Abstract
One of the most important operators in soft computing are the triangular norms (t-norms), as well as the combination among them. The ordinal sum of triangular norms on [0, 1] has been used to construct other triangular norms. However, on a bounded lattice, an ordinal sum of t-norms may not be a t-norm. Several necessary and sufficient conditions are presented in this paper for ensuring whether an ordinal sum on a bounded lattice of arbitrary t-norms is, in fact, a t-norm. Moreover, we show that a large set of ordinal sums verify these conditions. Hence, they are very interesting in order to verify whether an ordinal sum on a bounded lattice is a t-norm for a particular family of t-norms.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
