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The DEAT Business Rule Pattern Language

Russell R. Hurlbut, Ph.D.

Rule Pattern 32: Interpolation

Problem – Deriving a Point Value from a Range given Another Point Value and Range

Some business processes rely on calculations that must estimate a value that falls between two other values that provide an index into this desired value. This is often the case in lookup tables that are legally mandated or may have arisen out of traditional industry practice.

Solution

An interpolated value can be derived through enumeration of interpolation algorithm types. This pattern shares similarities with the Interval pattern, except here a continuous value is desired from provided discrete value rather than vice versa. Both patterns have floor and ceiling types. However, they are included only in this pattern for completeness. The same net effect is obtained from applying the Interval pattern first and then performing a direct lookup. The primary difference in the type domains is reflected in the opposite orientation of the two patterns. Instead of nearest, this Interpolation pattern defines a linear type.

Example – Tax Proration

A real estate contract stipulates that property taxes are to be prorated up to and including the day of closing based on the most recent tax assessment. A 365 day year is used.

Tax Proration Parameters

Target Attribute	Real Estate Tax Proration
*Dimensions*	1
*Source Attribute*	Day of Year
*Interpolation type*	linear

Example – Early Retirement Factor

A pension benefit is calculated and then reduced for early commencement before the normal retirement date for an employee. Based on the form of payment, if the spouse is designed as a surviving beneficiary the reduction amount takes into consideration both the ages of the employee and the spouse. A table provides lookup values in years. However, the plan calls for interpolation based on age in completed months. This example further highlights the similarities between the Interval and Interpolation patterns, since the age must first be quantitized using a floor interval rule before performing the linear interpolation on the table lookup.

Early Retirement Factor Parameters

Target Attribute	Early Reduction Factor
*Dimensions*	2
*Source Attribute 1*	Employee Age
*Source Attribute 2*	Spouse Age
*Interpolation type*	linear

UML Representation and Related Patterns

. The Interpolation business rule pattern maps to the Operation model element. This pattern is closely related to the Interval and Derivation Algorithm business rule patterns.

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