Entropy assessment for type-2 fuzziness

One of the sources of uncertainty, which perhaps is identified as parameter uncertainty, is the level of fuzziness in fuzzy system modeling. Given the optimum number of clusters and the cluster centers, one can explore type-2 membership values that capture the uncertainty of memberships. We explore variations of type-2 membership values with the entropy measure for an artificially created 12 data sets. Crisp to fuzzy data sets are constructed so that each data set has a different standard deviation within each cluster. In turn, each cluster has the same standard deviation for a given artificial data set. Members of a given artificial data set are generated randomly. Results are assessed by means of a particular entropy measure. It is shown that the content of the information uncertainty increases in certain ranges and decreases in other ranges of the level of fuzziness.