To Main Proceedings Document
Simulation of Qualitative Models to Support
Business Scenario Analysis
Karl R. Lang
Department of Information and Systems Management
Hong Kong University of Science & Technology,
Clear Water Bay, Kowloon, Hong Kong,
Phone: +852.2358.7633 Fax: +852.2358.2421,
Email: klang@ust.hk.
Abstract
When we look at the research that is concerned with the modeling and analysis of
business scenarios, we can recognize an unfortunate yet profound dichotomy of research
methodologies; qualitative versus quantitative research. There seems to be an almost
unbridgeable gap between the two approaches, which has also errected high barriers for
communication between the two corresponding research communities. On the one hand, we
have the “qualitative” or “behavioural” people who criticize quantitative methods as
inapplicable and far removed from most of the real-world situations that are observed in
organizational environments, and, on the other hand, we have the “quantitative” or
“mathematical” people who only believe in numbers and equations and accuse any research
that is not somehow based on a mathematical theory as unscientific. In the following discussion
we try to show that qualitativeness and quantitativeness are not mutually exclusive concepts.
Quite the contrary, we argue that they are, in many ways, closely related and that they form the
two ends along a common dimension of knowledge discovery and knowledge representation.
Based on recent work in qualitative reasoning, a newly emerging field in artificial intelligence,
we present a system that offers modeling and simulation capabilities while only requiring
qualitative information about the variables and relationships included in a model.
1. Introduction
The domains of the organizational sciences, management and economics are immensely
complex. Most theories describe just a small segment of the real world by abstracting from it
certain system entities and relate them in some way in order to explain or to predict a particular
economic phenomenon. Our knowledge about the real world is mainly derived from perceptions
and empirical observations. A theory can be viewed as an abstract system that describes some
well-defined real-world phenomenon which reveals implications of its underlying assumptions
and hypotheses. The principles of scientific deduction only allow us to draw conclusions that can
be deduced from the assumptions included in a theory. In order to be meaningful, a theory has to
be general, but at the same time specific enough to be amenable for empirical testing. For
example, a general theory that explains the behavior of all consumers of an economy at all times
and places is more relevant than one that is exclusively concerned with the behavior of a
particular consumer at a particular time and place. Theories of the former kind, although
conceptually ideal, do not exist in most problem settings or, at least, are not likely to be found.
For that matter, theories usually need to be restricted to certain classes, such as collections of
consumers with certain properties acting in some specific type of economy. According to Popper
(1959), a theory should be constructed in a falsifiable manner, that is, it must be specific enough
to refute it if empirical testing indicates that the hypotheses underlying a theory are not
consistent with observed data. A theory containing a hypothesis of the sort "at any time all x of a
certain kind will choose a particular action a under some specific circumstances" is more
meaningful than one which simply says that "at some time some x will choose a," because the
latter immunizes itself from falsification.
Performing scientific deduction requires a language to represent domain knowledge, and
an inference mechanism to derive implications from the knowledge expressed in that language.
Representation languages range from narrative languages, diagrams and other graphical
representations, mathematical structures to modeling languages for computer software systems.
Selecting the most appropriate representation language is task-specific and usually involves a
tradeoff between the high expressiveness of informal languages and the strong inferential power
of formalized languages. An important phase in the process of scientific reasoning is the
translation of domain knowledge into a particular representation language, usually referred to as
theory specification or model specification. This transition requires a good deal of abstraction,
and is the most vulnerable one in the whole process. Is the problem description consistent with
our perception of the real world phenomenon under study, and does it capture all its relevant
features? If both questions can be answered with yes, we can select and apply a suitable
inference method, and deriving the implications of the model or theory is then merely a technical
task which makes information implicitly encoded in the problem description explicit, that is,
deriving implications neither adds nor subtracts any information.
Typically, an economic (or organizational) system is modeled by identifying a set of
relevant system variables and specifying relationships among them. Once a model is set up ina
particular representation language we can pose questions, and analyze the model by selecting an
adequate solution method, which may include linguistic analyses, and interpreting the results.
