## Simplification of defuzzification in Fuzzy Logic

I have just noticed that my article on Datalog has had far more hits than my articles normally do. The unit conversion program arose because I was interested in another problem: preparing sets of accounts and investment track records. I have written a C program that already does that, but I am thinking of investing in the US market, and that introduces the problem of currency exhange. It raises the question: “how much is a share worth?”. The answer to that question is dependent on time, the value of a share, and the exchange rate. There is nothing necessarily especially difficult about programming a deterministic solution oneself, but it is the kind of problem that lends itself well to Datalog. It is a topic that I may well return to in a later post.

In the meantime, the whole point of my post is to throw out some ideas I had about Fuzzy Logic. Being an investor, I am interested in decision-making processes, and how mathematics and statistics might give me an edge. I am very very new to Fuzzy Logic, and still trying to absorb some basic terminology, and even underlying ideas.

So, it may seem a little presumptuous to say that I have some ideas that may contribute to the field of Fuzzy Logic. To that end, I have written a little article entitled “Simplification of defuzzification in Fuzzy Logic”. Its abstract is:

In the traditional Fuzzy Logic approach, each consequent is expressed as a fuzzy set. Typically, these sets are combined to form a complex shape whose COG (Centre of Gravity) is computed. This article argues that fuzzy consequents can be replaced by crisp consequents. By partitioning the solution space, a lot of elaborate modelling and computation is removed. An example is shown in which the simplified approach gives an answer which is very similar to a more elaborate process.

The article has lots of mathy-type terms, so I can’t really produce the content here. You can download or view a PDF version straight from my site, though: ftp://markcarter.me.uk/defuzz.pdf . Some knowledge of Fuzzy Logic is assumed, so don’t expect to be able to pick it up without knowing something about the field. I intend to write an introductory article for the complete beginner at some point. So, my apologies in advance if it is not quite the material you were hoping for. Be warned: I am terrible at reviewing my own work. There may well be inaccuracies in it. To me, the fun is more in coming up with the ideas than in the spell-checking.

I feel as if I am only just dipping below the surface of some of these concepts, and believe there may be some unification between Fuzzy Logic, Bayesian reasoning, and naive heuristic algorithms waiting to be uncovered.

I would really like to extend a huge “thank you” to the readers of my blog.