Discussion: Terminological difficulties in fuzzy set theory---The case of “Intuitionistic Fuzzy Sets”

  • Authors:

  • Didier Dubois;Siegfried Gottwald;Petr Hajek;Janusz Kacprzyk;Henri Prade

  • Affiliations:

  • IRIT, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, Cedex 4, France;Universitaet Leipzig, Institut fuer Logik und Wissenschaftstheorie, Beethovenstrasse 15, D-04107 Leipzig, Germany;Institute of Computer Science, Academy of Sciences, Pod vodarenskou vezi 2, 18207 Prague, Czech Republic;Systems Research Institute, Polish Academy of Sciences, ul. Newelska, 601-447 Warsaw, Poland;IRIT, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, Cedex 4, France

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2005

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Abstract

This note points out a terminological clash between Atanassov's ''intuitionistic fuzzy sets'' and what is currently understood as intuitionistic logic. They differ both by their motivations and their underlying mathematical structure. Furthermore, Atanassov's construct is isomorphic to interval-valued fuzzy sets and other similar notions, even if their interpretive settings and motivation are quite different, the latter capturing the idea of ill-known membership grade, while the former starts from the idea of evaluating degrees of membership and non-membership independently. This paper is a plea for a clarification of terminology, based on mathematical resemblances and the comparison of motivations between ''intuitionistic fuzzy sets'' and other theories.