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Chapter 5: Decision Tables
5.1 Introduction
The representation of expert knowledge in formal systems for developing knowledgemodels or expert systems require a number of subtasks. These include:
- The acquisition of models from knowledge sources (human experts, written
material)
- The formal representation of the knowledge using some formalism (e.g., if-
then rules, frames, objects, belief networks)
- The implementation of the knowledge in a computer program (e.g., using a
dedicated expert system shell or a basic programming language)
- Verifying and validating the knowledge system
None of these steps is trivial and in particular the acquisition of knowledge and
verification and validation of a knowledge model has often been a bottleneck in the
successful application of knowledge modeling techniques. The Decision Table is a
technique that has specific advantages in particular with regard to acquisition,
verification and validation phases. It can be seen as a method to arrange a set of if-
then rules related to some decisions in a table format. The table offers a very legible
way of representing the knowledge that greatly facilitates the mentioned tasks. At the
same time, it allows one to model very complex knowledge systems, as decision
tables can be linked to each other in an hierarchical structure.
In this chapter, we introduce the decision table formalism and describe how it can beused to model decision problems and develop knowledge models. The text of this
chapter is taken from the following sources:
Sections 5.2 5.4:
F. Witlox (1998) Modelling Site Selection: A relational Approach Based on
Fuzzy Decision Tables, Eindhoven University of Technology, Ph.D. thesis).
Sections 5.5 5.6
Arentze, T.A. (2003) The decision table as a design knowledge modeling
technique, lecture notes, Eindhoven University of Technology.)
5.2 What are Decision Tables?
A decision table (DT) - also termed an inference or logical tree - provides a schematic
view of the inference process of a decision-making process. Each decision rule of a
DT is composed of a premise (condition) and a conclusion (action). In its tree-like
representation, the premises and conclusions are shown as nodes, and the branches of
the tree connect the premises and the conclusions. The logical operators AND and
OR are used to reflect the structure of the if-then rules. As such, decision tables
(DTs) do not seem to differ much from a decision tree. Instead of specifying a table,
the choice maker constructs a graph of the decision alternatives emanating asbranches from a root node over a number leafs. There are, however, some important
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differences between both approaches. The advantage of the DT is that it provides a
more compact visual presentation and, thus, contributes to a better comprehension of
the choice problem. But probably the most important advantage is that using a DT the
completeness, correctness and consistency of the information input is easier to check.
Thus, in a way, a DT may be regarded as a special case of a decision tree because it
fulfils certain logical constraints.
Decision tables were initially introduced over three decades ago, primarily as a
method in software engineering for structuring computer programmes. It was found
that, as a formalism, DTs were very well-suited to describe and analyze problems that
contain procedural decision situations which are characterized by a set of influential
conditions, the state of which determines the execution of a set of actions
(CODASYL, 1982, p. 2-1). Later on, several other important application domains
such as manual decision-making, system analysis and design, representation of
complex texts, verification of knowledge bases, and knowledge acquisition emerged.
In recent years, the potentials of DTs as a conceptual modelling language for
representing qualitative and complex knowledge have been investigated (Lucardie,1994). In respect to this latter point, both Vanthienen (1986) and Lucardie (1994)
have developed specific software (e.g. PROLOGA95 and AKTS) for constructing
decision table based knowledge-based systems. These DT engineering workbenches
have created a significant added value to the use of the DT technique.
In this chapter, our goal is twofold. First, the concept of a DT is defined and some
new terminology introduced (Section 5.3). Second, the actual construction of a DT is
analyzed and explained in a step-by-step manner (section 5.4).
5.3 Definition of a decision table
A decision table (DT) is a table that represents the exhaustive set of mutually
exclusive conditional statements within a pre-specified problem area (Verhelst, 1980,
p. 9). It displays the possible actions that a decision-maker can follow according to the
outcome of a number of relevant conditions. The general structure of a DT is shown
in Figure 5.1.
An example of a specific DT is represented in Figure 5.2. This DT considers the
question whether a given neighbourhood shopping centres meet minimum
requirements regarding the available stores in the centre. The actions of the table
correspond to possible measures aimed at improving the store composition of the
shopping centre. The rules are based on a definition of what is generally considered a
basic package of daily good supply in the Dutch context.
