent
factors, America’s image depends on many factors other than drug usage at any given
moment; tourism, also, is dependent on factors other than drug usage; many factors, other
than drug usage, have an economic impact on America’s economy; and allocating monies
for treatment centers are dependent upon many factors at any given time and must
compete against other social needs vying for financial support.
Hence, drug usage, drug availability, American police interdiction, and
international police interdiction are the four factors that can be directly changed and will
be employed in an attempt to diminish the impact of drug usage in the United States for
purposes of this FCM.
Step 6: Simulating the Fuzzy Cognitive Map
In this section, the sixth step, running simulations on this hypothetical fuzzy
cognitive map implies introducing variations in all four changeable factors, enabling us to
perceive each changeable factor’s impact on the whole system. Each factor’s level
fluctuates, rather than remains immutable, when it is modified in the fuzzy cognitive map
and subsequently undergoes simulation runs. Realistically, each factor’s level during a
simulation run evolves simultaneously with all other factors, i.e., the initial variation in
the factor’s level functions as a perturbation that causes the whole system to lose its
equilibrium, causing the system to evolve until it reaches equilibrium again. What is
needed, consequently, is the acquisition of a perturbation that drives the system to a new
equilibrium state that is better than the old equilibrium state. In this hypothetical fuzzy
cognitive map, “improved” implies that it produces a lower level of drug availability and
drug usage-related problems in America.
6.1 Effect of Drug Usage
Table 6.1 below shows that drug usage is the first factor to be changed and that
simulations have been run for selected values. The table reveals the simulations’ final
state for various initial values associated with drug usage.

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Drug UsageFactor
0 20 40 60 80 100
American Image 90 85 80 50 40 10
Tourism 90 90 75 30 30 30
Drug Usage 45 47 50 54 57 59
Drug Availability 23 29 35 41 46 56
Treatment Centers 12 17 37 57 78 91
Economic Productivity 90 75 40 20 15 10
Table 6.1
As is evident from Table 6.1, drug usage’s initial and final levels differ. An initial
decrease in drug usage improves America’s image, tourism, and economic activity while
decreasing drug availability, the need for treatment centers, and drug usage, but not so
much. When initial drug usage is high, however, the final state reverses itself: a decrease
in America’s image, tourism, and economic activity, while increasing drug availability,
drug usage, and the need for treatment centers.
6.2 Effect of Drug Availability
The second set of simulations via Table 6.2 examines the effect of drug
availability; it, too, as before, employs a sample of initial levels for drug availability in
running the simulation.
Drug AvailabilityFactor
0 20 40 60 80 100
Tourism 90 88 75 32 32 32
Drug Usage 43 46 51 54 55 60
Table 6.2
Close inspection of Table 6.2 reveals that the effects of a decrease or increase in
the level of drug availability and the effects of a decrease or increase in the level of drug
usage mirror each other at corresponding levels. These symmetrical results should not
surprise us because of the strong positive correlation between both factors.

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6.3 Effects of Drug Usage and Drug Availability
This third set of simulations in Table 6.3 explores variations of both factors, drug
usage and drug availability, moving in identical directions and differing by identical
amounts.
Drug Usage and Drug AvailabilityFactor
0 20 40 60 80 100
Tourism 89 90 74 29 30 29
Drug Usage 44 47 50 55 56 60
Table 6.3
Table 6.3, again, mirrors results comparable to Table 6.1 and Table 6.2. These
results strongly suggest that, in order to decrease the negative impact of drugs in this
country, either a decrease in drug usage or a decrease in drug availability is perhaps
sufficient to stem the tide in our favor. In other words, we do not need a decrease in both
drug use and drug availability to improve the situation.
6.4 Effects of American Police Interdiction
Next, a series of simulations via Table 6.4 are conducted to gauge the effect of
police interdiction on the drug addiction problem in America. First, simulations are run
for variations on the level of American police interdiction.
American Police InterdictionFactor
0 20 40 60 80 100
Tourism 30 31 32 76 88 91
Drug Usage 61 52 45 38 30 25
Table 6.4

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As can be seen from Table 6.4, America’s image, tourism, and economic
productivity increase as American police interdiction increases. On the other hand, there
is an inverse relationship between American interdiction and drug usage, drug
availability, and treatment centers: as the former increases, the latter factors decrease.
Figure 6.5 Effects of International Police Interdiction
The next table below, Table 6.5, focuses on the effect of variations of
international police interdiction on drug addiction in America.
International Police InterdictionFactor
0 20 40 60 80 100
Tourism 29 31 32 75 86 90
Drug Usage 60 55 50 42 34 27
Table 6.5
The results of Table 6.5 reflect similar results obtained in the previous table: an
increase of police interdiction at the international level also increases America’s image,
tourism, and economic productivity. In addition, an inverse relationship also exists
between international police interdiction and drug usage, drug availability, and treatment
centers, i.e., as the former increases, the latter factors decrease.
Step 7: Modifying the Fuzzy Cognitive Map
This hypothetical fuzzy cognitive map has included factors and relationships
employed in the preceding sections to represent only one of numerous possible
perceptions of drug addiction in America. It is certainly conceivable that someone else
could generate a different fuzzy cognitive map.
That having been said, the current map has succeeded especially in substantially
diminishing drug usage and drug availability, the primary goal for this exercise. As a
result, achievement of the primary goal of this exercise obviates the need for any
modifications to this hypothetical fuzzy cognitive map and additional simulations.

