Decision trees

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A decision tree allows one to quantify decisions that need to be made.

Let us look at a simple "fix-it" decision tree for something that may or may not work properly and what might need to be done to make it work properly.

The simplest decision trees assume only two possibilities at each decision point are event point (state of nature).

The first question is: "does it move?". First decision

The possibilities here are "yes" or "no". In a one level binary decision tree, there is one decision and two outcomes. The "yes" corresponds to a "true" result and the "no" corresponds to a "false" result.

Here is the C code [#1]

#include <stdio.h>
int main() {
	// declarations
	char ch1;
	// input
	printf("Does it move? (y=yes, n=no)\n");
	scanf("%d ",&ch1);
	printf("You typed '%d'.\n",ch1);
	// process - none
	// output
	printf("\n");
	if (ch1 == 'y') {
		printf("It moves.\n");
		}
	else {
		printf("It does not move.\n");
		}
	return 0;
	}

Here are some examples of input and output for the above program code.

Here is an example input.

y

For the above example input, here is the expected output.

Does it move? (y=yes, n=no)
You typed '0'.
It does not move.

Here is an example input.

n

For the above example input, here is the expected output.

Does it move? (y=yes, n=no)
You typed '0'.
It does not move.

Should it move? The possibilities here are "yes" or "no". In a two level binary decision tree, there are two decisions and four possible outcomes. We now look at each of the four possible outcomes.

If we get a "yes, yes" we have a true positive. In this case, there is no logical problem. Note: If you test positive for cancer and you actually have cancer, then this is a true positive. There is no logical problem here even though the result is a tragedy from a personal perspective.

If we get a "no, no" we have a true negative. In this case, there is no logical problem.

If we get a "yes, no" we have a false positive. This is a logical problem. The solution here may be to use "duct tape" (to keep it from moving).

If we get a "no, yes" we have a false negative. This is a logical problem. The solution here may be to use "WD-40" (to help it to move).

Here is the fix-it decision tree. To further quantify what is happening, one can place or estimate probabilities for each yes-no decision.

Below are some code examples of the above decision tree concepts. Note: There are many ways in which these ideas could be programmed.

Often, "yes" is used for "true" and "no" is used for "false". So the above becomes the following.

yes-yes is true-true is true-positive.
yes-no is true-false is true-negative.
no-yes is false-true is false-positive.
no-no is false-false is false-negative.

Here is the C code [#2]

#include <stdio.h>
int main() {
	// declarations
	char ch1;
	char ch2;
	// input
	printf("Does it move? (y=yes, n=no)\n");
	scanf("%d ",&ch1);
	printf("You typed '%d'.\n",ch1);
	printf("Should it move? (y=yes, n=no)\n");
	scanf("%d ",&ch2);
	printf("You typed '%d'.\n",ch2);
	// process - none
	// output
	printf("\n");
	if (ch1 == 'y') {
		if (ch2 == 'y') {
			printf("It moves. It should move. True-positive. No problem.\n");
			}
		else {
			printf("It moves. It should not move. False-positive. Use duct tape.\n");
			}
		}
	else {
		if (ch2 == 'y') {
			printf("It does not move. It should move. False-negative. Use WD-40.\n");
			}
		else {
			printf("It does not moves. It should not move. True-negative. No problem.\n");
			}
		}
	return 0;
	}

Here are some examples of input and output for the above program code.

Here is an example input.

y
y

For the above example input, here is the expected output.

Does it move? (y=yes, n=no)
You typed '0'.
Should it move? (y=yes, n=no)
You typed '0'.
It does not moves. It should not move. True-negative. No problem.

Here is an example input.

y
n

For the above example input, here is the expected output.

Does it move? (y=yes, n=no)
You typed '0'.
Should it move? (y=yes, n=no)
You typed '0'.
It does not moves. It should not move. True-negative. No problem.

Here is an example input.

n
y

For the above example input, here is the expected output.

Does it move? (y=yes, n=no)
You typed '0'.
Should it move? (y=yes, n=no)
You typed '0'.
It does not moves. It should not move. True-negative. No problem.

Here is an example input.

n
n

For the above example input, here is the expected output.

Does it move? (y=yes, n=no)
You typed '0'.
Should it move? (y=yes, n=no)
You typed '0'.
It does not moves. It should not move. True-negative. No problem.

Normally, the if-then-else processing would be done in the processing part of the code.

C does not handle string processing very well.

So, in this course, some of the processing may be done in the output section of the code.