Abstract Is it always beneficial to create a new relationship (have follower/friend) in social network? This question can be formally stated as property of the centrality measure that defines importance actors network. Score monotonicity means adding an arc increases score target arc; rank improves relatively remaining nodes. It is known most centralities are both and monotone on directed, stro...

We consider scenarios in which long sequences of data are analyzed and subsequences must be traced that are monotone and maximum, according to some measure. A classical example is the online Longest Increasing Subsequence Problem for numeric and alphanumeric data. We extend the problem in two ways: (a) we allow data from any partially ordered set, and (b) we maximize subsequences using much mor...

A general theory of resource-bounded measurability and measure is developed. Starting from any feasible probability measure ν on the Cantor space C (the set of all decision problems) and any suitable complexity class C ⊆ C, the theory identifies the subsets of C that are ν-measurable in C and assigns measures to these sets, thereby endowing C with internal measure-theoretic structure. Classes C...

This paper has been motivated by general considerations on the topic of Risk Measures, which essentially are convex monotone maps de…ned on spaces of random variables, possibly with the so-called Fatou property. We show …rst that the celebrated Namioka-Klee theorem for linear, positive functionals holds also for convex monotone maps on Frechet lattices. It is well-known among the specialists th...

We construct an entanglement measure that coincides with the generalized concurrence for a general pure bipartite state based on wedge product. Moreover, we construct an entanglement measure for pure multiqubit states, which are entanglement monotone. Furthermore, we generalize our result on a general pure multipartite state.

In 1974, Sugeno introduced the notion of fuzzy measure and integral to evaluate nonadditive or non-linear quality in systems engineering. In the same year, Dobrakov independently introduced the notion of submeasure from mathematical point of view to show that most of the theory of countably additive measures remain valid for such measures. Fuzzy measures and submeasures are both special kinds o...

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 ...

Our main goal is to extend the domain of a monotone measure to a class of intuitionistic fuzzy sets. The extension is made by using of the Choquet integral.

zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎a strong convergence theorem for the common solutions of the problems is established in the framework of hilbert spaces‎.

We consider two singular limits: a fast reaction limit with non-monotone nonlinearity and regularization of the forward-backward diffusion equation. derive pointwise identities satisfied by Young measure generated these problems. As result, we obtain an explicit formula for even without non-degeneracy assumption used in previous works. The main new idea is application Radon–Nikodym theorem to d...