On entropy function and reliability indicator for D numbers

2019 ◽  
Vol 49 (9) ◽  
pp. 3248-3266 ◽  
Author(s):  
Jun Xia ◽  
Yuqiang Feng ◽  
Luning Liu ◽  
Dongjun Liu ◽  
Liguo Fei
2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Gianluca Teza ◽  
Michele Caraglio ◽  
Attilio L. Stella

AbstractWe show how the Shannon entropy function can be used as a basis to set up complexity measures weighting the economic efficiency of countries and the specialization of products beyond bare diversification. This entropy function guarantees the existence of a fixed point which is rapidly reached by an iterative scheme converging to our self-consistent measures. Our approach naturally allows to decompose into inter-sectorial and intra-sectorial contributions the country competitivity measure if products are partitioned into larger categories. Besides outlining the technical features and advantages of the method, we describe a wide range of results arising from the analysis of the obtained rankings and we benchmark these observations against those established with other economical parameters. These comparisons allow to partition countries and products into various main typologies, with well-revealed characterizing features. Our methods have wide applicability to general problems of ranking in bipartite networks.


2021 ◽  
pp. 114862
Author(s):  
Dragan Pamučar ◽  
Adis Puška ◽  
Željko Stević ◽  
Goran Ćirović
Keyword(s):  

1987 ◽  
Vol 25 (1-3) ◽  
pp. 387-398 ◽  
Author(s):  
Tomas Bohr ◽  
David Rand

2017 ◽  
Vol 24 (2) ◽  
pp. 653-669 ◽  
Author(s):  
Ningkui WANG ◽  
Daijun WEI

Environmental impact assessment (EIA) is usually evaluated by many factors influenced by various kinds of uncertainty or fuzziness. As a result, the key issues of EIA problem are to rep­resent and deal with the uncertain or fuzzy information. D numbers theory, as the extension of Dempster-Shafer theory of evidence, is a desirable tool that can express uncertainty and fuzziness, both complete and incomplete, quantitative or qualitative. However, some shortcomings do exist in D numbers combination process, the commutative property is not well considered when multiple D numbers are combined. Though some attempts have made to solve this problem, the previous method is not appropriate and convenience as more information about the given evaluations rep­resented by D numbers are needed. In this paper, a data-driven D numbers combination rule is proposed, commutative property is well considered in the proposed method. In the combination process, there does not require any new information except the original D numbers. An illustrative example is provided to demonstrate the effectiveness of the method.


2013 ◽  
Vol 756-759 ◽  
pp. 25-28 ◽  
Author(s):  
Chun Xia Li ◽  
Zhi Sheng Ding ◽  
Shi Lin Yan ◽  
Jun Ming Chen

Based on the experimental result of the flexure capability of reinforced concrete beams strengthened by carbon fiber sheets, the stress distribution changes only after steel yielding and carbon fiber sheets function better. However serious the extent of the damage is before strengthened, the tensile strain of main steel reaches about 1.6 times of the yield strain for the secondary grade of steel as failure happens. To satisfy the object reliability indicator, reliability is analyzed using the ratio of the steel strain at the balanced failure to the yield strain as variable to obtain its optimum value, which is coincide with the experimental result, and makes better consistency between calculated reliability indicator and object reliability indicator.


2005 ◽  
Vol 304 (1) ◽  
pp. 269-295 ◽  
Author(s):  
Joan Cerdà ◽  
Heribert Coll ◽  
Joaquim Martín

Author(s):  
Gediminas Adomavicius ◽  
Yaqiong Wang

Numerical predictive modeling is widely used in different application domains. Although many modeling techniques have been proposed, and a number of different aggregate accuracy metrics exist for evaluating the overall performance of predictive models, other important aspects, such as the reliability (or confidence and uncertainty) of individual predictions, have been underexplored. We propose to use estimated absolute prediction error as the indicator of individual prediction reliability, which has the benefits of being intuitive and providing highly interpretable information to decision makers, as well as allowing for more precise evaluation of reliability estimation quality. As importantly, the proposed reliability indicator allows the reframing of reliability estimation itself as a canonical numeric prediction problem, which makes the proposed approach general-purpose (i.e., it can work in conjunction with any outcome prediction model), alleviates the need for distributional assumptions, and enables the use of advanced, state-of-the-art machine learning techniques to learn individual prediction reliability patterns directly from data. Extensive experimental results on multiple real-world data sets show that the proposed machine learning-based approach can significantly improve individual prediction reliability estimation as compared with a number of baselines from prior work, especially in more complex predictive scenarios.


2011 ◽  
Vol 32 (4) ◽  
pp. 1400-1417 ◽  
Author(s):  
YUAN LI ◽  
ERCAI CHEN ◽  
WEN-CHIAO CHENG

AbstractBurguet [A direct proof of the tail variational principle and its extension to maps. Ergod. Th. & Dynam. Sys.29 (2009), 357–369] presented a direct proof of the variational principle of tail entropy and extended Downarowicz’s results to a non-invertible case. This paper defines and discusses tail pressure, which is an extension of tail entropy for continuous transformations. This study reveals analogs of many known results of topological pressure. Specifically, a variational principle is provided and some applications of tail pressure, such as the investigation of invariant measures and equilibrium states, are also obtained.


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