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Fuzzy Logic
manyvalued logic
Triangular Norm
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Conjunctors and their Residual Implicators: Characterizations and Construction Methods
Conjunctors and their Residual Implicators: Characterizations and Construction Methods,10.1007/s0000900701221,Mediterranean Journal of Mathematics,
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Conjunctors and their Residual Implicators: Characterizations and Construction Methods
(
Citations: 19
)
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Fabrizio Durante
,
Erich Peter Klement
,
Radko Mesiar
,
Carlo Sempi
. 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 onetoone 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.
Journal:
Mediterranean Journal of Mathematics  MEDITERR J MATH
, vol. 4, no. 3, pp. 343356, 2007
DOI:
10.1007/s0000900701221
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Citation Context
(3)
...Not only tnorms and tconorms, but also copulas, quasicopulas and even conjunctors in general ([
9
]), representable aggregation functions ([10]), and mainly uninorms ([11], [12], [13], [14], [15], [16])...
Sebastia Massanet
,
et al.
Implications generated from additive generators of representable unino...
...in [
14
]o r [19], where many interesting results can be found...
Michal Botur
,
et al.
Commutative basic algebras and nonassociative fuzzy logics
...CI is also known as the deresiduum of I (see e.g., [
20
])...
...Remark 7.4. From the above result and Definition 4.4, it is clear that the class of monotonic duality fitting implicators are exactly the class of fuzzy implications that satisfy (LNP) and (OP). Definition 7.5 (cf.[37,
20
])...
...Theorem 7.8. ([
20
], Theorem 3.2 and Proposition 3.3)...
...Now, we give a characterisation of monotonic leftcontinuous duality fitting conjuctors C, i.e., leftcontinuous commutative semicopula, such that their residuals IC are not only duality fitting implicators but also such that every Cfuzzy equivalence relation E on a set X is also an ICfuzzy equivalence relation and viceversa, i.e., E 2 CFECðX Þ( ) E 2 IFEIC ðXÞ. Theorem 7.9. ([
20
], Theorem 3.5)...
Balasubramaniam Jayaram
,
et al.
IFuzzy equivalence relations and Ifuzzy partitions
References
(17)
Residual implications revisited. Notes on the SmetsMagrez Theorem
(
Citations: 13
)
Michal Baczynski
Journal:
Fuzzy Sets and Systems  FSS
, vol. 145, no. 2, pp. 267277, 2004
Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes
(
Citations: 35
)
Bruno Bassan
,
Fabio Spizzichino
Journal:
Journal of Multivariate Analysis  J MULTIVARIATE ANAL
, vol. 93, no. 2, pp. 313339, 2005
Aggregation Operators: Properties, Classes and Construction Methods
(
Citations: 83
)
T. Calvo
,
A. Kolesarova
,
M. Komornikova
,
R. Mesiar
Published in 2002.
Pseudotnorms and pseudoBL algebras
(
Citations: 51
)
Paul Flondor
,
George Georgescu
,
Afrodita Iorgulescu
Journal:
Soft Computing  SOCO
, vol. 5, no. 5, pp. 355371, 2001
Contrapositive symmetry of fuzzy implications
(
Citations: 157
)
J' Anos C. Fodor
Journal:
Fuzzy Sets and Systems  FSS
, vol. 69, no. 2, pp. 141156, 1995
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Citations
(19)
Piecewise linear aggregation functions based on triangulation
(
Citations: 2
)
Bernard De Baets
,
Hans De Meyer
,
Radko Mesiar
Journal:
Information Sciences  ISCI
, vol. 181, no. 3, pp. 466478, 2011
On a new class of fuzzy implications: hImplications and generalizations
(
Citations: 1
)
Sebastià Massanet
,
Joan Torrens
Journal:
Information Sciences  ISCI
, vol. 181, no. 11, pp. 21112127, 2011
Implications generated from additive generators of representable uninorms: (h, e)implications
Sebastia Massanet
,
Joan Torrens
Conference:
IEEE Symposium on Foundations of Computational Intelligence  FOCI
, 2011
A characterization of residual implications derived from leftcontinuous uninorms
(
Citations: 4
)
Isabel Aguiló
,
Jaume Suñer
,
Joan Torrens
Journal:
Information Sciences  ISCI
, vol. 180, no. 20, pp. 39924005, 2010
Semicopulas, capacities and families of level sets
(
Citations: 4
)
Fabrizio Durante
,
Fabio Spizzichino
Journal:
Fuzzy Sets and Systems  FSS
, vol. 161, no. 2, pp. 269276, 2010