Problem area
CONDITION SET CONDITION SPACE
ACTION SET ACTION SPACE
Figure 5.1: The general structure of a decision table
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Choose centre-supply action
C1Number of supermarket
outletsNone One
More than
one
C2m2 gross floor space of the
supermarket- < 700 700 800 > 800 -
C3
All fresh products are
available - - no yes - -
A1Expand floor space of
supermarkets X
A2 Open large supermarket X
A3Open complementary
specialty stores X
R1 R2 R3 R4 R5 R6
(Source: Arentze, 1999)
Figure 5.2:Decision table for Centre-supply actions
Each DT is identified by the problem area it investigates (e.g. select a suitable
location). The table is split by a double line, both horizontally and vertically. The
horizontal line divides the table in a condition part (above) and an action part (below).
The vertical line divides the sets or stubs or subjects (left) from the spaces or entries
or states (right). The result is four quadrants: condition set [Ci], action set [Aj],condition space [SPACE (Ci)] and action space [SPACE (Aj)].
The condition setconsists of all the relevant conditions or attributes (inputs, premisesor causes) that have an influence on the decision-making process. For instance, in
respect to the choice of a business location, the set of relevant conditions consists of
all attributes that influence the process of selecting a location site. The example DT
(Figure 5.2) contains three conditions. More formally, Ci denotes a condition with
domain CDi (i = 1, ..., Cnum) with i, the numerical index indicating the condition, andCnum, the number of conditions.
The condition space specifies all possible combinations of condition states of the
conditions. The number of possible condition states is unlimited, at least in theory.
The condition space i.e. the set of condition states of a condition i could range
from two to any desired number. However, the more condition states used, the more
complex the decision table structure will be. Binary condition states (e.g. yes/no) are
termed "limited-entry" conditions. Condition states that can account for more than
two possible outcomes are termed "extended-entry" conditions. A DT that combines
both limited and extended entries is termed a "mixed-entry" DT. The example DT has
both limited and extended entry conditions and therefore is of the mixed type.Condition states that are irrelevant for a certain decision rule are marked with the so-
called "don' t care" entry (denoted: "-"). This "don't care" entry is equal to stating that
all condition states are allowed in a disjunction.
The action setcontains all the possible actions (outputs, conclusions or consequences)a decision-maker is able to take. This is to say that the action set points to the possible
choice outcomes if, for instance, an existing location with a number of specific
characteristics is processed through the DT. DTs can account for as many actions as
the decision-maker feels it necessary to introduce. The example DT has three actions
each of which can take on two values. The formal notation of an action set is as
follows.Aj (j = 1, ...,Anum) denotes an action set withj, the numerical index indicatingthe action, andAnum, the number of actions.
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The action space of an action j contains all the possible action states of that action.
The number of possible action states is also unlimited. However, frequently, DTs
confine the number of action states (not number of actions) to three. These are "-",
"X" and ".". The narrow line ("-") indicates that the particular action may not be
executed, the cross-sign ("X") implies that the particular action must be followed, and
a dot (".") signifies an undefined action state. This method is also used in the exampleDT.
The strict separation between conditions and actions may not always be as simple as it
might look. Some actions are bound to a condition, implying that they have to be
executed before testing the condition, while others may already be executed after
testing one or more conditions. Also, condition sets and action sets may themselves
refer to other decision tables. For example, an action may involve a call to a procedure
to perform some task, or a condition may be defined by another decision table. A
decision table called in that way by another decision table is termed an action- or a
condition-subtable. These subtables play an important role in structuring the decision
problem and permit a more thorough and detailed analysis (see below).
Finally, any vertical linking of an element out of the condition space with an element
of the action space produces a so-called logical rule [R]. This logical rule is in fact a
simple conditional statement or an "if...then" decision rule. For example, rule R2 of
the example DT states: if(C1 = one AND C2 < 700) then do A1.
Apparently, in order to account for exhaustiveness and exclusiveness, two logical
constraints must be fulfilled for each condition state of a DT. The first constraint
states that the union of all condition states of a condition (CSi) should be equivalent to
the domain of that condition (CDi). The second constraint states that the intersection
between different condition states of a condition should yield the empty set.
5.4 Construction of a decision table
Verhelst (1980, p. 23) distinguishes three methods to construct a decision table or
decision table system: (i) a direct method on the basis of singular (simple) decision
rules; (ii) a direct method on the basis of composite (complex) decision rules; and (iii)
a search method. Although, these three methods are different on a number of factors
(see below), they deal with comparable stages or steps when converting a decision
problem into a DT. The main difference between them is the order in which these
stages are treated and the way they are worked out. In sum, five stages may bedistinguished (Vanthienen, 1986; Vanthienen and Wets, 1994, p. 269):
(i) Definition of conditions, condition states, actions and action states for the
specific choice problem;
(ii) Specification of the problem in terms of decision rules;
(iii) Construction of the DT on the basis of the decision rules;
(iv) Check for completeness, contradictions and correctness;
(v) Simplification, optimization and depiction of the DT.
