Results Data Set #2 Data set #2 was Breast Cancer data made public by Mangasarian & Wolberg [18] [19]. This data set was also briefly reported in our previous paper. The methodology has now been greatly expanded with adjustment of individual membership functions and use of the genetic algorithm. Data set parameters are as follows:
1. Sample code number id number
2. Clump Thickness 1 - 10
3. Uniformity of Cell Size 1 - 10
4. Uniformity of Cell Shape 1 - 10
5. Marginal Adhesion 1 - 10
6. Single Epithelial Cell Size 1 - 10
7. Bare Nuclei 1 - 10
8. Bland Chromatin 1 - 10
9. Normal Nucleoli 1 - 10
10. Mitoses 1 – 10
11. Class 2= benign; 4 = malignant
The predicted classification is either benign or malignant. Standard deviation of membership functions were adjusted using the genetic algorithm. Sets were aggregated as an averaging process similar to equation (11) and selection made on the basis of which was the larger. Summary of results are in the table C.
Again results from the fuzzy approach are very good but not better that statistical logistical regression. They are in some respect comparable. Results for data set #2 were considerably better than those for data set #1 possibly because data set #2 had more attributes from which to establish set memberships. All results were really comparable with results of other researchers as reported earlier in this paper.
The Fitness chart developed by the genetic algorithm software for data set #2 is presented as Figure 2. It shows that the genetic algorithm has approached asymptotically a horizontal line and further iterations may not produce improvement unless there are local minimums. Considering the nature of the problem, local minimums are unlikely.