However, our knowledge about economic systems is inherently incomplete and full of
uncertainties. Hence, developing an economic model requires some sort of abstraction and/or
approximation. Since quantitative solution methods provide the most powerful inference
mechanisms, it is desirable to represent the particular system under consideration as a
quantitative model. But this is only possible if the real-world phenomenon under study can be
expressed within the strict confines of a formal, quantitative representation language, and
necessitates precise knowledge about the involved relationships, which usually means that we
need to be able to formulate exact, and possibly tremendously complicated, functional
relationships between the system variables. Assuming that there is indeed a true model exactly
describing the behavior of the real world economic phenomenon, it is, in general, too complex to
be discovered and remains unknown to the modeler.
The purpose of this paper is to examine the needs for representing qualitative
relationships when developing models or formulating theories in the organizational sciences,
information systems, management and economics. In the remainder of the paper, we will review
current approaches of treating qualitative knowledge, identify existing shortcomings, and suggest
a somewhat more formal methodology which enables theorists to do a more rigorous analysis of
qualitative theories and qualitative model using the support of modern computing technologies.
2. The Representation of Organizational Relationships:
Qualitative versus Quantitative A pproaches
When we look at the research that is concemed with problems from the business domain,
we can recognize an unfortunate yet profound dichotomy of research methodologies; qualitative
versus quantitative research. There seems to be an almost unbridgeable gap between the two
approaches, which has also errected high barriers for communication between the two
corresponding research communities. On the one hand, we have the “qualitative” or
“behavioural” people who criticize quantitative methods as inapplicable and far removed from
most of the real-world situations that are observed in organizational environments, and, on the
other hand, we have the “quantitative” or “mathematical” people who only believe in numbers
and equations and accuse any research that is not somehow based on a mathematical theory as
unscientific. In the following discussion we try to show that qualitativeness and quantitativeness
are not mutually exclusive concepts. Quite the contrary and similar to Coyle (1999), we argue
that they are, in many ways, closely related and that they form the two ends along a common
dimension of knowledge discovery and knowledge representation.
When dealing with partially known systems, there are several approaches one might take
in coping with incomplete and uncertain knowledge. Quantitative analysis restricts itself to well
known mathematical structures, like linear equation systems or mathematical optimization
models, and tries to find an approximate model that is close enough to the true model to give
useful insights. Stochastic methods treat system variables as random, or impose error terms in
order to cover the true relationships. The latter approach requires additional assumptions about
the probability distribution of random variables which is often beyond the knowledge available.
For that reason, and to keep the model tractable from a computational point of view, random
variables are usually chosen to be normally distributed; a commitment that has to be justified but
is too often neglected. Quantitative approaches have the advantage of producing precise results,
but frequently one lacks confidence in the appropriateness of the underlying model. Precise
answers, on the other hand, are often not even of primary interest when conducting
organizational studies; qualitative information like signs of impacts and effects, ranges and
directions of change of goal variables can be sufficient for satisfactorily explaining and
predicting the behavior of organizational systems. In many situations most of the knowledge at
hand is of a qualitative nature; for example, knowledge of the signs or possibly magnitudes (e.g.,
low/medium/high) of variables rather than exact numerical values, or partial knowledge of the
shape of functional relationships (e.g, monotonicity).
Reasoning with incomplete or qualitative information has actually a fairly long tradition
in the area of economis; see, for example, Samuelson (1947) and Lancaster (1962). Because
qualitative economic analysis had been essentially developed prior to the era of modem
computer technology, it was limited in scope by the absence of computational power. Recent
research in qualitative reasoning, a new field that has emerged from artificial intelligence, see
Weld and deKleer (1990), is based on a similar motivation as qualitative economics. Qualitative
reasoning attempts to provide a framework that allows one to model dynamic systems in
qualitative terms. Basically unaware of the related work in qualitative economics, qualitative
reasoning has developed a small number of representation languages and computer-supported
inference mechanisms for qualitative modeling in the physics and engineering domains,
sometimes reinventing techniques already known in the economics literature. Iwasaki and Simon
(1986) first recognized the link between qualitative reasoning and qualitative economics. The
research in qualitative reasoning has raised new interest in qualitative analysis in economics and
first applications can be found in Farley and Lin (1990), Berndsen and Daniels (1991), and Lang
et al (1995). A more comprehensive discussion of qualitative modeling and reasoning issues
which extends into the management area is presented in Lang (1993).
