Atanassov's Intuitionistic Fuzzy Sets as a Classification Model

  • Authors:

  • J. Montero;D. Gómez;H. Bustince

  • Affiliations:

  • Facultad de Matemáticas, Universidad Complutense, Madrid, Spain;Escuela de Estadística, Universidad Complutense, Madrid, Spain;Automática y Computación, Universidad Pública de Navarra, Pamplona, Spain

  • Venue:
  • IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
  • Year:
  • 2007

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Abstract

In this paper we show that Atanassov's Intuitionistic Fuzzy sets can be viewed as a classification model, that can be generalized in order to take into account more classes than the three classes considered by Atanassov's (membership, non-membership and non-determinacy). This approach will imply, on one hand, to change the meaning of these classes, so each one will have a positive definition. On the other hand, this approach implies the possibility of a direct generalization for alternative logics and additional valuation states, being consistent with Atanassov's focuss. From this approach we shall stress the absence of any structure within those three valuation states in Atanassov's model. In particular, we consider this is the main cause of the dispute about Atanassov's model: acknowledging that the name intuitionisticis not appropriate, once we consider that a crisp direct graph is defined in the valuation space, formal differences with other three-state models will appear.