Download A Comparison Model for Uncertain Information in

2012 International Conference on Uncertainty Reasoning and Knowledge Engineering
A Comparison Model for Uncertain Information in Expert System
Yeow Wei Liang and Rohana Mahmud
Department of Artificial Intelligence
Faculty of Computer Science and Information Technology
University of Malaya
Kuala Lumpur, Malaysia
[email protected], [email protected]
Abstract—Expert system has been widely used since it was
created as early as 1970s. One of the challenges that expert
systems faced is to deal with uncertain information. Even
though there are many uncertainty management approaches
which can deal with problems of different types, the term
uncertain information is not clearly defined. This paper
reviews some of the uncertainty management in order to
highlight, compare and clarify the differences of these
approaches in terms of the application area and target area of
problem solving. With this, we propose a comparison model
which can serve as a guide in selecting a suitable uncertainty
management with the consideration of three uncertain
information categories: event, evidence and variable. These
three categories are different in terms of their area of problem
solving.
a decision in solving a problem [2]. However, human
experts can still make judgments by adapting to situation
and provide a probable solution intelligently or with their
past experiences. Nevertheless, the ability of human expert
to deal with problematic information is difficult to be
replicated into an expert system. Researchers are constantly
finding ways to manage inexact information in expert
system which are close to human expert’s ability [3].
This paper reviews the trends and general information
regarding the uncertainty management in expert systems in
section II. In section III, selected uncertainty management
approaches are discussed and compared in terms of the
method in managing uncertainty and the target area of
uncertainty management. Moving on to section IV, a
comparison model is proposed to be used to compare the
uncertainty management in terms of the uncertain
information levels, which are event, evidence and variable.
Keywords - expert system; uncertainty management;
certainty-factor; bayesian; probabilistic; fuzzy logic;
I.
INTRODUCTION
II.
Expert system is the result of the lesson learned from the
Artificial Intelligence work and the first generation chemical
analysis expert system, DENDRAL[1]. Researchers in
Artificial Intelligence realized that the method of reasoning
does not contribute very much in the intelligent behavior of
an intelligent system, but it is more of the knowledge which
the system needs to reason with. With the past experiences
in intelligent systems and first generation expert systems,
the emphasis had move to the knowledge, as claimed by the
father of expert system, Edward Feigenbaum at Stanford
University “In the knowledge lies the power”. The
methodology in building a system with knowledge-oriented
approach is known as Knowledge Engineering (KE), and the
product of the development is a knowledge-based system or
also known as expert system [2].
General purpose reasoning (GPS) techniques, developed
before expert systems, which separates the problem solving
from knowledge are now considered to be too limited in
solving real problems [2]. This is due to the fact that
encoding rich source of knowledge within a program is the
most important. Besides, expert system which is developed
to be well-focused on a narrow issue is more efficient and
effective than system which is able to address broad areas of
problem. In solving a problem, human expert often face
problematic information. This could be due to the unreliable
information source, or lack of adequate information to make
UNCERTAINTY MANAGEMENT
Uncertainty management is one of the research areas in
expert system. The research area of uncertainty management
in expert systems are in the decline since the 90’s, as
reported by Liebowitz, [4], over his observation in the three
World Congress of Expert Systems. Uncertainty
management was once very actively being research and
being adopted in several expert systems, such as the
MYCIN [5], PROSPECTOR [6], and more with various
approaches on different timeframe. Some uncertainty
models are developed to complement the limitation or to
extend the usage of other models, and some are entirely
different, and is useful for different types of problems in
uncertainty [7].
In the recent years, most expert systems had been treating
the uncertainty models lightly, and exploit other new
methods, such as fuzzy expert system which address the
uncertainty using fuzzy set theory [8-11]. However, some
other expert systems aim to solve problem without concern
on uncertainty, because uncertainty is either not significant
or is negligible [12]. Anyway, there are some expert systems
have looked into uncertainty issue by adopting suitable
model, such as [13, 14]. This trend can be seen in a review
done by Shiau, [15], whereby the uncertainty management is
no longer visible as a major category in expert system
research. Instead, the fuzzy expert system is considered to be
the solution for uncertainty management in her paper, can be
978-1-4673-1460-2/12/$31.00 ©2012 IEEE
127
observed in the trend study between year 1995 and 2008.
This also implies that the report written by Liebowitz based
on his observation before the year 1997 is persisting until
very recent.
