Convex combinations of continuous t-norms with the same diagonal function

✍ Scribed by R. Mesiar; A. Mesiarová-Zemánková

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 230 KB
• Volume: 69
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.08.076

✦ Synopsis

The problem of whether a non-trivial convex combination of two continuous t-norms with the same diagonal function can be a t-norm is studied. It is shown that in both cases -of two nilpotent and of two strict t-norms -a non-trivial convex combination of t-norms with common diagonal function is associative only if the two t-norms involved coincide. For general continuous t-norms a similar result follows. An example of a convex class of non-continuous t-norms is also included.