In reality, the construction of decision tables is often not a linear process, as the above
procedure seems to suggest because of the complexity of the task. The different stages
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indicate a way to structure this task. In what follows, we elaborate on each of these
five stages.
When building a DT, an essential and rather straightforward first step is the
identification of the conditions and actions and their associated states that have an
influence on the decision problem. In this respect, the three above-mentioned DT
construction methods strongly resemble conventional quantitative or other qualitativeapproaches. Usually, the expert is asked to list or name all conditions that are deemed
important in evaluating a choice alternative. These verbal records or protocols can be
completed with conditions derived from other sources (e.g. literature survey). As
such, a combination of condition-determining approaches is used that define the
influential conditions both a priori and a posteriori to the expert's answers. Next, the
condition states are defined. It is important to note that the expert is not limited to
only two states. The expert is able to express as many states as he or she feels
necessary in order to logically evaluate a certain condition. All attributes are evaluated
in terms of their logical condition states; whether they are limited or extended entries
is not important. This offers a greater flexibility to the researcher. Also, the use of
(different) multiple response categories implies that conditions are allowed to interact(so-called conceptual interaction). Linked with the aspect of condition categorization
is that also dependencies between conditions are taken into account (so-called
conditional relevance). As such, a condition like "distance" can be categorized into
three, five, or, for that matter, any other number of different categories. Comparable
to the condition and condition state specification, the possible actions and action states
need to be determined. Again, this can be accomplished by asking the expert what
possible actions he or she anticipates in considering the choice alternatives. The
number of actions will depend on the nature of the choice problem, and is therefore
not limited.
As a rule, conditions and actions have to be unambiguous, relevant and realistic to the
expert. All condition recurrences, as well as all complementary conditions, should be
avoided. Conditions that depend upon other conditions should separately be treated,
and ranked in such a way that dependent conditions follow independent conditions. In
respect to the categorization of the conditions, two important logical requirements
must be fulfilled: exhaustiveness and exclusiveness. Exhaustiveness means that the
DT must account for all possible states that a condition is able to take. The exclusivity
requirement refers to the fact that each combination of condition states has to be
included in one and only one column of the DT. A brief example will perhaps further
clarify both logical requirements. Suppose, for an arbitrary chosen condition
"distance" (d), the condition states are specified as follows: d < 100, 100 d 150, d> 150. It is c1ear that this condition categorization is exclusive because no single
distance can at the same time fall in more than one category. In addition, the
categorization is also exhaustive because all possible distances are captured in either
one of the three condition states. Therefore, an important property of using decision
tables is that the condition states are mutually exclusive but jointly form an exhaustive
set.
The second stage in the construction process concerns the specification of the decision
rules. A decision rule is a logical vertical link between elements of the condition space
(antecedent or premise) and action space (consequent or conclusion). It can be
compared with a simple "if...then" decision rule. By this is meant: if faced with a
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number of conditions, then execute a certain action. This kind of decision rule
corresponds to the form of a disjunct set of conjoint conditional statements.
With respect to the three above DT construction methods, different decision rules or
techniques are applied. In the first direct method, singular (or simple) "if...then"
decision rules are advanced. This implies that each possible combination of conditionstates will lead to exactly one and only one action state or column of the table. The
result is a totally unambiguous, but rather complex DT. To illustrate, if a location site
is characterized by nine conditions, all defined in terms of only two condition states,
this will result in 29 (or 512) singular decision rules. Clearly, such a table is too
complex to be interpreted.
The second direct method deals with composite (or complex) "if...then" decision rules
and is somewhat more difficult to understand. Composite rules are based on the
combination of singular rules in such a way that in a column for a particular
condition, its associated states are being contracted. Thus, singular rules are joined to
form a composite rule. A brief example may clarify this somewhat further. Supposethat a DT consists of only two conditions (Cl and C2) with associated condition states(CS11, CS12) and (CS21, CS22, CS23). In a singular DT, this would result in six columns
or six singular decision rules. Assume further that forCS12, the condition states ofC2become irrelevant. Thus, in the CS12-column, CS21, CS22 and CS23 may be combined in
a single state, namely the so-called "don't care" entry (denoted: "-"). The result is a
composite DT that has only four columns (three singular rules and one composite
rule). Such grouping or contraction of condition states may cause a loss of overview,
and with it, a loss of the simplicity needed to control the exclusivity and exhaustivity
requirements of the DT. Therefore, composite rules are only used for problems that
are relatively simple and easy to understand.
