Modal and Topological Operators Defined over IFSs

  • Krassimir T. Atanassov
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 283)


This Chapter includes several operators over IFSs which have no counterparts in the ordinary fuzzy set theory.

Initially, following [11, 39], we introduce two operators over IFSs that transform an IFS into a fuzzy set (i.e., a particular case of an IFS). They are similar to the operators “necessity” and “possibility” defined in some modal logics. Their properties resemble these of the modal logic (see e.g. [227]).


Convex Hull Modal Logic Geometrical Interpretation Minimal Convex Standard Rule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria

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