Novel set-theoretic definitions of common fuzzy hedges,theory and application

Abstract

The subject of this paper is fuzzy linguistic hedging, used to modify membership functions. Our investigation will exceed the traditional definition given by Zadeh (and others), upon which our research is based. We will present new and more general definitions for four of the most commonly used hedges. These hedges are very, more or less, positively and negatively. The effect of applying each hedge to a membership function will be described both qualitatively and quantitatively in this paper. We will also describe conditions under which a specific hedge is valid, chart the examples, and explore the properties of the hedge operations. A software program called FuzzyMarkx has been developed for understanding and applying the above four hedges to list of data. It is specially designed for altering school grade distributions. It allows users to view the new grades, the grade distribution as well as the graphical representation of the hedge being applied.