Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.

Fuzzy statistics: hypothesis testing

Abstract: Our method of estimation of parameters in statistics uses a set of confidence intervals producing a triangular shaped fuzzy number for the estimator. Using this fuzzy estimator in hypothesis testing produces a fuzzy test statistic and fuzzy critical values in fuzzy hypothesis testing. We show how these fuzzy sets may be used to derive the usual conclusion of: (1) reject the null hypothesis, or (2) do not reject the null hypothesis.

Prediction and identification using wavelet-based recurrent fuzzy neural networks

Abstract: This paper presents a wavelet-based recurrent fuzzy neural network (WRFNN) for prediction and identification of nonlinear dynamic systems. The proposed WRFNN model combines the traditional Takagi-Sugeno-Kang (TSK) fuzzy model and the wavelet neural networks (WNN). This paper adopts the nonorthogonal and compactly supported functions as wavelet neural network bases. Temporal relations embedded in the network are caused by adding some feedback connections representing the memory units into the second layer of the feedforward wavelet-based fuzzy neural networks (WFNN). An online learning algorithm, which consists of structure learning and parameter learning, is also presented. The structure learning depends on the degree measure to obtain the number of fuzzy rules and wavelet functions. Meanwhile, the parameter learning is based on the gradient descent method for adjusting the shape of the membership function and the connection weights of WNN. Finally, computer simulations have demonstrated that the proposed WRFNN model requires fewer adjustable parameters and obtains a smaller RMS error than other methods.

An Optimal Fuzzy System for Color Image Enhancement

Abstract: A Gaussian membership function is proposed to fuzzify the image information in spatial domain. We introduce a global contrast intensification operator (GINT), which contains three parameters, viz., intensification parameter t, fuzzifier fh, and the crossover point muc, for enhancement of color images. We define fuzzy contrast-based quality factor Qf and entropy-based quality factor Qe and the corresponding visual factors for the desired appearance of images. By minimizing the fuzzy entropy of the image information with respect to these quality factors, the parameters t, fh, and muc are calculated globally. By using the proposed technique, a visible improvement in the image quality is observed for under exposed images, as the entropy of the output image is decreased. The terminating criterion is decided by both the visual and quality factors. For over exposed and under plus over exposed images, the proposed fuzzification function needs to be modified by taking maximum intensity as the fourth parameter. The type of the images is indicated by the visual factor which is less than 1 for under exposed images and more than 1 for over exposed images