Measuring the directional distance between fuzzy sets

The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a variety of applications, such as Computing With Words. In this paper, we highlight this utility and introduce a distance measure which takes the direction between sets into account. We provide details of its application for normal and non-normal, as well as convex and non-convex fuzzy sets. We demonstrate the new distance measure using real data from the MovieLens dataset and establish the benefits of measuring the direction between fuzzy sets

Design and implementation of fuzzy logic controllers

The main objectives of our research are to present a self-contained overview of fuzzy sets and fuzzy logic, develop a methodology for control system design using fuzzy logic controllers, and to design and implement a fuzzy logic controller for a real system. We first present the fundamental concepts of fuzzy sets and fuzzy logic. Fuzzy sets and basic fuzzy operations are defined. In addition, for control systems, it is important to understand the concepts of linguistic values, term sets, fuzzy rule base, inference methods, and defuzzification methods. Second, we introduce a four-step fuzzy logic control system design procedure. The design procedure is illustrated via four examples, showing the capabilities and robustness of fuzzy logic control systems. This is followed by a tuning procedure that we developed from our design experience. Third, we present two Lyapunov based techniques for stability analysis. Finally, we present our design and implementation of a fuzzy logic controller for a linear actuator to be used to control the direction of the Free Flight Rotorcraft Research Vehicle at LaRC