In the third approach, the search method, yet another technique is applied, which is
called equivalence class or rule class. The idea was advanced by the Decision Table
Task Group of CODASYL (1982). Equivalence class ruling denotes all simple
decision rules that have identical or equivalent action states, regardless of the
combination of the condition states. Therefore, decision rules are assumed
functionally equivalentif they point to identical action states although they are basedon different combinations of condition states. For example, translated to the choice of
business location, two location sites are assumed functionally equivalent if both
locations, although having very different characteristics, can perform an equivalent
function (i.e. site suitability) for an economic activity. To further illustrate the search
method and the technique of functional equivalence in DTs, we refer to the abstract
DT presented in Table 5.1 (Verhelst, 1980, pp. 72-73; CODASYL, 1982, pp. 5.9-
5.11).
Table 5.1: Construction of an abstract multiple-hit DT using the search method
Condition C1 a b
Condition C2 c d e f g h
Condition C3 Y N Y N Y N Y N Y N Y N
Action A1 X X
Action A2 X X X X
Action A3X X
Action A4 X X
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Decision rule R1 R2 R3 R4 R5Frame of functional
equivalence1 2 3 4 5
Suppose that an analyst, when constructing a DT, has come to a situation as depicted
in Table 5.1. So far, five decision rules have been identified, and in this early stage of
the construction process, it is clear that the decision rules R2 and R4 fall within thesame frame of functional equivalence. This is because the two particular decision
rules exhibit the same configuration of action states, although their associated
condition states (acN and adN) are different. When such a frame of functional
equivalence is detected, the analyst is interested in whether a statement like "a no for
condition C3, always implies that both actions A2 and A4 must be executed?" is true.There are two possible outcomes: either this statement is not true, in which case the
analyst continues in further defining decision rules R6, R7, etc., until a new frame offunctional equivalence is observed for which the same procedure is then followed; or,
the statement is presumed true, in which case the analyst confronts the expert with
other combinations of conditions states ofCl and C2 (C3 still being equal to "no"), and
examines whether actionA2 andA4 still have to be executed. To reduce the complexityof the analyst's task, one is able to work statistically. For instance, the expert is
confronted with only 50% or 75% of all possible combinations of condition states of
Cl and C2. If in all cases the result stays unchanged, one may take for granted that a
"no" forC3 automatically results in executingA2 andA4. The remainder of the analysiscan then be concentrated on what the expert will do if C3 takes the condition state
"yes". A consequence of functional equivalence is that the DT will not lead to a
unique choice, but represents a number of functionally equal choices. It is important
to note here that DT's satisfy the necessary conditions for reconstructing decision
rules defining functional equivalence.
With respect to the definition of decision rules, it is also useful to refer to theexistence of what is termed the ELSE rule (Verhelst, 1980, p. 90; CODASYL, 1982,
p. 3.41). The ELSE rule is a rule that is executed when none of the other decision
rules in a DT are satisfied. It may be viewed as a kind of "catch-all" when all other
rules fail. Usually, the ELSE rule is placed as the last decision rule in a DT. The
application of the ELSE rule brings with it two important drawbacks: (i) the control
for completeness is lost, and (ii) the DT becomes less manageable and interpretable as
several decisions are put together in one single column. Consequently, the use of the
ELSE rule should be avoided.
The third stage deals with the actual construction of the DT on the basis of the defined
decision rules. The ranking of conditions and actions in the table is not subject to astrict hierarchy. However, certain logic in the condition order should help in the task
of interpreting and optimizing the DT (see also stage 5). Usually, dominant or so-
called veto conditions are put at the top of the table because of their non-
compensatory character. Also, in view of optimization, it is better to list conditions
which have fewer condition states before conditions with relatively more condition
states. Similar, conditions which are deemed more important to the choice problem
need to be followed by the more impractical (or theoretical) conditions. After all, it is
less plausible or likely that a decision-maker will disregard an attribute which seems
to have a greater hearing upon the choice problem than that he or she will ignore a
more impractical but theoretically possible influential attribute. Usually, conditionsappear only once in the DT. By being able to organize and rearrange conditions and
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condition states in a DT, it is clear that the DT formalism supports the systematic
account of conditional relevance of attributes and conceptual interactions between
attributes. Both mechanisms underlie the concept of functional equivalence.