The motivation for taking a qualitative perspective has various reasons. Firstly, for many
problems there is simply not enough information available to formulate a quantitative model,
thus prohibiting the application of quantitative methods. We call this situation modeling systems
with incomplete knowledge or information. Secondly, partially known systems encompass
imprecise and uncertain information. This is called modeling systems with imprecise knowledge
or information. Thirdly, even if it were possible to acquire complete and precise knowledge, the
modeler is often not really interested in the details of the system, in other words, the modeler
prefers a qualitative description. The latter case adopts a point of view which is typical for a top
level management perception of an organization, and is especially suited for addressing strategic
business issues. Fourthly, research in, for example, organizational science and economics,
pursues as one of its main goals the development of general theories about certain classes of
firms. In this context, one might be interested in a qualitative framework that allows you to
abstract knowledge from a collection particular organizations, which might be fairly specific,
into more general descriptions, retaining the qualitative information that represents only
significant distinctions and characterizes all members of the class. Analyzing such a generalized,
qualitative model draws implications that hold for all specific, possibly quantitative, models that
are instances of this class.
In business related areas like organization science, management, business
communication, and others, qualitative approaches are widely used in order to investigate
problem scenarios and to develop theories. Work in the management science (MS) and decision
support systems (DSS) areas, on the other hand, have traditionally been emphasizing quantitative
methodologies. A common pitfall of traditional MS/DSS approaches is their rigid representation
of modeling information. Usually, modelers are forced to formulate the relationships of a model
as a set of quantitative constraints, typically constraints of one specific kind such as algebraic or
differential equations. However, the importance and relevance of a more formal treatment of
qualitative knowledge representations and qualitative inference methods has recently been
recognized in the MS/DSS literature as well (Hamscher et al, 1995, Stein and Zwass, 1995, and
Hinkkanen et al, 1995).
From an opposite angle on the subject, Monge (1990) and Weick (1989) have observed
that theoretical and empirical organization science and management (OS/MT) research has been
impeded by the lack of appropriate conceptual and computational tools to model inexactly,
vaguely, incompletely or, in other words, qualitatively specified systems. In most cases
qualitative descriptions are presented as purely verbal formulations, that is, in an informal
manner. Despite the usefulness of verbal formulations, additional more formal methods are often
desired in order to overcome certain vaguenesses in describing complex systems. The absence
thereof has contributed to a dominance of linguistic analyses in most of the theoretical OS/MT
research, and also to numerous ill-advised applications of statistical test methods and regression
analyses in empirical work (Weick, 1984). Hence, Monge (1990) has concluded that current
research in the social sciences is suffering from the lack of computational systems for processing
qualitative information. He calls for a mathematical representation language that provides a
useful compromise between expressiveness and inferential power. Emphasizing the modeling of
dynamic systems he describes crucial features of such a hypothetical language including
provisions for continuous as well as discrete processes integrating qualitative and quantitative
information. Present qualitative OS/MT studies rely chiefly on verbal discourses or other
informal approaches, but in order to formulate, test and verify theories more formalized methods
are needed. Therefore we argue that organizational computing systems must be able to represent
and process qualitative information more thoroughly than present MS/DSS systems.
3. A Formal Specification of Qualitative Relationships
Before we propose a formal approach for specifying qualitative relationships we need to
discuss in more concrete terms what we mean by qualitativeness. We are not aware of a
commonly accepted definition of the the term “qualitative” in the context of research methods.
