T-norms and t-conorms on a family of lattices

This paper provides a complete classification of all t-norms on a family of lattices in terms of t-norms on discrete chains. Moreover, the cardinal of some classes on discrete chains is computed. Therefore, the number of t-norms on the family of lattices is obtained. Also, new results involving Archimedean and divisible t-norms are presented. Finally, we bring out dual results for t-conorms. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper provides a complete classification of all t-norms on a family of lattices in terms of t-norms on discrete chains, and computes the cardinal of some classes on discrete chains. The number of t-norms on the family of lattices is obtained. New results involving Archimedean and divisible t-norms are also presented, along with dual results for t-conorms.