The fourth stage examines the DT with regard to the requirements of completeness,
contradiction and correctness. Here, an automatic check is presented to detect certain
specification errors. First, the check for completeness verifies whether the tablecontains decision rules, which have empty action states. In other words, an incomplete
DT is a table in which decision rules are missing. If this is observed, it can be
rectified. Second, the DT is controlled for contradictions. A contradiction occurs if,
leaving aside the ELSE rule, two action states which exclude one another must be
executed at the same time. Such a contradiction usually follows from a bad
specification of the condition states. Third, if a DT is complete and no decision rules
are contradictory, this still does not mean that the decision rules are correct. The
correctness of a decision rule depends on the expert's interpretation. As a result to the
exclusive and exhaustive character of DTs, all potential condition states are combined
to generate action states, including those combinations of condition states that result
in unwanted, unrealistic and overlooked action states. In this stage of DT construction,these action states may be spotted and defined so that the DT will produce only valid
decision rules. In practice, this comes down to investigating whether every individual
decision rule is correct (Verhelst, 1980, p. 18).
The fifth and final stage deals with the simplification, optimization and depiction of
the DT. Optimization in this context refers to the minimization of the number of
decision rules in a DT. In other words, redundancy in the decision rules should be
avoided. There are several ways to optimize the lay-out and execution time of a DT.
Table contraction is one possibility, row order optirnization another (Vanthienen and
Dries, 1994, p. 227)
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Table contraction (or rule collapsing) refers to the minimization of the number of
columns for a given condition order by combining (groups of) columns which lead to
the same action configuration. In other words, the number of columns is reduced by
contracting singular to composite decision rules. Table contraction should always be
preceded by the check for completeness, contradictions and correctness. The reason is
that once the table has been contracted, it is difficult to uncover decision rule errors.
Row order optimization opens the possibility of decreasing the number of (contracted)
columns by changing the order in which the conditions are noted in the table. For a
table with n conditions, this implies a choice between n! alternative condition orders.
Some rankings, however, might not be feasible due to previous constraints (e.g.
condition dependencies).
A third way to optimize and structure a DT is by using subtables. A subtable may be
defined as a decision table wherein actions function as conditions in an upper-level
decision table. Subtables may themselves be subject to other subtables. Figure 5.3
shows a simple abstract example of a three-level decision table system with subtables.Figure 5.4 shows an example of how a decision table can be optimized using both the
techniques of table contraction and row order optimisation.
(a) Full table
C1 Y N
C2 Y N Y N
C3 Y N Y N Y N Y N
A1 X X A2 X X X X
A3 X X X R R1 R2 R3 R4 R5 R6 R7 R8
(source: Lucardie, 1988, p.74)
Figure 5.3. The structure of a three-level DT with subtables
Level 3 Level 2 Level 1
C7
C8
C9
C10
C11
C12
C13
C14
C3
C4
C5
C6
C1
C2
C3
C4
C5
C6
C1
C2
A1
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(b) Table contraction
C1 Y N
C2 Y N
C3 Y N Y N Y N
A1 X
X
A2 X X X
A3 X X
R R1 R2 R3 R4 R5 R6
(c) Row order optimization
C3 Y N
C1 Y N
C2 Y N
A1 X X
A2 XA3 X X
R R1 R2 R3 R4
(Source: Vanthienen and Wets, 1994, pp. 270 272)
Figure 5.4: Optimization of a DT using two different transformations
In Figure 5.3 on the highest level (level 1) only two conditions (Cl and C2) explain the
action state ofA1. It can, however, be noted that both Cl and C2 are subject to theoutcome of the subtables defined on the second level, andalso subject to the results of
the subtables specified on the third level. Therefore, defining C7, C8, C9 and C10 results
in the specification of both C3 and C4, which in turn defines the condition state ofCl,
Thus, Cl is defined as a combination of four other condition states (CS7, CS8, CS9 andCS10). In a similar way, C2 is also defined as a combination of four condition states(CS11, CS12, CS13 and CS14). Note that, in this simple example, the conditions C3, C4, C5and C6 do not have to be specified because they are determined by the outcome of the
two subtables on the third level. This property of generating knowledge from lower
level condition state information is an important advantage of using a DT system.
An additional characteristic of using subtables is that the concepts defining the
conditions on higher levels may be more abstract than those on lower levels. Or, the
higher (lower) the level in a DT, the more abstract (concrete) the concepts may be
defined. Usually, this property entails that a condition relating to an abstract concept
may be further specified through the use a condition subtable. Conditions in a
condition-subtable may in turn be further worked out in a subtable at lower level and
so on. In many applications, DTs are connected through such condition-subtable links
giving rise to an entire hierarchical system of decision tables. The highest level table
specifies in abstract terms the decision rules in a problem domain. Subsequently, a
system of subtables elaborates in more concrete terms these abstract concepts. The
conditions used at the end points of the hierarchy should be defined in such a way that
they can be matched with the observable attributes (Arentze et al., 1996, p. 8).
