Entropy for fuzzy regression analysis

Prediction by regression plays an important role in intelligent systems. To construct a regression model for fuzzy numbers, this paper decomposes a fuzzy number into two parts: the position and fuzziness. The former is represented by the elements with membership value l and the latter by the entropy of the fuzzy number; both have crisp values. The conventional regression analysis is applied to find the relationship between the position (and entropy) of the fuzzy response variable and that of the fuzzy explanatory variables. Given a set of fuzzy explanatory variables, the position and entropy of the estimated fuzzy responses are calculated from the regression model. Via the one-to-one correspondence between a fuzzy number and its entropy, the estimated fuzzy response is obtained.