There are many methods in uncertainty management,
which can be classified in several measures, such as: additive
probabilities, coherent lower previsions, belief functions, and
possibility measures [7]. Whichever the measures are, these
measures are being closely related to numerical and
probabilities. For example, certainty-factor is dealing with
measures of belief within the value of 1 and -1, where the
positive value means belief and the negative value means
disbelief [5]. On the other hand, probabilistic approach in
decision making assumes that the human judgment of
uncertainty is actually based on probability [16]. These
numerical values are usually the interpretation of the experts
based on their judgment or belief on uncertain evidence [3].
However, Raufaste [16] suggested that human judgment on
uncertainty is qualitative in essence. Furthermore, human
expert often having difficulties in expressing their
knowledge in numerical form [17].
III.
[21]. If prior data is lacking, the knowledge engineer should
consider other approaches in building an expert system.
Another alternative approach in uncertainty management
is the certainty-factor model, which is used in MYCIN [5].
MYCIN is an expert system used to assist medical
practitioners in diagnosing blood infections and diseases.
The certainty-factor is developed to address the limitation of
probability approach as described previously. The certaintyfactor value is used to determine the certainty of the system
regarding the hypothesis made. In order to build the
certainty-factor systems, the certainty-factor values must be
acquired from medical experts. These values are indeed
based on the medical expert subjective interpretation
without considering any of the probability rules [21]. This
approach is more natural compared to probabilistic
approach, because the numbers are not gotten statistically.
Certainty-factor measures the belief or disbelief using
values that range from -1 to 1. For more information, please
refer [18] for the better understanding of this model.
Fuzzy logic is very popular among researchers which
deal with imprecise or vague information. Expert system
which adopts fuzzy logic in resolving uncertainty is known
as fuzzy expert system. Fuzzy expert system is an alternative
approach in managing uncertainty and vague information,
which models the ability of human to make rational
decisions [19] . Fuzzy expert system is getting popular and
more research is moving towards this area [15]. Fuzzy logic
is very essential in most domains, as fuzzy expert system had
been proven quite successful in many areas which deal with
UNCERTAINTY MANAGEMENT APPROACHES
In this paper, we compared some of the well established
uncertainty management approaches to highlight the
differences and also to explore the potential to be used in
different areas. We had chosen to compare the classical
probabilistic methods, Bayesian approach, certainty-factor
model[18], and also fuzzy logic [19]. A detailed description
and methodology of each uncertainty management can be
found in [20].
From all of the four approaches, both classical probability
approach and Bayesian approach requires the application of
mathematical probability in uncertainty management. The
main difference between classical probability and Bayesian
theory is that Bayesian theory is also an a posteriori
probability (inversed probability), which makes Bayesian
theory have further advantage compared to classical
probability that do not exhibit the real world
characteristics[2]. With a posteriori probability, Bayesian
approach is very useful in drawing inference and reasoning,
and also in predictions. One of the example is the
PROPECTOR [6], a geological consultation system for
mineral exploration. The PROSPECTOR is used to obtain
the likelihood of the ore deposits in the exploration sites and
also to recommend the best location to drill in the site. The
PROSPECTOR models and emulates the experts reasoning
process in accessing a prospect site. Bayesian’s theory is
used to propagate the probabilities throughout the inference
network. Even though probabilistic approach has the well
developed ability to represent unknown truth [20], it relies
heavily on past data (prior probability). Most knowledge
engineers face problem in getting these past data to develop
expert system for accurate results, especially domain which
has vast and diverse information to reason with. The
probability is also expensive to obtain through experiments
Figure 1. Example of Membership Function of Temperature
vague knowledge [9]. As a highlight, fuzzy logic deals with
fuzzy quantifiers. These quantifiers are the linguistic
variables which consist of fuzzy sets are defined by the
experts or users. For example, a linguistic variable,
Temperature might have fuzzy sets of low, medium, or high.
The degree of low can be obtained by associating the input
value to the membership function, or vice versa. Figure I
illustrate the graph of the membership function for the
variable Temperature.
Based on the reviews of the four uncertainty management
models and approaches, we summarize the comparison in a
table form, as in Table I. As opposed to the reviews done by
[20] which compares the uncertainty management models
128
individually, here we compare them by analyzing the method
in eliciting the uncertainty values and the target area or
problem solving. This we can unveil the actual area if
TABLE I.
Model/Approach
Classical Probability
Bayesian Theory
Certainty-factor
Fuzzy Logic
IV.
uncertain information which the uncertainty management
models intend to address.