5.5 Examples of decision tables in planning and design
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Example 1
An existing situation, no matter whether it concerns a building or an urban area, needs
to be continuously monitored to see whether, as a consequence of changes over time,
it still comes up to given objectives and constraints. If not, then there is a problem that
needs an intervention of some kind. Thus, the task here is to 1) analyze the
performance of an existing building or urban system and 2) compare the performancewith planning/design standards. Several variants of the task exist that we may wish to
represent in a DT. In order of increasing complexity, these include:
1. The DT just checks whether or not there is a problem;
2. In addition to 1, the DT also gives a diagnosis of the problem;
3. In addition to 2, the DT also suggests an intervention.
Consider the following example:
Example 1
A shopping centre attracts too few customers and the risk exists that one or more
stores in the centre will be forced to close. An analysis reveals that the poor
performance is not caused by a decline of the catchment-area population or by
increased competition from neighbouring centres. Rather, the centre has become
less attractive over the years due to a declining attractiveness of shopping streets.
So, in this case, we can conclude:
1. There is a problem (if we do not intervene the centre will loose
quality);
2. The cause of the problem is a decline of attractiveness of shopping
streets;
3. It is wise to intervene and refurbish the centre.
A DT that performs detection of the problem, diagnosis and intervention
suggestion all in one step may look like the following:
Performance of shopping centre
C1 Number of visitors < Norm >= Norm
C2 Demand shortage Yes No -
C3 Maintenance - < Norm >= Norm -
A1 Problem Viability Maintenance Unknown NoneA2 Suggested intervention Close Refurbish Unknown None
R1 R2 R3 R4
Demand shortage of shopping centre
C1 Population base < Norm >= Norm
C4 Competition - < Norm >= Norm
A1 Demand shortage Yes Yes No
R1 R2 R3
Examples 2 and 3
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Before making a plan/design, experts are asked to establish the (functional or
technical) requirements the design must meet, considering the needs and constraints
imposed by users, policies, the environment, etc.
Example 2
The number and size of meeting rooms needed in an office building depends onthe activities of the organization to be accommodated. The critical factors include
the frequency formal meetings take place, the number of persons involved in
meetings and the frequency of central meetings involving all employees of the
organization. The decision table in such a case may look as follows.
Required number and size of meeting
rooms
C1 Formal meetings take place No Yes
C2Number of persons involved in a
formal meeting- < 5 [5,10)
C3
Frequency (/week) formal
meetings- < 2 [2,5) >= 5 < 2 [2,5)
C4Frequency (/week) formal
central meetings- - - < 2 >= 2 - -
A1Required number of meeting
rooms0 0 0 1 2 3 0
A1Required size of meeting rooms
(m2)0 0 0 15-30 15-30 15-30 0
R1 R2 R3 R4 R5 R6 R7
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Example 3
There are different levels of protecting an office building against burglary
possible and the appropriate level for an organization will depend on
characteristics of the organization. The following decision table could represent
the decision rules.
Required level of burglary protection
C1 Protection of persons required Yes No
C2Protection of vital processes
required- Yes No
C3 Burglary sensitive items present - - Yes No
C4Loss of burglary sensitive items
is fatal- - No Yes -
C5Storage of burglary sensitive
items in safe is possible- - Yes No Yes No -
A1Required level of burglary
protectionHigh High No Medium No High No
R1 R2 R3 R4 R5 R6 R7
Example 4 and 5
This task of analyzing and evaluating solutions is relevant in different problem
contexts, including:
1. Eliminating infeasible solutions;
2. Making a choice between alternative solutions;
3. Making a decision on whether or not to accept a plan/design proposal, for
example, from a developer.
Analysis and evaluation refers to different problems. Analysis involves an assessmentof the performance on some criterion and evaluation refers to a comparison of the
actual performance with objectives/constraints. Therefore, variables such as
suitability, feasibility and utility would typically be used in an evaluation context,
whereas more value neutral terms are used to express analysis results. Even though
analysis and evaluation are different, from a knowledge modelling perspective they
are equivalent in the sense that both involve some classification of solutions. The
following examples illustrate an analysis and evaluation step respectively.
