A New Probability Transformation Approach Of Mass Function

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Among its associated studies, a pivotal challenge is the transformation of mass functions into probability distributions which can enhance the robustness and reliability of decision-making. In this paper, influence factor is constructed by considering the impact of transformation between multi-element propositions and single-element This ambiguity is due to vagueness rather than randomness. Even if these approaches do not assume any particular probability distribution for the gray level values, they suffer from the fact that mass values are derived in a heuristic manner. The mass functions may also be derived from probabilities.

However, the probabilistic methodologies often rely on prior knowledge of probability density function (PDF) of the considered random variables (RVs). In this study, a new formulation called the fourth-moment pseudo-normal transformation (FMNT) is employed to perform the probabilistic analysis of a tunnel support system. In this paper we discuss the properties of the intersection probability, a recent Bayesian approximation of belief functions introduced by

MATH 550: The Probability Integral Transform

Solved 1. Suppose the probability mass function of X is | Chegg.com

Copula Transformations It is sometimes useful to be able to transform a random variable with one distribution into a random variable with another. e.g. How do I turn a N(1; 4) random variable Z into an Exp(2) random variable, Y ? By the PIT, Z N(1; 4) , U := In the fields of science and engineering, complex dynamical systems often involve multiple response processes with intricate probabilistic dependencies [1], [2]. To capture the joint probability density function (PDF) of these response processes poses a significant challenge due to its complex and nonlinear nature, making it difficult to be tackled by using traditional 2.1 The Main Theorem We rst start with the simplest case where A and B are both subsets of the real line R. Let x 2 A. The number pA(x) means that, in the in nitesimal interval [x; x + x), there exists pA(x) x amount of \probability mass.“ Here, x is a \di erential quantity“ such that ( x)2 = 0. Assume that f is continuous and in nitely di erentiable. The function f sends the interval [x; x

Therefore, a new probabilistic transformation of interval-valued belief structure is put forward in the generalized power space, in order to build a subjective probability measure from any basic belief assignment defined on any model of the frame of discernment.

In order to explore the fractal characteristic in Dempster–Shafer evidence theory, a fractal dimension of mass function is proposed recently, to reveal the invariance of scale of belief entropy. When mass function degenerates to probability, the fractal dimension is equivalent to classical Renyi information dimension only with $$\\alpha = 1$$ α = 1 , which can measure the The information volume of mass function (IVMF) is an effective tool for measuring the uncertainty of basic probability assignments in power sets. Howe

Abstract Smets proposes the Pignistic Probability Transformation (PPT) as the decision layer in the Transferable Belief Model (TBM), which argues when there is no more information, we have to make a decision using a Probability Mass Function (PMF). 1 Discrete Random Variables For X a discrete random variable with probabiliity mass function fX, then the probability mass function fY for Y = g(X) is easy to write. fY (y) =

A new probability transformation method based on a correlation coefficient of belief functions, International Journal of Intelligent Systems 34 (6) (2019) 1337–1347.

Lecture 9: Transformations; Joint Distributions

The probability results of four transformed methods for element 7.
Probability Density Under Transformation
A new probabilistic transformation of belief mass assignment
Fractal-based basic probability assignment: A transient mass function

在概率论中，概率质量函数（probability mass function，简写为pmf）是离散随机变量在各特定取值上的概率。 Request PDF | On Jun 1, 2025, Haocheng Shao and others published Influence factor-based transformation method for translating mass function to probability in Dempster–Shafer evidence theory

To alleviate this problem, this study proposes a model named probability mass function GANs (PMF-GAN), which handles the inherent limitation of GANs. The PMF-GAN framework employs kernels, histogram transformation, and probability mass function (PMF) distance for distribution learning. The high-precision estimation of a multimodal probability density function is a difficult problem in many engineering fields. We propose a new method to improve the estimation accuracy based on the fractional moment-based maximum entropy method with a nonlinear transformation and a multi-peak recognition method. For the translation parameters in the

Probability Mass Function

In the decision-making process, transforming the mass function into the decision probability can remove the uncertainty of knowledge and thus reduce the difficulty of decision making. For this reason, this paper puts forward a novel transformation approach based on the value function of prospect theory. The new approach considers the support degree of the single subset from the In Dempster–Shafer evidence theory, how to use the basic probability assignment (BPA) in decision‐making is a significant issue. The transformation of BPA into a probability distribution

Among its associated studies, a pivotal challenge is the transformation of mass functions into probability distributions which can enhance the robustness and reliability of decision-making. In this paper, influence factor is constructed by considering the impact of transformation between multi-element propositions and single-element Similar to the information volume in probability theory, Deng [29] proposes the information volume of mass function in DST based on fractal and maximum Deng entropy, which can express the uncertainty more general. In this paper, a new weighted evidence combination on the basis of the distance between evidence and entropy function is presented. The proposed approach is identified as two procedures.

A novel combination rule for conflict management in data fusion

A new OVG-based probability transformation was proposed to transform BPAs into probabilities in this paper. In the proposed transformation method, given one body of BPAs, an OVG can be obtained

We give a new interpretation of basic belief assignment transformation into probability distribution, and use directed acyclic network called belief evolution network to describe the causality

However, the transformation method cannot make reasonable allocation when a certain singleton is not contained in the multi-subset focal elements. From a geometric interpretation of Dempster’s combination rule, Cuzzolin [51] defined a new decision probability transformation method in the framework of DS evidence theory. In this paper, we propose in Dezert-Smarandache Theory (DSmT) framework, a new probabilistic transformation, called DSmP, in order to build a subjective probability measure from any basic belief Similar to the information volume in probability theory, Deng [29] proposes the information volume of mass function in DST based on fractal and maximum Deng entropy, which can express the uncertainty more general.

When the transformation \ (r\) is one-to-one and smooth, there is a formula for the probability density function of \ (Y\) directly in terms of the probability density function of \ (X\). Download scientific diagram | The probability results of four transformed methods for element 7. from publication: A New Probability Transformation Based on the Ordered Visibility Graph | One of The information volume of mass function (IVMF) is an effective tool for measuring the uncertainty of basic probability assignments in power sets. Howe

In this paper, we introduce a Transient Mass Function (TMF) based on the process of pignistic probability transformation to forge a link between probabilistic and evidential information. As a transient state of BPA, the TMF not only considers the structural features of the focal element but also maintains its numerical content.

A new insight for probability transformation is provided, using the negation operation to obtain additional information of mass functions from the opposite side, and mass functions can be transformed to probabilities by proportion reasonably. Smets proposes the Pignistic Probability Transformation (PPT) as the decision layer in the Transferable Belief Model (TBM), which argues when there is no more information, we have to make a decision using a Probability Mass Function (PMF). In this paper, the Belief Evolution Network (BEN) and the full causality function are proposed by introducing causality in

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