Membership function

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

Fundamentals of Statistics with Fuzzy Data

Abstract: Introduction.- Set-valued Data.- Modeling of fuzzy data.- Random fuzzy sets.- Aspect of statistical Inference.- Convergence of random fuzzy sets.- Fuzzy Statistical Analysis and Estimation.- Testing Hypothesis with Fuzzy Data.- Fuzzy Time Series Analysis and Forecasting.

Minimal fuzzy memberships and rules using hierarchical genetic algorithms

Abstract: A new scheme to obtain optimal fuzzy subsets and rules is proposed. The method is derived from the use of genetic algorithms, where the genes of the chromosome are classified into two different types. These genes can be arranged in a hierarchical form, where one type of gene controls the other. The effectiveness of this genetic formulation enables the fuzzy subsets and rules to be optimally reduced and, yet, the system performance is well maintained. In this paper, the details of formulation of the genetic structure are given. The required procedures for coding the fuzzy membership function and rules into the chromosome are also described. To justify this approach to fuzzy logic design, the proposed scheme is applied to control a constant water pressure pumping system. The obtained results, as well as the associated final fuzzy subsets, are included in this paper. Because of its simplicity, the method could lead to a potentially low-cost fuzzy logic implementation.

Fuzzy Maps: A New Tool for Mobile Robot Perception and Planning

Abstract: An essential component of an autonomous mobile robot is the exteroceptive sensory system. Sensing capabilities should be integrated with a method for extracting a representation of the environment from uncertain sensor data and with an appropriate planning algorithm. In this article, fuzzy logic concepts are used to introduce a tool useful for robot perception as well as for planning collision-free motions. In particular, a map of the environment is defined as the fuzzy set of unsafe points, whose membership function quantifies the possibility for each point to belong to an obstacle. The computation of this set is based on a specific sensor model and makes use of intermediate sets generated from range measures and aggregated by means of fuzzy set operators. This general approach is applied to a robot with ultrasonic rangefinders. The resulting map building algorithm performs well, as confirmed by a comparison with stochastic methods. The planning problem on fuzzy maps can be solved by defining various path cost functions, corresponding to different strategies, and by searching the map for optimal paths. To this end, proper instances of the A* algorithm are devised. Experimental results for a Nomad 200™ robot moving in a real-world environment are presented. © 1997 John Wiley & Sons, Inc.

How the learning of rule weights affects the interpretability of fuzzy systems

Abstract: Neuro-fuzzy systems have recently gained a lot of interest in research and applications. These are approaches that learn fuzzy systems from data. Many of them use rule weights for this task. In this paper we discuss the influence of rule weights on the interpretability of fuzzy systems. We show how rule weights can be equivalently replaced by modifications in the membership functions of a fuzzy system. We elucidate the effects rule weights have on a fuzzy rule base. Using our neuro-fuzzy model NEFCLASS we demonstrate the problems of using rule weights in a simple example, and we show that learning in fuzzy systems can be done without them.