Example 4
The extent to which a (office) building facilitates internal transport of goods is aperformance aspect that is relevant for at least some types of organizations. The
following decision table describes a method to assess this performance aspect
based on attributes of the building.
Capacity of internal goods transport
C1 Goods are deliverable at the
entranceNo Yes
C2 Intermediate storage of goods
can be implemented
NoYes No Yes
C3 Width of alleys to intermediate
storage place- < 180 >= 180 - < 180 >= 180
A1 Capacity of internal goodstransport
Low Low Average Low Average High
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R1 R2 R3 R4 R5 R6
Example 5
A location is feasible for a shopping centre if there is sufficient market potential
for a shopping centre at the location, the location is well accessible and a new
centre would not distract too much turn over from existing centres. This rule canbe represented in a DT as follows:
Feasibility of candidate location for
shopping centre
C1 Market potential for a shopping
centre< Norm >= Norm
C2 Accessibility of the location - < Norm >= Norm
C3 Impact on existing shopping
centres- - < Norm >= Norm
A1 Location is feasible for shopping
centreNo No No Yes
R1 R2 R3 R4
Example 6 and 7
In making a choice, a number of alternative solutions are given and a decision is to be
made which alternative to select as the solution. We distinguish two possible subtypes
of this problem. First, the alternative solutions have not been evaluated on relevant
criteria. Then, the decision table should define under which conditions which
alternative is to be chosen.
Example 6
If it is feasible to develop a shopping centre at a given location, the question
becomes what class of shopping centre should be developed. Planners generallydistinguish three or four orders depending on the size and store mix. For example,
a low-order centre includes only stores for daily-goods and typically serves a
neighbourhood, whereas a large-order centre also includes stores for non-daily
goods and typically serves a whole city. The simple rule stating that the highest
possible order is to be preferred could be represented in a DT as follows:
Choice of shopping centre size
C1 Market potential = X2
A1 Shopping centre size Low order Medium order High order
R1 R2 R3
where X1 and X2 is the minimum market potential needed for a medium-order and
large-order respectively.
Second, the alternatives have been evaluated on a number of relevant criteria. If
there is a solution that outperforms all other solutions on each criterion, then
making a choice is easy. However, in general this is not the case and making a
choice requires trading-off criteria. We argue that the decision table is not a
suitable technique for this task. In many cases it is more natural to express the
relative importance of criteria by using quantitative weights and calculate an
overall score for each alternative based on these weights. To represent this method
by a decision table, the condition space should be fully split up to express all
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possible combinations of weights in separate columns. In contrast, a simple
quantitative model would represent the method in a much more efficient way.
Example 7
The suitability of a solution is given by the following weighting scheme (numbers
between brackets are weights):
Criterion Performance Combined weight
Economic impact (0.6) High (0.7) 0.420Average (0.2) 0.120
Low (0.1) 0.060Environmental impact (0.3) High (0.5) 0.150
Average (0.3) 0.090Low (0.2) 0.060
Social impact (0.1) High (0.8) 0.080Average (0.15) 0.015
Low (0.05) 0.005
Following this weighting scheme, a decision table representation would give:
Suitability of candidate location for
shopping centre
C1 Economic impact High
C2 Environmental impact High Av Low
C3 Social impact High Av Low High Av Low High
A1 Suitability 0.65 0.585 0.575 0.59 0.525 0.515 0.56
R1 R2 R3 R4 R5 R6 R7
which is needlessly cumbersome.
5.6 Combining decision tables and quantitative methods
In many cases, a solution to a decision problem requires the application of a
combination of quantitative and qualitative knowledge. In DTs, it is relatively
straightforward to integrate quantitative models that perform some calculation for
example to determine the value of a condition variable or to execute an action. How
this can be done can best be shown by some examples.
Example 1
Electric power supply in office buildings is usually expressed in Wattper nett-m2
floor space. The demand of electric power by an organization can be calculated as
a function of the amount of lighting and electric devices needed. The following
DT evaluates the extent to which available supply in a building matches the
electric energy consumption rate of a given organization.
Availability electric power supply
C1 Electric power demand
(W/netto-m2)
< 0.95 * {Electric
power supply
(W/netto-m2)}
[0.95 *{Electric
power supply
(W/netto-m2)},
1.05 *{Electric
power supply
(W/netto-m2)}]
> 1.05 *{Electric
power supply
(W/netto-m2)}
A1 Availability electric power
supply
Undersupply Sufficient Oversupply
R1 R2 R3
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In the table, the condition variable Electric power demand (W/netto-m2) isdefined by a quantitative function, whereas the value of Electric power supply
(W/netto-m2) can be retrieved from a database. If the DT is executed and thevalue of the condition variable is unknown, the DT calls the function and, after
having received the value from the function, proceeds to evaluate the conditionstatements on the right hand side of the table.
