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A Survey on Nullnorms on Bounded Lattices

  • Gül Deniz ÇaylıEmail author
  • Funda Karaçal
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)

Abstract

Nullnorms are generalizations of triangular norms (t-norms) and triangular conorms (t-conorms) with a zero element to be an arbitrary point from an arbitrary bounded lattice. In this paper, we study nullnorms on bounded lattices. We examine some properties of nullnorms considering the concepts of idempotency, local internality, conjunctivity and disjunctivity on bounded lattices. We investigate relationships between such concepts for nullnorms on bounded lattices and some illustrative examples are added to clearly show connections between these. Moreover, we give two methods to obtain nullnorms on bounded lattices with a zero element by using the given nullnorm and t-norm (t-conorm) with some constraints.

Notes

Acknowledgments

The authors are very grateful to the anonymous reviewers and editors for their helpful comments and valuable suggestions.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesKaradeniz Technical UniversityTrabzonTurkey

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