Defuzzification process of fuzzy sets in RDBMS

Question

I have a table that stores all values..eg x1, x2, x3 which determines fuzzy sets. Degree of membership is assigned to each using mathematical functions for Low, Med, High.

My rule 1 states that if x1 is high AND x2 is medium then probability of output is z. I then take min{x1,x2} to evaluate the rule. Rule 2 states that if x2 is high OR x3 is medium then output is max{x2,x3}.

Now to defuzzify I take aggregation of rule consequences to find out the output of the 2 rules. I have all degrees of membership defined (0 to 1) for x1 x2 x3 for each rule.

How do I defuzzify?

Answer 1

Okay, first of all, are you using a probabilistic logic or a fuzzy logic. While similar, they're not identical. If you're really modeling probabilities here, then you need to look into this via Bayes Theorem as a conditional probability.

If these are really fuzzy truth values, then you need to have a model of set-membership, which we need to know.