The underlying structure in Atanassov's IFS

Abstract

In this paper we shall stress the key relevance of addressing a specific structure for the valuation space in Atanassov's IFS, which may help to establish certain di®erences with other related models. In particular, we point out that each one of the valuation states proposed by Atanassov plays a different role, so they should be distinguished from their particular properties with respect to the other valuation states. In the same way, we realize that those three valuation states are not interchangeable and that each state should in principle allow a clear definition, as in any standard classification problem, always subject to potential direct estimation. Considering for example a transition (directed) graph in order to connect states provides in addition a new framework for useful more general models, taking simultaneously into account several logics when needed and avoiding the still binary heritage in Atanassov's model.