Editing Decision tree (section)

== Decision-tree building blocks ==

=== Decision-tree elements ===
[[Image:Decision-Tree-Elements.png|center|]]

Drawn from left to right, a decision tree has only burst nodes (splitting paths) but no sink nodes (converging paths). So used manually they can grow very big and are then often hard to draw fully by hand. Traditionally, decision trees have been created manually – as the aside example shows – although increasingly, specialized software is employed.

=== Decision rules ===
<!-- linked from redirect [[Decision rules]] -->
The decision tree can be [[Linearization|linearized]] into '''decision rules''',<ref>{{Cite journal | doi = 10.1016/S0020-7373(87)80053-6| title = Simplifying decision trees| journal = International Journal of Man-Machine Studies| volume = 27| issue = 3| pages = 221–234| year = 1987| last1 = Quinlan | first1 = J. R. | citeseerx = 10.1.1.18.4267}}</ref> where the outcome is the contents of the leaf node, and the conditions along the path form a conjunction in the if clause. In general, the rules have the form:
: ''if'' condition1 ''and'' condition2 ''and'' condition3 ''then'' outcome.

Decision rules can be generated by constructing [[Association rule learning|association rules]] with the target variable on the right. They can also denote temporal or causal relations.<ref>K. Karimi and H.J. Hamilton (2011), "[https://arxiv.org/abs/1004.3334 Generation and Interpretation of Temporal Decision Rules]", International Journal of Computer Information Systems and Industrial Management Applications, Volume 3</ref>

=== Decision tree using flowchart symbols ===
Commonly a decision tree is drawn using [[flowchart]] symbols as it is easier for many to read and understand. Note there is a conceptual error in the "Proceed" calculation of the tree shown below; the error relates to the calculation of "costs" awarded in a legal action.

[[File:DecisionCalcs.jpg|center]]

=== Analysis example ===
Analysis can take into account the decision maker's (e.g., the company's) preference or [[utility function]], for example:

[[Image:RiskPrefSensitivity2Threshold.png|center]]

The basic interpretation in this situation is that the company prefers B's risk and payoffs under realistic risk preference coefficients (greater than $400K—in that range of risk aversion, the company would need to model a third strategy, "Neither A nor B").

Another example, commonly used in [[operations research]] courses, is the distribution of lifeguards on beaches (a.k.a. the "Life's a Beach" example).<ref>{{Cite book|title=Principles of Operations Research: With Applications to Managerial Decisions|last=Wagner|first=Harvey M.|date=1975-09-01|publisher=Prentice Hall|isbn=9780137095926|edition=2nd|location=Englewood Cliffs, NJ|language=English|url-access=registration|url=https://archive.org/details/principlesofoper00wagn}}</ref> The example describes two beaches with lifeguards to be distributed on each beach. There is maximum budget ''B'' that can be distributed among the two beaches (in total), and using a marginal returns table, analysts can decide how many lifeguards to allocate to each beach.
{| class="wikitable"
|+
!Lifeguards on each beach
!Drownings prevented in total, beach #1
!Drownings prevented in total, beach #2
|-
|1
|3
|1
|-
|2
|0
|4
|}
In this example, a decision tree can be drawn to illustrate the principles of [[diminishing returns]] on beach #1.
[[File:Beachdecisiontree.png|alt=|none|thumb|Beach decision tree]]

The decision tree illustrates that when sequentially distributing lifeguards, placing a first lifeguard on beach #1 would be optimal if there is only the budget for 1 lifeguard. But if there is a budget for two guards, then placing both on beach #2 would prevent more overall drownings.
[[File:Lifeguards.png|thumb|Lifeguards|alt=|center]]

=== Influence diagram ===
Much of the information in a decision tree can be represented more compactly as an [[influence diagram]], focusing attention on the issues and relationships between events.

[[Image:Factory2 InfluenceDiagram.png|center|frame|The rectangle on the left represents a decision, the ovals represent actions, and the diamond represents results.]]