In this paper we study the subclass of left-continuous t-norms (*n) which are definable by an arbitrary continuous t-norm (*) and a weak (i.e. non necessarily involutive) negation n by putting x (*n) y = 0 if x less than or equal to n(y), x (*n) y = x (*) y otherwise, thus generalizing the construction of the so-called nilpotent minimum t-norms. We provide the characterization of weak negations compatible with a given continuous t-norm and conversely which are the continuous t-norrns compatible with a given weak negation function. (C) 2002 Elsevier Science B.V. All rights reserved.
Montagna, F., Cignoli, R., Esteva, F., Godo, L. (2002). On a class of left-continuous t-norms. FUZZY SETS AND SYSTEMS, 131(3), 283-296 [10.1016/S0165-0114(01)00215-9].
On a class of left-continuous t-norms
MONTAGNA, FRANCO;
2002-01-01
Abstract
In this paper we study the subclass of left-continuous t-norms (*n) which are definable by an arbitrary continuous t-norm (*) and a weak (i.e. non necessarily involutive) negation n by putting x (*n) y = 0 if x less than or equal to n(y), x (*n) y = x (*) y otherwise, thus generalizing the construction of the so-called nilpotent minimum t-norms. We provide the characterization of weak negations compatible with a given continuous t-norm and conversely which are the continuous t-norrns compatible with a given weak negation function. (C) 2002 Elsevier Science B.V. All rights reserved.
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https://hdl.handle.net/11365/7109
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