9 research outputs found

    Linear extensions and order-preserving poset partitions

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    We examine the lattice of all order congruences of a finite poset from the viewpoint of combinatorial algebraic topology. We will prove that the order complex of the lattice of all nontrivial order congruences (or order-preserving partitions) of a finite nn-element poset PP with n3n\geq 3 is homotopy equivalent to a wedge of spheres of dimension n3n-3. If PP is connected, then the number of spheres is equal to the number of linear extensions of PP. In general, the number of spheres is equal to the number of cyclic extensions of PP

    Distorted Copulas: Constructions and Tail Dependence

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    Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails

    Information boundedness principle in fuzzy inference process

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    summary:The information boundedness principle requires that the knowledge obtained as a result of an inference process should not have more information than that contained in the consequent of the rule. From this point of view relevancy transformation operators as a generalization of implications are investigated

    Shuffles of copulas

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    none2We show that every copula that is a shuffle of Min can be described in terms of a push--forward of the doubly stochastic measure induced by the copula MM by means of a specific transformation of the unit square. This fact allows to generalize the notion of shuffle by replacing the measure induced by MM with an arbitrary doubly stochastic measure, and, hence, the copula MM by any copula CC.Si tratta di una notevole estensione del concetto di shuffle basata su delicati risultati di teoria ergodicaF. DURANTE; P. SARKOCI; C. SEMPIDurante, Fabrizio; P., Sarkoci; Sempi, Carl

    Remarks on Two Product-like Constructions for Copulas

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    summary:We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the \ast -product and the \star -product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min
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