In this paper, we extend monotone monomials as large itemsets in association rule mining to monotone DNF formulas. First, we introduce not only the minimum support but also the maximum overlap, which is a new measure how much all pairs of two monomials in a monotone DNF formula commonly cover data. Next, we design the algorithm dnf cover to extract coverings as monotone DNF formulas satisfying ...

Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0, A] are obtained under both the Hellinger distance and the L(p)(Q) distance, where 1 ≤ p < ∞ and Q is a probability measure on [0, A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.

In this paper, we extend a monotone iterative technique for nonlocal fractional differential equations with finite delay in an ordered Banach space. By using the monotone iterative technique, theory of fractional calculus, semigroup theory and measure of noncompactness, we study the existence and uniqueness of extremal mild solutions. An example is presented to illustrate the main result.

The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Hölder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee ...

We show that the only dynamic risk measure which is law invariant, time consistent and relevant is the entropic one. Moreover, a real valued function c on L∞(a, b) is normalized, strictly monotone, continuous, law invariant, time consistent and has the Fatou property if and only if it is of the form c(X) = u−1 ◦ E [u(X)], where u : (a, b) → R is a strictly increasing, continuous function. The p...

In this paper, we establish a new coherent risk measure on Lp, which refer to as the monotone mean Lp-deviation measure. Then, related properties are discussed. Furthermore, from perspective of acceptance set, discuss relationship between and Sharpe ratio Finally, extend multivariate setting.

A well-known inequality due to Harris and Kleitman [4, 10] states that any two monotone subsets of {0, 1} are non-negatively correlated with respect to the uniform measure on {0, 1}. In [15], Talagrand established a lower bound on the correlation in terms of how much the two sets depend simultaneously on the same coordinates. In this paper we show that when the correlation is averaged over all ...

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...

We investigate a monotone link between Bayesian confirmation measures and rule support and confidence. In particular, we prove that two confirmation measures enjoying some desirable properties are monotonically dependent on at least one of the classic dimensions being rule support and confidence. As the confidence measure is unable to identify and eliminate non-interesting rules, for which a pr...