We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(·,·)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an...

This note proposes a generalization of the weak decomposition axiom recently introduced by Ebert (2010) [U. Ebert (2010), The decomposition of inequality reconsidered: Weakly decomposable measures, Mathematical Social Sciences 60(2): 94-103]. The generalization of this axiom relies on the introduction of weaker weighting functions based both on the size of the population and the mean income. Re...

We investigate factorizations of regular languages in terms of prime languages. A language is said to be strongly prime decomposable if any way of factorizing the language yields a prime decomposition in a finite number of steps. We give a characterization of the strongly prime decomposable regular languages and using the characterization we show that every regular language over a unary alphabe...

Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to the well-known set characterizing dependency models that are isomorphic to undirected graphs. We also brieey discuss a potential application of our results to ...

The present methods for obtaining the optimal LewenesteinSanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein-Sanpera decomposition by using semidefinite programming. Specially, we obtain the optimal Lewenstein-Sanpera decomposition for some examples such as: Bell decomposable state, Iso-concurrence sta...

The purpose of this project is to show observations taken from the Iterative Proportional Scaling algorithm when used with data taken from Hierarchical LogLinear Models. We show with empirical proof that the difference between decomposable and non-decomposable graph models used is not exceedingly different. For the purpose of this project we looked at the properties of the two, three, and four ...

We explore the properties of subgraphs (called Markovian subgraphs) of a decomposable graph under some condition. For a decomposable graph G and a collection γ of its Markovian subgraphs, we show that the set χ(G) of the intersections of all the neighboring cliques of G contains ∪g∈γχ(g). We also show that χ(G) = ∪g∈γχ(g) holds for a certain type of G which we call a maximal Markovian supergrap...