Uncertainty bounds of Fuzzy C-Regression Method

The fuzzy C-regression Method (FCRM) based on fuzzy C-means (FCM) clustering algorithm was proposed by Hathaway and Bezdek to solve the switching regression problems, and it was applied to fuzzy models by many to build more powerful fuzzy inference systems. The FCRM methods require initialization parameters which are in need for proper identification, since uncertain information can create imperfect expressions, which may hamper the predictive power of these models. This paper investigates the behavior of the FCRM models under uncertain parameters. The upper and lower bounds of the membership values can be identified based on the limits of level of fuzziness parameter around the certain information points such as local functions and ensemble point values. This is a further step to identify the footprint-of-uncertainty of membership values when FCRM is used. It is shown that the uncertainty of membership values induced by the level of fuzziness parameter can be identified based on first order approximations of the membership value calculation function.