The Origin of Fuzzy Extensions
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2015
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Springer
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Bustince, H., Barrenechea, E., Fernández, J., Pagola, M., Montero, J.: The Origin of Fuzzy Extensions. En: Kacprzyk, J. y Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence. pp. 89-112. Springer Berlin Heidelberg, Berlin, Heidelberg (2015)
Abstract
Many different kinds of sets have been defined within the framework of fuzzy sets . This paper focusses 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 extens