New construction approaches of uninorms on bounded lattices

Abstract

This article continuous to investigate the construction approaches for uninorms on bounded lattices. We introduce some new methods to obtain uninorms with an identity $e\in L\mathrm{\setminus }\{0,1\}$ by using closure (interior) operators on a bounded lattice L. As a by-product of these methods, we present two families of idempotent uninorms on bounded lattices. Furthermore, we provide some corresponding examples to illustrate that our methods can differ for different closure (interior) operators.

Keywords:

• Bounded lattice
• closure operator
• uninorm
• interior operator
• t-norm
• t-conorm

Acknowledgments

The author expresses her sincere thanks to the editors and reviewers for their most valuable comments and suggestions in improving this paper greatly.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Gül Deniz Çaylı

Gül Deniz Çaylı received BSc degree in Mathematics from Afyon Kocatepe University (2011), MSc degree in Mathematics (2014) and PhD degree in Mathematics (2018) from Karadeniz Technical University. Since 2012, she has been a member of the Department of Mathematics, Faculty of Science, Karadeniz Technical University, Trabzon, Turkey, where she is currently an Associate Professor. Her research interests are fuzzy logic, triangular norms and conorms, uninorms, nullnorms and aggregation functions.