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 assoc
✦ LIBER ✦
Convex combinations of strict t-norms
✍ Scribed by Milan Petrík
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 209 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1432-7643
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In knowledge representation, when we have to use logical connectives, various continuous t-norms and t-conorms are used. In this paper, we show that every continuous tnorm and t-conorm can be approximated, to an arbitrary degree of accuracy, by a strict Archimedean t-norm (t-conorm).