In the context of multicriteria decision making whose aggregation process is based on the Choquet integral, bi-capacities can be regarded as a natural extension of capacities when the underlying evaluation scale is bipolar. The notion of entropy, recently generalized to capacities to measure their uniformity, is now extended to bi-capacities. We show that the resulting entropy measure has a ver...

The often used Nusselt number is critically questioned with respect to its physical meaning. Based on a rigorous dimensional analysis, alternative assessment numbers are found that in a systematic way separately account for the quantitative and qualitative aspect of a heat transfer process. The qualitative aspect is related to the entropy generated in the temperature field of a real, irreversib...

1. A finitary probability space (=all probability measures on a fixed finite support) can be faithfully represented by a partial order equipped with a measure of content (e.g. Shannon entropy). 2. This partial order can be obtained via a purely order-theoretic systematic procedure starting from an algebra of properties. This procedure applies to any poset envisioned as an algebra of properties.

The uncertainty in a set of discrete outcomes is the entropy. In some text books an explanation for this assertion is often another assertion: the entropy is the average minimum number of yes-no questions necessary to identify an item randomly drawn from a known, discrete probability distribution. It would be preferable to avoid these assertions and search for the heart of the matter where does...

Several strong limit theorems axe proved for sums of logarithms of mth order spacings from general distributions. In all given results, the order of the spac­ ings is allowed to increase to infinity with the sample size. These results provide a nonparametric strongly consistent estimator of entropy as well a s a charac­ terization of the uniform distribution on [0,1]. Furthermore, it is shown t...

In this article we mainly define the information entropy [3], [11] and prove some its basic properties. First, we discuss some properties on four kinds of transformation functions between vector and matrix. The transformation functions are LineVec2Mx, ColVec2Mx, Vec2DiagMx and Mx2FinS. Mx2FinS is a horizontal concatenation operator for a given matrix, treating rows of the given matrix as finite...

Zhang in 2012 introduced a nonparametric estimator of Shannon’s entropy, whose bias decays exponentially fast when the alphabet is finite. We propose a methodology to estimate the bias of this estimator. We then use it to construct a new estimator of entropy. Simulation results suggest that this bias adjusted estimator has a significantly lower bias than many other commonly used estimators. We ...

Parrondo's paradox involves two losing games of chance. The paradox is that a winning situation is produced when the two games are played in a random sequence in accordance with fixed probabilities. In this paper we investigate the relationship between these parameters and the entropy rates of the games.

In this paper, we have proposed the concept of weighted generalized residual entropy of order α and type β, and have shown that the proposed measure characterizes the distribution function uniquely.

This study investigated the extent to which cognitive measures of individual differences predict strategy shifts in a series of procedural-motor curve-drawing tasks. College students participated in a task which required them to trace or draw various forms of a figure-8 before completing a battery of cognitive tests. Three distinct drawing strategies emerged, and the tendency to vary these stra...