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.

Conjunctors and their residual implicators: characterizations and construction methods

DURANTE, FABRIZIO;SEMPI, Carlo
2007-01-01

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/103214
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