Fuzzy Logic for Retention Management: Millington, Funge and Games

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Six months ago I bought a copy of a 2009 textbook entitled, “Artificial Intelligence for Games” by Millington and Funge. It sat on the bottom of a tall column of information management books, patiently waiting to be singled out (for reading rather than dusting). Last week, I picked it up and promptly dropped it. It flipped open to page 382.

Records colleagues, do you know what “fuzzy logic” is? I inadvertently applied it to a retention management exercise I performed for a client last year and once you’ve read this article you may find you’ve done the same.

Funge and Games

According to Millington and Funge, game theory uses a traditional logic technique called a “predicate,” a quality or description of something to outline a character. There is no degree to the predicate; it exists or it doesn’t.

Predicates come in “sets.” “Classical sets” are simple: everything to which the predicate applies is in the set, and everything else is outside. Fuzzy logic transmutes classical sets to “fuzzy sets”: it assigns a value to the predicate. For example, a character with an ammo value of .07 is more armed than .03. In other words, a numeric degree, called a degree of membership, is applied.

For each set, a degree of membership of 1 is given to something completely in the fuzzy set. Similarly, the value of 0 indicates something completely outside the fuzzy set. When we look at the rules of logic you’ll find that all the rules of traditional logic still work when set memberships are either 0 or 1.

Suddenly, everything can partially belong to the set and some items can belong to more than one. Here 0 and 1 become important. Something completely in the fuzzy set is given a degree of membership of one; the value of zero indicates something outside the fuzzy set (relax: you can use any range of numeric values -- not probability or percentages, though -- to represent the degree of membership). For the purposes of this conversation, we’ll keep to 0 and 1.

Meanwhile, “anything can be a member of multiple sets at the same time. A character may be both hungry and hurt, for example.” This applies to classical and fuzzy sets. We no longer have mutually exclusive character traits. There are different degrees of membership for each set. “The fuzzy equivalent of mutual exclusion is the requirement that membership degrees sum to 1.”

An Illustration

When the book opened on page 382, here’s the diagram on that page:

Exclusive Mapping CMSWire Fuzzy Logic Article.jpg

The first and second have similar states and the third diagram has three. Do you see? The authors describe these states as “crisp”. The fuzzy rules to describe the above looks like:

Input 1 state AND…AND input n state THEN output state

So, Millington and Funge tell us, using the three inputs in the illustration above, we might have rules such as:

corner-entry AND going-fast THEN brake
corner-entry AND going-slow THEN accelerate
corner-entry AND going-slow THEN accelerate
corner-exit AND going-slow THEN accelerate

Each clause in a rule is a state from a different crisp input. Clauses are always combined with a fuzzy AND. We might have the following degrees of membership:

Corner-entry: .1
Corner-exit: .9
Going-fast: .4
Going-slow: .6

Then the results are:

Brake = min (.1, .4) = .1
Accelerate= min (.9, .4) = .4
Accelerate = min (.1, .6) = .1
Accelerate = min (.9, .6) = .6

So, the final value for break is .1, and the final value for accelerate is .6.

Learning Opportunities

Our Attorneys Are Going To Love This

Retention management software is a database of references that compile citations based on a number of factors (industry, governing body, public or private company, leg/reg, etc). These citations build records series organically for each company department or function. In turn the departments’ records series create a holistic records retention schedule -- a macro view of how information moves through your company.

Records retention schedules are unique. Some companies choose to insert a second column called “Best Practices” next to the legal citations column.

This is perilous for the Records Manager who has only software to depend upon, because retention software does not distinguish between a legal citation (for example, “this citation is an absolute must to attach to an HR record type thanks to THIS precedent”) and best practice (“meh -- it’s similar enough to match, but the company isn’t obligated to it”).

How do you assign citations to one column or the other? Use fuzzy logic. Note how my approach to designating legal citations versus best practices grew more sophisticated:


First draft: a simple SWOT analysis. Far from encompassing. Incomplete.

Second draft: very close. Note the pre-sets to 1 and 0? The rules are crisp, too. However, the math behind the sliding scale is too tough a formula to be used across multiple industries. Incomplete.

Third draft: the easiest for the C-level to understand. Rules are crisp and minimum math. Close to complete.

I used the logic rules of the third pictorial to create a rough draft records retention schedule. I had the luxury of submitting to an attorney for their review before presenting to senior leadership (always a good idea: support your local attorney).

I wasn’t too far off: they edited 15% of the two columns. When you compare the fuzzy logic illustration from the textbook with my second and third pictorials, perhaps it’s easy to see why I drew correlations. Advanced math doesn’t guarantee that you will sail through the entire records retention schedule build, but it certainly helps you maintain your chosen architectural design.

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