T-norms induced by metrics on boolean algebras
From Mathfuzzlog
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| Title: | t-norms induced by metrics on boolean algebras | |
| Journal: | Soft Computing | |
| Volume | 10 | |
| Number | ||
| Pages: | 995 - 1000 | |
| Year: | 2006 |
Abstract
Let dν be the metric associated with a strictly positive submeasure ν on some boolean algebra 
. If dν is bounded from above by 1, Eν = 1 − dν is a (fuzzy) similarity relation on at least w.r.t.the Lukasiewicz t-norm, but possibly also w.r.t. numerous further t-norms.
In this paper, we show that under certain assumptions on and ν, we may associate with ν in a natural way a continuous t-norm w.r.t. which Eν is a similarity relation and which, in a certain sense, is the weakest such t-norm. Up to isomorphism, every continuous t-norm arises in this way.