COMPARISON OF UNCERTAINTY MODELS AND APPROACHES
Method to Elicit Uncertainty Value
Purely based on mathematical probability. Prediction of
a posteriori events are based on prior probability
provided by experts.
Using mathematical probability to predict prior
evidence based on a posteriori evidence. Experts should
provide the past data.
Values obtained from expert’s subjective interpretation.
Involve user past experience in determining values.
Values can be interpreted and classified by the
uncertainty terms. The overall certainty-factor value is
the product of all the premises in the rules.
Values obtained from user interpretation and
experimentation. User defined linguistic variables and
fuzzy sets, based on past experience or experiments.
Target Area/Problem Solving
Prediction of a posteriori event [20]
Prediction of evidence or event in an
inference network. Nearly universal in
application [20].
Used to judge uncertain evidence or
conclusion. Deals with evidence
interms of their belief or disbelief of
each hypothesis [20].
Deals with imprecise and vague
information or fuzzy quantifiers [20].
with the event, the “bottle” is not important but the whole
statement as an event. Now, if we would further increase the
detail of the event to “A man holding a big bottle walking in
the park”, the word big will be qualified as a variable, size.
For fuzzy expert system which deals with variable, the word
big is the not the input value for the variable size. The event
is not important, since the concern of fuzzy expert system is
only the size of the bottle.
COMPARISON MODEL
To demonstrate the categories of uncertain information
which each uncertainty management deals with, a Venn
diagram (see Figure 2) is used to illustrate this. The Venn
diagram consists of three subsets (areas of uncertain
information), the event, evidence and variable which the
expert system reason with. These categories also confirmed
based on the review on 56 expert systems from academic
articles (from conferences and journals) which adopt
different models and approaches. The review consists of 3
expert systems which adopt Bayesian theory, 5 expert
systems with certainty-factor, 11 fuzzy expert systems and
the remaining 38 expert systems adopt unknown uncertainty
management or did not specified at all. Below is the
explanation of each of these areas of uncertain information:
i. Event – refers to the occurrence or phenomenon.
For example: The sky is cloudy, hence it will
rain today.
ii. Evidence – refers to anything which is used to
determine or to support a truth. For example:
The animal has four legs and only eat grass,
hence it is a cow.
iii. Variable – refers to quantifiable or non-quantifiable
attribute which can be associated to a value.
For example:
(Quantifiable) Length – long, short;
(Non-quantifiable) Looks – pretty, ugly.
These categories are not mutually exclusive. In the event
where variable can be found, the overlap section is known as
the event variable. Similarly, for any evidence which can be
translated into variables, the product is the evidence variable.
The event and evidence are different. To differentiate event
and evidence, we can take as an example: “A man holding a
bottle walking in the park”. The whole statement is an event.
However, depending on what the expert system reasons with.
If an expert system reasons with evidences, then the “bottle”
will be the subject. However, if the expert system reasons
Figure 2. Intersection between event, evidence, and variable
From this example, we can say that fuzzy logic is very useful
in dealing with fuzzy variables, but not useful in resolving
uncertainty for an event. From there, we could explain why
we see the emerging of fuzzy expert systems, especially in
the field of engineering, manufacturing, computer-aideddesign, control systems, and even medical. These expert
systems are dealing with variables, but not the event. It could
be the evidence variable or event variable. However, in real
life, “event evidence variable” is meaningless, since the
evidence is understood to be the product of an event.
Again, we are able to analyse whether or not a claim is
true. For example, Lindley [22] claimed that probability can
129
perform better than anything which can be done with fuzzy
logic, believe functions or other similar techniques. We can
now judge in which area that probability deals with, to
compare with what fuzzy logic (for example). From the
comparison model, we are sure that the claim might not be
true for all situations. Fuzzy logic which deals with variables
is not necessarily replaceable by probability, because
probability cannot resolve the vagueness of variable posses.
For example, the word low temperature is fuzzy, whereby
low temperature can be interpreted as 0.3 degree low, 0.7
degree medium. These values are not statistical value, but
they are the degree of association between low and medium.
Instead, the strength of probabilistic theories is the event and
evidence, but not variables.
V.
Giarratano, J. and G. Riley, Expert System: Principles and
[3]
Systems and Technologies. 2011: ACM.
Almulla, M., H. Yahyaoui, and I. Kamal. Trustpert: a reputation
model for collaboration in MANETs using fuzzy expert systems. in
KCESS '11 Proceedings of the Second Kuwait Conference on eServices and e-Systems 2011: ACM.
