Image processing has to deal with many ambiguous situations. Fuzzy set theory is a good mathematical tool for handling the ambiguity or uncertainty. In order to apply the fuzzy theory, selecting the fuzzy region of membership function is an fundamental and important task. Most researchers use a predetermined window approach which has inherent problems. There are several formulas for computing the entropy of a fuzzy set. In order to overcome the weakness of the existing entropy formulas, this paper defines a new approach to fuzzy entropy and uses it to automatically select the fuzzy region of membership function so that an image is able to be transformed into fuzzy domain with maximum fuzzy entropy. The procedure for finding the optimal combination of a, b and c is implemented by a genetic algorithm. The proposed method selects the fuzzy region according to the nature of the input image, determines the fuzzy region of membership function automatically, and the post-processes are based on the fuzzy region and membership function. We have employed the novelly proposed approach to perform image enhancement and thresholding, and obtained satisfactory results.