scholarly journals Information Volume of Mass Function

Author(s):  
Yong Deng

Given a probability distribution, its corresponding information volume is Shannon entropy. However, how to determine the information volume of a given mass function is still an open issue. Based on Deng entropy, the information volume of mass function is presented in this paper. Given a mass function, the corresponding information volume is larger than its uncertainty measured by Deng entropy. In addition, when the cardinal of the frame of discernment is identical, both the total uncertainty case and the BPA distribution of the maximum Deng entropy have the same information volume. Some numerical examples are illustrated to show the efficiency of the proposed information volume of mass function.

Author(s):  
Lipeng Pan ◽  
Yong Deng

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective.


Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 691 ◽  
Author(s):  
Jiapeng Li ◽  
Qian Pan

Dempster–Shafer theory has been widely used in many applications, especially in the measurement of information uncertainty. However, under the D-S theory, how to use the belief entropy to measure the uncertainty is still an open issue. In this paper, we list some significant properties. The main contribution of this paper is to propose a new entropy, for which some properties are discussed. Our new model has two components. The first is Nguyen entropy. The second component is the product of the cardinality of the frame of discernment (FOD) and Dubois entropy. In addition, under certain conditions, the new belief entropy can be transformed into Shannon entropy. Compared with the others, the new entropy considers the impact of FOD. Through some numerical examples and simulation, the proposed belief entropy is proven to be able to measure uncertainty accurately.


Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1122 ◽  
Author(s):  
Yonggang Zhao ◽  
Duofa Ji ◽  
Xiaodong Yang ◽  
Liguo Fei ◽  
Changhai Zhai

It is still an open issue to measure uncertainty of the basic probability assignment function under Dempster-Shafer theory framework, which is the foundation and preliminary work for conflict degree measurement and combination of evidences. This paper proposes an improved belief entropy to measure uncertainty of the basic probability assignment based on Deng entropy and the belief interval, which takes the belief function and the plausibility function as the lower bound and the upper bound, respectively. Specifically, the center and the span of the belief interval are employed to define the total uncertainty degree. It can be proved that the improved belief entropy will be degenerated to Shannon entropy when the the basic probability assignment is Bayesian. The results of numerical examples and a case study show that its efficiency and flexibility are better compared with previous uncertainty measures.


Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1061
Author(s):  
Yu Zhang ◽  
Fanghui Huang ◽  
Xinyang Deng ◽  
Wen Jiang

The Dempster-Shafer theory (DST) is an information fusion framework and widely used in many fields. However, the uncertainty measure of a basic probability assignment (BPA) is still an open issue in DST. There are many methods to quantify the uncertainty of BPAs. However, the existing methods have some limitations. In this paper, a new total uncertainty measure from a perspective of maximum entropy requirement is proposed. The proposed method can measure both dissonance and non-specificity in BPA, which includes two components. The first component is consistent with Yager’s dissonance measure. The second component is the non-specificity measurement with different functions. We also prove the desirable properties of the proposed method. Besides, numerical examples and applications are provided to illustrate the effectiveness of the proposed total uncertainty measure.


Author(s):  
Wen Jiang ◽  
Shiyu Wang

Interval-valued belief structure (IBS), as an extension of single-valued belief structures in Dempster-Shafer evidence theory, is gradually applied in many fields. An IBS assigns belief degrees to interval numbers rather than precise numbers, thereby it can handle more complex uncertain information. However, how to measure the uncertainty of an IBS is still an open issue. In this paper, a new method based on Deng entropy denoted as UIV is proposed to measure the uncertainty of the IBS. Moreover, it is proved that UIV meets some desirable axiomatic requirements. Numerical examples are shown in the paper to demonstrate the efficiency of UIV by comparing the proposed UIV with existing approaches. 


Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 842 ◽  
Author(s):  
Lipeng Pan ◽  
Yong Deng

How to measure the uncertainty of the basic probability assignment (BPA) function is an open issue in Dempster–Shafer (D–S) theory. The main work of this paper is to propose a new belief entropy, which is mainly used to measure the uncertainty of BPA. The proposed belief entropy is based on Deng entropy and probability interval consisting of lower and upper probabilities. In addition, under certain conditions, it can be transformed into Shannon entropy. Numerical examples are used to illustrate the efficiency of the new belief entropy in measurement uncertainty.


Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 73 ◽  
Author(s):  
Kangyang Xie ◽  
Fuyuan Xiao

The negation of probability provides a new way of looking at information representation. However, the negation of basic probability assignment (BPA) is still an open issue. To address this issue, a novel negation method of basic probability assignment based on total uncertainty measure is proposed in this paper. The uncertainty of non-singleton elements in the power set is taken into account. Compared with the negation method of a probability distribution, the proposed negation method of BPA differs becausethe BPA of a certain element is reassigned to the other elements in the power set where the weight of reassignment is proportional to the cardinality of intersection of the element and each remaining element in the power set. Notably, the proposed negation method of BPA reduces to the negation of probability distribution as BPA reduces to classical probability. Furthermore, it is proved mathematically that our proposed negation method of BPA is indeed based on the maximum uncertainty.


Author(s):  
Helena Gaspars-Wieloch

Purpose – scenario planning is very helpful when the decision maker deals with uncertain issues. Probabilities are also frequently applied to such problems. In the paper, we examine the correctness of combining probabilities with scenario planning in economic decisions which are usually made under uncertainty. The goal of the article is to find and discuss cases where the use of probabilities in scenario planning is appropriate and cases where such an approach is not desira-ble. Research methodology – in order to achieve this target, we first make a concise literature review of existing approaches concerning the application of probabilities to scenario planning. Then, we investigate and compare diverse decision mak-ing circumstances presented by means of numerical examples and differing from each other with regard to the nature of the decision problem (way of payoff estimation, novelty degree of the problem, access to historical data etc.) and the de-cision maker’s objectives and preferences (one-shot or multi-shots decisions, attitude towards risk). We explore the newsvendor problem, the spare parts quantity problem, the project selection problem and the project time management with scenario-based decision project graphs. Findings – the work contains both recommendations already described in the literature and suggestions formulated by the author. We get to the point that scenario planning is unquestionable support for decision making under uncertainty, however, the use of probabilities as an accompanying tool may be necessary and justified in some specific cases only. Their significance depends for instance on (1) the number of times a given variant is supposed to be executed; (2) the de-cision maker’s knowledge about the considered problem; (3) the novelty degree of the problem; (4) the decision maker’s conviction that the probability values really reflect his/her attitude towards risk. The analysis of numerical examples leads us to the conclusion that scenario planning should not be linked with the likelihood (1) for one-shot decisions problems; (2) for decision problems related to different kinds of innovation; (3) in the case of lack of certainty which type of proba-bility definition ought to be applied to a given situation; (4) if the decision maker anticipates new future factors not in-cluded in historical data. Research limitations – in the paper we mainly analyse one-criterion problems and payoff matrices with data precisely de-fined. Further conclusions can be obtained after investigating multi-criteria cases and examples with interval payoffs. We limit our research to selected probability definitions. Nevertheless, a wider review can lead to new interesting observa-tions. Practical implications – the aforementioned findings are crucial in such domains as economic modeling and decision the-ory. The results of the research can be used in planning, management, and decision optimization. They provide valuable guidelines for each decision maker dealing with an uncertain future. Originality/Value – authors of previous papers related to this topic have already formulated many significant conclusions. However, this contribution examines the problem from a new point of view since it concentrates on novel decisions, con-cerning unique, innovative or innovation projects (products). It encourages the decision makers to treat problems usually called in the literature “stochastic problems” (i.e. with known probability distribution) as “strategic problems” (i.e. with unknown probability distribution). This is especially the case of the newsvendor problem and the spare parts quantity problem


1988 ◽  
Vol 1 (21) ◽  
pp. 48 ◽  
Author(s):  
Akira Kimura

The probability distribution of the maximum run of irregular wave height is introduced theoretically. Probability distributions for the 2nd maximum, 3rd maximum and further maximum runs are also introduced. Their statistical properties, including the means and their confidence regions, are applied to the verification of experiments with irregular waves in the realization of a "severe sea state" in the test.


2018 ◽  
Vol 2018 ◽  
pp. 1-25
Author(s):  
Weiping Wang ◽  
Meiqi Wang ◽  
Xiong Luo ◽  
Lixiang Li ◽  
Wenbing Zhao

This paper is concerned with the passivity problem of memristive bidirectional associative memory neural networks (MBAMNNs) with probabilistic and mixed time-varying delays. By applying random variables with Bernoulli distribution, the information of probability time-varying delays is taken into account. Furthermore, we consider the probability distribution of the variation and the extent of the delays; therefore, the results derived are less conservative than in the existing papers. In particular, the leakage delays as well as distributed delays are all taken into consideration. Based on appropriate Lyapunov-Krasovskii functionals (LKFs) and some useful inequalities, several conditions for passive performance are established in linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the feasibility of the presented theories, and the results reveal that the probabilistic and mixed time-varying delays have an unstable influence on the system and should not be ignored.


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