chapter 5 - decision tables

8/4/2019 Chapter 5 - Decision Tables

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7M840 Chapter 5

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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7M840 Chapter 5

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.

chapter 5 - decision tables

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