Common folklore sometimes suggests that qualitative research refers to methodologies that don’t
involve mathematical terms. While this may be true in many cases it, in our opinion,
oversimplifies matters and unnecessarily limits the scope of qualitative research. From the above
discussion it should be clear that mathematics is a neutral formalism and can simply been viewed
as a language for expressing knowledge about this world, a language, or rather a set of
languages if we want to distinguish different mathematical disciplines, that does not have to be
but certainly can be useful when developing scientific theories. Rather than trying to resolve the
difficult task of presenting an explicit definition of qualitativeness, we introduce a couple of
examples, requiring only a minimal amount of mathematical formalism, which will illustrate
what kind of relationships we have primarily in mind when we talk about qualitativeness.
Theories in management typically encompass general statements which apply to whole
classes of organizations. Hence, management theories try to discover commonalities among all
organizations (of a certain class) with general validity, which can sometimes only tenuously be
described as certain trends, influences or tendencies. A widely used practice in research areas
such as organization science, management, and behavioral information systems is to use
qualitative descriptions in order to formulate causal and functional relationships as general
propositions. Qualitative statements are typically based on hypothesized monotonic relationships
of the form if variable X is increased (or decreased) then variable Y will increase (or decrease).
As an illustration take, for example, (a) Cooprider (1990) who states the qualitative proposition
"Increasing the level of partnership among organizational units leads to an increase in the
productivity of the entire organization", and (b) Huber (1990) who hypothesizes that "For a
highly centralized organization, use of computer-assisted communication and decision-support
technologies (that is, information technology (IT)) leads to more decentralization.". Each of
these two propositions verbally expresses a monotonic relationship between two variables, which
is very common in the OS/MT literature. Qualitative relationships of this kind can very well be
represented as so-called (increasing) monotonic function constraints (Mt constraints). Thus, we
propose represent this kind of qualitative knowledge and specify relationship (a) as a qualitative
QSIM constraint
(a) PRODUCTIVITY =M+(PARTNERSHIP),
and relationship (b) similarly as
(b) DECENTRALIZATION =Mt(IT).
Another type of qualitative relationship, called qualitative derivative, arises when the rate
of change of one variable determines the value of another. In cash-flow management, for
example, one might say that the cash-netflow, that is, the difference between cash-inflow and
cash-outflow, is determined over time by the rate of change of cash held by a company.
Research in the finance area typically employs quantitative methods when developing and
analysing cash-flow models although the precise rate of change of cash funds or other system
variables can only be guessed crudely. In a qualitative approach one would simply specify
(c) CASH-NETFLOW =f'(CASH),
without having to detail the exact nature of this functional relationship.
Examples (a)-(c) show how an important set of hypotheses and propositions can be
expressed slightly more formal and concise as corresponding qualitative relationships. This
reformulation would provide little leverage if was not possible to do something with these
qualitative relationships. As it turns out, it is essentially this representation that forms the basis
for qualitative reasoning systems. A theory expressed as a qualitative model consisting of a set
of such qualitative relationships, can be analyzed with qualitative reasoners, which will derive
implications entailed by the proposed relationships. The qualitative inference mechanism will
detect potential conflicting statements or plain contradictions, and will reveal possible outcomes
conistent with the specified theory. Qualitative Analysis is characteristically different from its
quantitative counterpart in its more liberal information requirement and its inherently ambiguous
inferences. The next section will briefly overview the work in the qualitative reasoning field
before we present, in the following section, a little illustrative example of a qualiative reasoning
study.
4. Qualitative Reasoning - A Brief Review
Original research in qualitative reasoning in artificial intelligence, respectively qualitative
physics as it was often called, was driven by the question how do humans reason about the
physical world? The observation was made that humans function quite successfully in daily
situations like boiling water in a tea kettle, pouring into a cup, avoiding car collisions while
driving, etc,. without fully understanding these phenomena. This observation led to the
conclusion that it must be possible to develop a qualitative physics, which would not require
complex equations as in standard physics, and to build commonsense reasoning systems that
would be able to explain and predict the behavior of physical systems.
In order to give a rough picture of the behavior of a physical system, which is all what is
often needed, it is not necessary to provide a complete and precise mathematical description of
the system. Many insightful concepts can be described by qualitative distinct behaviors of a
physical system. Representation languages of qualitative reasoning systems are based on high
abstractions of real systems as a model representation. This means that some information is lost,
thus the answers derived by the inference mechanism cannot be exact. To resolve this intrinsic
ambiguity, more knowledge would be required.
