Some new construction methods for t-norms on bounded lattices

ABSTRACT

In this paper, three methods for constructing triangular norms on a bounded lattice L from t-norm W on sub-lattice $[a,b]$ of L are investigated. An example is added to reveal the difference of three construction methods. The smallest t-norm in the class of all triangular norms on a lattice L whose restriction to the subinterval $[a,b]$ of L is a priori fixed t-norm W is determined.

KEYWORDS:

• t-norm
• bounded lattice
• construction method
• subinterval

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ümit Ertuğrul  http://orcid.org/0000-0003-0672-8134

M. Nesibe Kesicioğlu  http://orcid.org/0000-0002-2754-7458

Funda Karaçal  http://orcid.org/0000-0002-2602-1788

Additional information

Notes on contributors

Ümit Ertuğrul

Ümit Ertuğrul is an assistant professor in the department of mathematics at Karadeniz Technical University since 2017. He obtained the bachelor's degree in Study of mathematics-secondary school teacher accreditation (2010), M.Sc. degree in Mathematics (2012) and PhD degree in the department of Mathematics (2017) in Karadeniz Technical University. He has over 5 publications in international peer-reviewed journals.

M. Nesibe Kesicioğlu

M. Nesibe Kesicioğlu has been working as an associate professor in the department of mathematics at Recep Tayyip Erdoğan University since 2016. She obtained the bachelor's degree in the department of mathematics (2003), M.Sc. degree in Mathematics (2006) and PhD degree in the department of Mathematics (2012) in Karadeniz Technical University. She has over 10 publications in international peer-reviewed journals.

Funda Karaçal

Funda Karaçal is a professor of Mathematics at Karadeniz Technical University. She holds Bachelor's Degree from Study of mathematics-secondary school teacher accreditation, M.Sc. degree in Mathematics (1996) and Ph.D. degree in Mathematics (2001) from Karadeniz Technical University. Her research interests are fuzzy logic, triangular norms and aggregation functions. The bibliography of professor Karaçal comprises more than 35 publications in international peerreviewed journals, lots of presentations in international conferences.