[10] Zuhtuogullari, K., I. Saritas, and N. Allahverdi. The application of
[9]
fuzzy expert cooling system for multi core microprocessors and
mainboards. in CompSysTech '09 Proceedings of the International
Conference on Computer Systems and Technologies. 2009: ACM.
[11] Damousis, I., D. Tzovaras, and M. Strintzis, A fuzzy expert system for
the early warning of accidents due to driver hypo-vigilance. Personal
and Ubiquitous Computing, 2009. 13(1): p. 43-49.
[12] Dimoulas, C., G. Papanikolaou, and V. Petridis, Pattern classification
and audiovisual content management techniques using hybrid expert
systems: A video-assisted bioacoustics application in abdominal
sounds pattern analysis. Expert Systems with Applications, 2011.
[13] Ooshaksaraie, L., et al., RP< sup> 3</sup> CA: An expert system
applied in stormwater management plan for construction sites in
Malaysia. Expert Systems with Applications, 2011.
[14] Dymova, L., P. Sevastianov, and K. Kaczmarek, A stock trading
expert system based on the rule-base evidential reasoning using Level
2 Quotes. Expert Systems with Applications, 2012.
[15] Shiau, W.L., A profile of information systems research published in
expert systems with applications from 1995 to 2008. Expert Systems
with Applications, 2011. 38(4): p. 3999-4005.
[16] Raufaste, E., R. da Silva Neves, and C. Mariné, Testing the
descriptive validity of possibility theory in human judgments of
uncertainty. Artificial intelligence, 2003. 148(1): p. 197-218.
[17] Lauritzen, S.L. and D.J. Spiegelhalter, Local computations with
probabilities on graphical structures and their application to expert
systems. Journal of the Royal Statistical Society. Series B
(Methodological), 1988: p. 157-224.
[18] Shortliffe, E.H. and B.G. Buchanan, A model of inexact reasoning in
medicine. Mathematical biosciences, 1975. 23(3): p. 351-379.
Programming. 1998, Boston: PWS Publishing Company.
[19] Zadeh, L.A., Fuzzy logic. Computer, 1988. 21(4): p. 83-93.
Amaya Cruz, G. and G. Beliakov, On the interpretation of certainty
[20] Ng, K.C. and B. Abramson, Uncertainty management in expert
factors in expert systems. Artificial Intelligence in Medicine, 1996.
systems. Ieee Expert, 1990. 5(2): p. 29-48.
8(1): p. 1-14.
[4]
Allahverdi, N. and G. Altan. A fuzzy expert system design to monitor
patient's condition during heart surgery. in CompSysTech '11
REFERENCES
[2]
[8]
Proceedings of the 12th International Conference on Computer
This paper had clarified the area of uncertain information
of each uncertainty management deal with. Before selecting
an uncertainty management, researchers should consider to
which extend the expert system reason with. As highlighted
in this paper, there are three areas which we have to
consider: event, evidence or variable. Even though some
researchers claim that one approach deal with everything
compared to the other, they should also review their thought
based on the categories which is discussed in this paper. The
comparison model in this paper is created based on the
review of other expert systems by looking at the
fundamentals. This study is useful for researchers who wish
to implement an uncertainty model into expert system for a
new field. However, this study only involves quantitative
uncertainty management approaches. Since qualitative
models are quite rare in the uncertainty management of
expert systems, we did not take qualitative models into
account. Furthermore, qualitative approach used totally
different method in handling uncertainty, which we cannot
compare in this review paper.
Lindsay, R., et al., Dendral. 1980, New York: McGraw-Hill.
Walley, P., Measures of uncertainty in expert systems. Artificial
intelligence, 1996. 83(1): p. 1-58.
CONCLUSION
[1]
[7]
[21] Durkin, J. and J. Durkin, Expert systems: design and development.
Liebowitz, J., Worldwide perspectives and trends in expert systems:
1998: Prentice Hall PTR.
An analysis based on the three world congresses on expert systems.
[22] Lindley, D.V., The Probability Approach to the Treatment of
AI magazine, 1997. 18(2): p. 115.
[5]
Shortliffe, E.H., Computer-based medical consultations: MYCIN.
[6]
Duda, R.O. and R. Reboh, AI and decision making: The
Uncertainty in Artificial Intelligence and Expert Systems. Statistical
Science, 1987. 2(1): p. 17-24.
Vol. 388. 1976: Elsevier New York.
PROSPECTOR experience. Artificial Intelligence Applications for
Business. Norwood, NJ: Ablex Publishing Corp, 1984.
130