Qualitative simulation [Kuipers, 1989], the best known and most widely used qualitative
reasoning system, describes a system in terms of qualitative quantities and functional
relationships from which it generates all consistent behaviors of the system. QSIM was
specifically designed to model continuous dynamic systems traditionally formulated
quantitatively as a set of algebraic or differential equations. The general goal of QSIM is to
represent the structure of a mechanism or system (modeling), and to predict its possible
behaviors (simulation), that is, reasoning from structure to behavior. QSIM was designed with
the following requirements in mind:
* Models should express what is known about a system
* Models should not require assumptions beyond what is known
* Models must be tractable to derive useful predictions
* Model predictions must match actual behaviors
A QSIM model comprises qualitative constraints plus an initial state from which it
predicts possible behaviors. A system is described in terms of qualitative variables called
quantities . A quantity is defined as a finite, totally ordered set of symbolic landmark values.
Landmarks are qualitatively distinct values such as, for example, low/medium/high or
negative/zero/positive. The user needs to provide a model specification that includes the
definition of all system variables. Qualitative constraints describe relationships among
quantities. QSIM offers qualitative arithmetic constraints like addition, multiplication etc,.
qualitative classes of functional relationships like the class of monotonically increasing or
decreasing functions (M+/M" functions), and the class of constant functions.
All qualitative reasoning systems are founded on a qualitative mathematics that was
basically developed in the economics field decades ago [Samuelson 1947, p.23-29]. Table 1, for
example, depicts qualitative addition of two variables, x and y. In this basic qualitative
description variables can assume the qualitative values positive (pos), zero (zero), or negative
(neg). Adding two positive variables, that is, x=pos and y=pos, definitely yields a sum that is
positive as well, x+y=pos (row I of table 1). The sum of a negative term, say x=neg, and a
positive term, say y=pos, on the other hand, is indetermined and can be positive, zero or
negative. This is exactly the inherent ambiguity in qualitative analysis resulting from incomplete
knowledge, ambiguity which coincides with the real world whenever two conflicting forces,
which cannot be precisely described in numerical terms, are simultaneously at work.
Quantitative approaches claim time and again precise scientific results while problem-intrinsic
ambiguity is simply swept under the carpet and not shown in the quantitative model specfication.
Recently, qualitative calculi have been extended to allow reasoning systems to represent
qualitative values of more finely grained magnitudes.
x+y pos Zero neg (y)
I pos pos pos pos/zero/neg
II (x) zero pos zero neg
Ill neg | pos/zero/neg neg neg
Table 1: Qualitative Addition
5. Conclusion
In this paper, we have discussed major assumptions underlying quantitative and
qualitative research methodologies and have put a special focus on the representation of
organizational relationships which can be used as the basis of specifying models and theories in
management and economics. We have suggested a qualitative modeling approach which would
allow researchers to use computational software tools in order to derive automatically the
implicit consequences of a proposed theory.
In future research we would like to connect qualitative reasoning particularly to system
dynamics modeling. The reason for this twofold. First, system dynamics is a major modeling
framework in management and organization science. Second, and more importantly, system
dynamics include influence diagram as an important tool for modeling complex and poorly
understood systems. It often used as a first effort to structure and organize the system variables
and relevant relationships that have been extracted or derived from an original problem
description. For that purpose, the relationships in influence diagrams are typically at a qualitative
level, similar to those described in section 3 of the current paper. Hence, we believe that
qualitative reasoning techniques can be applied to provide both a representational and a
computational tool to support the analysis of influence diagrams. In some cases, perhaps, it
wouldn't be necessary to specify a fully quantified simulation model in order to derive useful
predictions for policy making or other modelling purposes. Combining the flexibility and
expressiveness of the graphical representation of influence diagrams with the computational
power of qualitative reasoning systems could provide a significant enhancement of the system
dynamics modeling approach.
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