Computing fuzzy partitions

One of the most typical ways to compute fuzzy partitions is to use quantiles of the data. The module utils contains a series of functions to generate fuzzy partitions for all the supported kinds of fuzzy sets. The easiest way to compute these partitions is with the utils.construct_partitions function, specifying the fuzzy set desired:

import utils

fz_type_studied = fs.FUZZY_SETS.t2
precomputed_partitions = utils.construct_partitions(X, fz_type_studied)

Categorical variables

Quantiles are meaningless for a variable that holds names, or one that is just a 0/1 flag. construct_partitions detects those variables and gives them a crisp partition instead: one fuzzy set per category, which is 1 exactly on that category and 0 everywhere else. A variable is detected as categorical when its values are not numeric, or when it only takes whole numbers and at most five different ones:

categorical_mask = utils.detect_categorical_mask(X)  # what construct_partitions detects on its own

Pass categorical_mask yourself to decide it instead of the detection, or detect_categorical=False to treat every variable as numerical. BaseFuzzyRulesClassifier accepts the same two arguments and uses them when it optimizes the partitions itself.

About the precomputed partitions

Partitions computed using these method use three linguistic variables per fuzzy variable. We chose that number as it creates easily understandable low, medium and high partitions. For the case of IV-fuzzy sets, the trapezoids constructed, both the lower and upper memberships present 1 values in the same points. For the case of General Type 2 Fuzzy sets check General Type 2.