The origin of fuzzy extensions

Abstract

Many different kinds of sets have been defined within the framework of fuzzy sets. This paper fo-cusses on those fuzzy set extensions that address the difficulties that experts find in order to build the membership values. In particular, we analyze type-2 fuzzy sets, interval-valued fuzzy sets, Atanassov’s intuitionistic fuzzy sets, or bipolar sets of type-2 and Atanassov’s interval-valued fuzzy sets. After stating a general approach to these extensions, we remark some structural problems in the extension problem and stress some applications for which the results obtained with extensions are better than those obtained with Zadeh’s fuzzy sets.