Example 2
In general, planners consider the opening of a facility (e.g., a shopping centre) in
an area (e.g., neighbourhood) if there is enough market potential and there are
currently no facilities (of that type) present in the area. This simple decision rule
is expressed in the following DT:
Reconsider facility provision
C1 There are facilities in the
zone
No Yes
C2 Market potential for a
facility unit
Insufficient Dubious OR
Sufficient
Insufficient Dubious OR
Sufficient
A1 Close facility unit No No Yes No
A2 Open facility unit No Yes No No
A3 Determine facility unit
size
No Yes No Yes
R1 R2 R3 R4
The table illustrates the use of a procedure call in the action section of the table.
A1 and A2 are conventional action variables that are assigned a value in execution
of the table. However, A3 is special in that it refers to a procedure for, in this case,determining the (optimal) size of a new facility unit given the characteristics of
the area and the facility. In columns R2 and R4 the procedure is activated.
Furthermore, it is worth nothing that C2 also involves a call to a quantitative
method, namely a function computing the market potential of the area for a
facility. Thus, the table illustrates a case where procedure or function calls are
included in both the condition and action section.
5.7 Executing decision tables
Executing a DT involves evaluating the condition statements from top to bottom untila unique column is selected and, next, executing the action specified in that column.
Since the execution procedure is fully structured it is possible and in fact
straightforward to automate this procedure and let the computer execute DTs, for
example, in the context of a larger design or decision support system or some other
information system.
To write a program that can execute DTs a few notes are in order. Most importantly,
the program should be able to find the values of relevant condition variables for
identifying the appropriate column. An if-needed procedure can be written in such a
way that it can be used for any condition variable and any decision table. The method
should be based on the following rule.
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If the value of the condition variable is unknown than try to find it by consulting the
following sources:
1. If the condition variable is a call to a function than execute the function;
2. If the condition variable is defined in a subtable than execute the subtable;3. If the value of the condition variable is stored in the database than retrieve
the value from the data base;
4. Ask the user to enter the value.
The method should try the sources in this order and stop the moment the value of the
condition variable is found. Asking the user is the last resort in this procedure. With
respect to the choice of a dialog form, the variable type is important. If the condition
variable is a categorical variable, the dialog used should include a list box (or some
other closed form) from which the user can select the right category. If, on the other
hand, the condition variable is a continuous variable (e.g., quantitative) an edit box in
which the user can enter input in a free format is more adequate. In the last case, it isimportant to check whether the answer given falls in the allowed range of the variable
and return an error message if the value is outside the range.
5.8 References
Arentze, T.A. (1999) A Spatial Decision Support System for the Planning of Retailand Service Facilities. Ph.D. Thesis. Eindhoven University of Technology.
Arentze, T.A., G.L. Lucardie, H. Oppewal, H.J.P. Timmermans (1996) A Functional
Decision Table Based Approach to Multi-Attribute Decision Making. Paperpresented at the 3rd International Conference on Retailing and Consumer
Services Science held in Telfs/Buchen, Austria, 22-25 June, 1996.
CODASYL (1982) A modern appraisal of decision tables. Report of the decision
table task group of the conference on data systems languages (CODASYL).
New York, Association for Computing Machinery (ACM).
Lucardie, G.L. (1994)Functional object-types as a foundation of complex knowledge-
based systems. Rijswijk, TNO Bouw, Ph.D. thesis.
Vanthienen, J. (1986) Automatiseringsaspecten van de specificatie, constructie enmanipulatie van beslissingstabellen. Leuven, Katholieke Universiteit Leuven,Departement Toegeapste Economische Wetenschappen, Ph.D. thesis, Nr. 60.
Vanthienen, J. and E. Dries (1994) Illustration of a decision table tool for specifying
and implementing knowledge based systems,International Journal on Artificial
Intelligence Tools, 3, 267-288.
Vanthienen, J., G. Wets (1994) From decision tables to expert system shells, Data &Knowledge Engineering, 13, 265-282.
Verhelst, M. (1980) De praktijk van beslissingstabellen. Deventer and Antwerp,Kluwer.
Witlox, F. (1998) Modelling Site Selection: A relational Approach Based on Fuzzy
Decision Tables , Eindhoven University of Technology, Ph.D. thesis.