Fuzzy sets for words: a new beginning

Abstract

This paper begins with a delineation of two approaches to fuzzy sets, abstract mathematics and models for words. It demonstrates, by using Karl Popper's Falsificationism, the present approach to fuzzy sets (FSs) for words is scientifically incorrect. A new theory of fuzzy sets is then presented for words that is based on collecting data from people -person MFs-that reflect intra- and inter-levels of uncertainties about a word, and defines a word FS as the union of all such person fuzzy sets. It also demonstrates that intra-uncertainty about a word can be modeled using type-2 person fuzzy sets, and that inter-uncertainty about a word can be modeled by means of an equally weighted union of each person's type-2 fuzzy set. Finally, it proposes a methodology for obtaining a parsimonious parametric type-2 fuzzy set approximation to the aggregated type-2 person FSs. This new theory of fuzzy sets for words is testable and is therefore subject to refutation.