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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The third author was supported by the grant VEGA 1/3006/06 and MSM 619 8898 701. The fourth author gratefully acknowledges the support of the project “Metodi Stocastici in Finanza Matematica” of the Italian M.I.U.R.
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Durante, F., Klement, E.P., Mesiar, R. et al. Conjunctors and their Residual Implicators: Characterizations and Construction Methods. MedJM 4, 343–356 (2007). https://doi.org/10.1007/s00009-007-0122-1
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DOI: https://doi.org/10.1007/s00009-007-0122-1