Fabrizio Durante, Carlo Sempi, Radko Mesiar, Erich Klement,
"Conjunctors and their residual implicators: characterizations and construction methods"
, in Mediterranean Journal of Mathematics, Vol. 4, Nummer 3, Seite(n) 343-356, 2007, ISSN: 1660-5446
Original Titel:
Conjunctors and their residual implicators: characterizations and construction methods
Sprache des Titels:
Englisch
Original Kurzfassung:
In many practical applications of fuzzy logic it seems clear that one needs more flexibility
in the choice of the conjunction: in particular, the associativity and the commutativity of
a conjunction may be removed. Motivated by these considerations, we present several classes
of conjunctors, i.e. binary operations on [0,1] that are used to extend the boolean conjunction
from {0,1} to [0,1], and characterize their respective residual implicators. We establish
hence a one-to-one correspondence between construction methods for conjunctors and construction
methods for residual implicators. Moreover, we introduce some construction methods directly in the class
of residual implicators, and, by using a deresiduation procedure, we obtain new conjunctors.
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