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Step 8: Simulating the Modified Fuzzy Cognitive Map
Given that the primary goal for this exercise was achieved via the selected
simulations of the factors and relationships, no simulations will be needed for a modified
fuzzy cognitive map. Instead, the conclusions reached from these simulations will be
discussed in the ninth and final section.
Step 9: Conclusions
Several conclusions can be drawn from the results derived from the previously
obtained simulations. The first and most important one is that neither drug usage nor
drug availability can be totally eliminated, at least not based on the relationships between
the current selections of factors in the fuzzy cognitive map. Nonetheless, the results
obtained from the simulations can conceivably reduce the level of drug addiction and
drug availability, while simultaneously reducing and increasing other factors. The
prerequisite steps essential for achieving this are enumerated below. The data between
square brackets are selected to justify each step.
1. Vigilant American police interdiction, supported with appropriate budgetary
allocations, is essential for substantially reducing both drug usage and drug
availability [Table 6.4].
2. Vigilant international police interdiction is also essential for making
substantial inroads in reducing drug usage and drug availability in America
[Table 6.5].
3. The need for treatment centers can be significantly reduced with vigilant
American and international police interdiction [Tables 6.4 and 6.5.].
4. Economic productivity can increase and improve enormously with police
interdiction and a reduction in drug usage and drug availability [Tables 6.1,
6.2, 6.3, 6.4, and 6.5].
5. Tourism can also improve immensely with police interdiction and a reduction
in drug usage and drug availability [Tables 6.1, 6.3, 6.3, 6.4, and 6.5].
6. America’s image abroad, backed by effective police interdiction, can improve
very much with a sizeable reduction in drug usage and drug availability
because it reflects a safer environment [Tables 6.1, 6.2, 6.3, 6.4 and 6.5].
The results of this hypothetical fuzzy cognitive map reflect, to be sure, only one
of numerous possible views of drug addiction in America. The map’s relationships could
certainly have been rearranged, and additional factors could be included, such as
governmentally supported federal programs to educate youth on the problems of drug
addiction, drug cartels, profits, and corruption. In the last section, implications for using
fuzzy cognitive maps for interdisciplinary reading are discussed.

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Implications for Interdisciplinary Reading
Although FCMs have been and continue to be used extensively for planning and
decision-making in numerous fields (Stylios, C.D., Georgopoulos, V.C., & Groumpos,
P.P., n.d.), especially in the physical and social sciences, their relevance could
realistically be integrated in interdisciplinary reading assignments that either focus on a
specific content area or that cut across more than one discipline. For example, students,
at least those at the secondary level, could be taught to incorporate FCMs when reading
topics that focus primarily in the sciences (e.g., global warming, acid rain, salmonella and
E.coli poisoning, various experiments on topics in chemistry, biology, and physics, and
epidemics due to AIDS, the flu, and Ebola), or primarily in the social sciences (e.g., the
Middle East crisis, the current oil crisis, international relations, economic recessions,
political elections at all governmental levels, the American Civil War, the Great
Depression, or revolutions for liberty in America, France, and Russia), or primarily in
literature, art, and music (e.g., ethical, religious, moral, and philosophical issues
stemming from different countries’ major novels, poetry, paintings, sculpture, or musical
compositions), or in mathematics (e.g., methods for teaching proofs, or the utility of
algorithms and heuristics). There certainly are several suggested topics stated above that
actually cut across at least two, and conceivably three, disciplines because some problems
simply do not fit tightly into only one discipline.
In utilizing FCMs in school settings, it should be stressed that having groups of
students articulate their rationale for selecting specific factors or concepts for their chosen
topic or problem, determining the causal relations amongst these factors or concepts, and
assigning weights to the factors or concepts are what matter most in having them engage
in these exercises. It is precisely the need to articulate their choices that enhances both
their understanding of the class material in terms of breadth and depth and their ability to
recall said material. Since learning entails both comprehension and recall, FCMs clearly
have a role in molding our students into independent problem-solving thinkers, a critical
attribute needed for successful competition in today’s global economies.
References
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16____________________________________________________________________________________
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