Computational Intelligence

De veloping a Fuzzy Controller 301

Note that for practical systems, H

DT

and H

PP

are often normalized so that they

produce values between 0 and 1; H

K

is inherently normalized. Also note that higher

values of fuzziness are not necessarily “better” in an application. Remember that

maximum fuzziness is represented by a membership function with a membership

value of 0.5 over its entire domain (which is almost certainly useless).

Fuzziness measures are often used to measure the relative fuzziness of various

models, selecting the model to “harden” that is least fuzzy. For example, in the case

of cluster validity functions, the partition of the data that has