Code Fragment 151 Audit Predictor Rules

% Now print rules in workspace rules_text = showrule(fismat) rules_text =

1. If (income is low) and (flags is no_flags) and (deductions is standard) and (accuracy is not poor) then (audit__risk is low) (1)

2. If (income is low) and (flags is no_flags) and (deductions is standard) and (accuracy is compulsive) then (audit_risk is low) (1)

(accuracy is poor) then (audit_risk is medium) (1)

4. If (income is low) and (flags is not no_flags) then (audit_risk is high) (1)

5. If (income is middle) and (flags is no_flags) and (deductions is standard) and (accuracy is not poor) then (audit_risk is low) (1)

6. If (income is middle) and (flags is no_flags) and (deductions is itemized) and (accuracy is not poor) then (audit_risk is medium) (1)

7. If (income is middle) and (flags is one_or_two) and (deductions is itemized) then (audit_risk is medium) (1)

8. If (income is middle) and (flags is three_or_more) then (audit_risk is high) (1)

9. If (income is middle) and (flags is one_or_two) and (deductions is miscellaneous) and (accuracy is poor) then (audit_risk is high) (1)

10. If (income is high) and (flags is no_flags) and (deductions is itemized) and (accuracy is not poor) then (audit_risk is medium) (1)

11. If (income is high) and (deductions is miscellaneous) and (accuracy is not compulsive) then (audit_risk is high) (1)

12. If (income is high) and (flags is three_or_more) and (deductions is miscellaneous) then (audit_risk is high) (1)

FIGURE 15-1 Graphical display of audit predictor.

Graphical Illustration

The following figures illustrate this inference system:

1. Figure 15-1, "Graphical display of audit predictor," illustrates the entire structure of the inference system. Note that the number of rules is shown, as are the membership functions on the left. From the inputs and the rules, the inference system provides an output measurement which is shown on the right.

2. Figure 15-2, "Income membership functions," shows the membership function for income. As the rules often refer to income ("if income is high,...then..."), this membership function translates a dollar figure of income into a conceptual description such as high or low. The membership function for "middle income" is centered in the range of $40,000 to $73,000 in annual income for the year 2000.

FIGURE 15-2 Income membership functions.

3. Figure 15-3, "Audit flag membership function," shows the membership function for audit flags.

4. Figure 15-4, "Surface of rules," provides a 3-D view of the likelihood of an audit, based on income and the number of flags. Note that the actual function is 4-D, but only 3 dimensions can be shown on this surface graph.

5. Figure 15-5, "Ruleviewer for audit risk FIS," provides a comprehensive graphical illustration of the effect of the various inputs, membership functions, and rules on the resulting value from the FIS. In this graphic, the inputs used are an annual income of $75,000, 5 audit flags, itemized deductions, and mediocre accuracy. These are shown in the first four columns of distribution graphics in the figure. As there are 12 rules, each input is evaluated in the 12 rows.38

383 Some rules may not involve some inputs. In this case, the distribution box is blank. You can confirm that rule no. 8 does not involve two of the inputs, and therefore two boxes on row 8 are blank.

Tin Audi! pfwtitor: Flig Momtwrsftip Function

Tin Audi! pfwtitor: Flig Momtwrsftip Function

FIGURE 15-3 Audit flag membership function.

Nasi

FIGURE 15-3 Audit flag membership function.

The audit predictor FIS evaluates such characteristics as resulting in a high probability of an audit. This is consistent with common sense; a person who makes mistakes on his return, and whose return contains a number of audit flags, should be audited more frequently than the typical taxpayer. What cannot be shown in this figure is that the ruleviewer in the MATLAB toolbox is interactive, allowing you to see how the FIS evaluates multiple scenarios quite quickly.

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