Interesting, this sounds like you are implementing a GA for finding association rules.

My suggestion is that you take some hints from finding association rules using apriori-algorithm (Agrawal 1993), where for rule A -> B, Support is the the percentage S of training sets containing "A U B" and Confidence is the percentage K% of transactions sets that containing A also contain B.

So, going back to your question, if |A| is zero, there is from my point of view no need to compute any rule, i.e. the fitness of the chromosome would be zero too.

if the fitness function is 1/f(x) and there is a chance that f(x) may become zero, it is better to take the fitness function as 1/(1+abs(f(x))).

The fitness function is of the form fitness = w1 * support + w2 * confidence ;

where w1 and w2 are small weight values.

If the problem is the representation of the fitness function, there are different ways to convert the fitness measurement to not only about the dividing by zero but also more readable and understandable fitness values:

*Standardized fitness: makes the best value of standardized fitness equal 0, has a a lesser value of raw fitness and a lower numerical value is always a better value.

s_i = f_max - f_i

*Adjusted fitness: lies between 0 and 1 and it is larger for better individuals in the population.

a_i = 1 / (1 + s_i)

*Normalized fitness: It ranges between 0 and 1. It is larger for better individuals in the population and the sum of the normalized fitness values is 1. For more info on this see Boltzmann distribution.

n_i = a_i / (a_1 + a_2 + ... + a_k)  

where the denominator sum over all a_i.

Thanks to all. I found that I was doing something wrong on my own. Actually the denominator should not be wrong for my association rule mining with GA.

The no. of training sets in ga no must be empty, thus to calculate the fit function if lAl is zero you can solve inverse problem.,  means the max of fit function is represented as min.