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Characterizing Ordinal Sum for t-norms and t-conorms on Bounded Lattices

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

Abstract

The ordinal sum of triangular norms on the unit interval has been proposed to construct new triangular norms. However, considering general bounded lattices, the ordinal sum of triangular norms and conorms may not generate triangular norms and conorms. In this paper, we study and propose some new construction methods yielding triangular norms and conorms on general bounded lattices. Moreover, we generalize these construction methods by induction to a ordinal sum construction for triangular norms and conorms, applicable on any bounded lattice. And some illustrative examples are added for clarity.

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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