Combs method
The Combs method is a method of writing fuzzy logic rules described by William E. Combs in 1997. It is designed to prevent combinatorial explosion in fuzzy logic rules.
It takes advantage of this logical equality: [(p and q) then r] = [(p then r) or (q then r)].
Combinatorial explosion
Suppose we have a fuzzy system that considers N variables at a time, each of which can fit into at least one of S sets. The number of rules necessary to cover all the cases in a traditional fuzzy system is SN, whereas the Combs method would need only S×N rules. The table below contains some examples:
| Variables | Sets | Rules | Rules w/ Combs |
|---|---|---|---|
| 2 | 3 | 9 | 6 |
| 2 | 5 | 25 | 10 |
| 2 | 7 | 49 | 14 |
| 3 | 3 | 27 | 9 |
| 3 | 5 | 125 | 15 |
| 3 | 7 | 343 | 21 |
| 4 | 3 | 81 | 12 |
| 4 | 5 | 625 | 20 |
| 4 | 7 | 2401 | 28 |
| 5 | 3 | 243 | 15 |
| 5 | 5 | 3125 | 25 |
| 5 | 7 | 16,807 | 35 |
This shows that the Combs method is probably unnecessary for systems that consider only a few sets and a few variables at a time, but some means of taming the combinatorial explosion is needed to allow a complex system.
This article will focus on the Combs method itself. To learn more about the way rules are traditionally formed, see fuzzy logic and fuzzy associative matrix.
The Combs method
Suppose we were designing an artificial personality system that determined how friendly the personality is supposed to be towards a person. The personality would consider its own fear, trust, and love in the other person. A set of rules in the Combs system might look like this:
| Fear | Very Low THEN Very High | Low THEN High | Medium THEN Medium | High THEN Low | Very High THEN Very Low |
|---|---|---|---|---|---|
| Trust | Very Low THEN Very Low | Low THEN Low | Medium THEN Medium | High THEN High | Very High THEN Very High |
| Love | Very Low THEN Very Low | Low THEN Low | Medium THEN Medium | High THEN High | Very High THEN Very High |
The table translates to:
[IF Fear IS VeryLowFear THEN Friendship IS VeryHighFriendship OR IF Fear IS LowFear THEN Friendship IS HighFriendship OR IF Fear IS MediumFear THEN Friendship IS MediumFriendship OR IF Fear IS HighFear THEN Friendship IS LowFriendship OR IF Fear IS VeryHighFear THEN Friendship IS VeryLowFriendship] OR [IF Trust IS VeryLowTrust THEN Friendship IS VeryLowFriendship OR IF Trust IS LowTrust THEN Friendship IS LowFriendship OR IF Trust IS MediumTrust THEN Friendship IS MediumFriendship OR IF Trust IS HighTrust THEN Friendship IS HighFriendship OR IF Trust IS VeryHighTrust THEN Friendship IS VeryHighFriendship] OR [IF Love IS VeryLowLove THEN Friendship IS VeryLowFriendship OR IF Love IS LowLove THEN Friendship IS LowFriendship OR IF Love IS MediumLove THEN Friendship IS MediumFriendship OR IF Love IS HighLove THEN Friendship IS HighFriendship OR IF Love IS VeryHighLove THEN Friendship IS VeryHighFriendship]
External link
- The Combs Method for Rapid Inference - the original paper