1,721,106 research outputs found
Ordinal sums
No full textWe prove that the ordinal sum of n-copulas is always an n-copula and show that
every copula may be represented as an ordinal sum, once the set of its idempotents is known.
In particular, it will be shown that every copula can be expressed as the ordinal sum of copulas
having only trivial idempotents. As a by-product, we also characterize all associative
copulas whose n-ary forms are n-copulas for all n
The lattice-theoretic structure of the sets of triangular norms and semi-copulas
No full textWe prove the denseness of semi-copulas in a class of aggregation operators; several related results are proved
Multi-attribute aggregation operators
No full textThis paper deals with the idea of aggregation. A new, enlarged notion of aggregation operator is given, along with a classification of classical properties into some main groups. The concept of multi-attribute aggregation operator, which incorporates many classical aggregation methods, is provided. An extension of different properties to multi-attribute aggregation operators is proposed. © 2011 Elsevier B.V. All rights reserved
Semilinear copulas
No full textA family of copulas, called semilinear, is constructed starting with some assumptions about the linearity of the copulas along some segments of the unit square. This family contains some other
known families of copulas (e.g., Cuadras--Aug\'e, Fr\'echet) and has a nice statistical interpretation. Several construction methods are provided, especially concerning aggregation of semilinear copulas, and a special form of ordinal sum construction is introduced. Some results about related families of quasi--copulas
and semi--copulas are hence given
Copulas constructed from horizontal sections
Full text linkIn analogy with the study of copulas whose diagonal sections have
been fixed, we study the set of copulas for which a horizontal section has been given. We first show that this set is not empty, by explicitly writing one such copula, which we call \textit{horizontal copula}. Then we find the copulas that
bound both below and above the set . Finally we determine the expressions for Kendall's tau and Spearman's rho for the horizontal and the bounding copulas
Conjunctors and their residual implicators: characterizations and construction methods
Full text linkIn 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 that are used to extend the boolean conjunction
from to , 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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