Probability Rules Cheat Sheet. Basic probability rules with examples
The basic probability assignment (BPA) as an example.
Basic probability assignment table.
Basic probability assignment to each line and their combination m(L1
(PDF) Methods to Obtain Basic Probability Assignment in Evidence Theory
accumulated basic probability assignment of each cycle
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# BASIC CONCEPTS OF PROBABILITY THEORY #
Selected Assignment Questions of Probability Part 2
Probability introduction, assignment of probability
STA301 Statistics & Probability Assignment 1 Spring 2024 Virtual University of Pakistan
Introduction to probability and Statistics Week 4 Quiz Assignment Solution
Lec2/Basic Probability/GTU Exam Questions
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Determination of Basic Probability Assignment Based on Probability
In the application of Dempster-Shafer (D-S) evidence theory, the determination of basic probability assignment (BPA) is a key step. How to determine BPA is an open issue. To solve this problem, a new method to determine BPA based on probability distribution is proposed in this paper. First, the approximate distribution of training set is constructed. Next, the distance is proposed according to ...
A new method to determine basic probability assignment from training
However, how to determine the basic probability assignment (BPA), which is the main and first step in D-S theory, is still an open issue. In this paper, based on the normal distribution, a method to obtain BPA is proposed. The training data are used to build a normal distribution-based model for each attribute of the data.
Probability Assignment
A basic probability assignment is a mapping m from the set of all subsets of a universal finite nonempty set X to the interval [0, 1], but it need not meet all the probability measure requirements. From: North-Holland Series in Applied Mathematics and Mechanics, 2004
A novel method to determine basic probability assignment in Dempster
Moreover, the proposed basic probability assignment generation method is extended by K-nearest neighbor (K-NN) algorithm. The detailed implementation of the proposed method is demonstrated by several numerical examples. As an extension, a classifier called KKC is constructed according to the developed approach, and its classification effect ...
Generating method and application of basic probability assignment based
In the Dempster-Shafer (D-S) evidence theory, how to transform the objective data in reality into the basic probability assignment (BPA) is still an open issue. Based on this problem, a new method of generating BPA based on interval number distance model and reliability is proposed. First, construct the interval number model under each attribute. Second, calculate the interval number ...
PDF Lecture Notes 1 Basic Probability
ω∈Ω. P({ω}) = 1 • The probability of any other event A(by the additivity axiom) is simply P(A) = X. ω∈A. P({ω}) EE 178/278A: Basic Probability Page 1-15. • Examples: For the coin flipping experiment, assign P({H}) = pand P({T}) = 1 −p, for 0 ≤ p≤ 1 Note: pis the bias of the coin, and a coin is fair if p=1 2.
An improved method to determine basic probability assignment with
Finally, Dempster's combination rule is used to combine multiple basic probability assignments to get the final basic probability assignment. The experiments on Iris data set that is widely used in classification problem illustrated that the proposed method is effective in determining basic probability assignment and classification problem ...
A New Method to Determine Basic Probability Assignment Based on
Dempster-Shafer evidence theory(D-S theory) is a widely used method in information fusion fields. The significant step in applying D-S theory is to determine the basic probability assignment(BPA). But how to determine BPA appropriately is still a problem to be solved. In this paper, we propose a new formula for calculating the similarity of interval numbers and introduce attribute weights ...
A new generation method of basic probability assignment based on the
Dempster-Shafer evidence theory is an important technique to fuse uncertain information and make decisions. As the first step of applying the evidence theory in practical applications, the generation of basic probability assignment(BPA) directly affects the subsequent fusion and decision-making. However, it is still a difficult and open issue. This paper proposed a new method to generate BPA ...
An improved method to construct basic probability assignment based on
The determination of basic probability assignment (BPA) is a crucial issue in the application of Dempster-Shafer evidence theory. Classification is a process of determining the class label that a sample belongs to. In classification problem, the construction of BPA based on the confusion matrix has been studied. However, the existing methods ...
PDF Dempster-Shafer's Basic Probability Assignment Based on Fuzzy
called basic probability assignment (BPA) or mass function. This probability assigns evidence to a proposition (hypothesis). The derivation of the BPA is the most crucial step since it represents the knowledge about the application as well as the uncertainty incorporates in the selected information source. BPA definition remains
Basic probability assignment to probability distribution function based
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 ...
An Improved Approach for Generation of a Basic Probability Assignment
Generation of basic probability assignment will be based on two methods: (1) using the function value of Gaussian distribution, and (2) using the probability intervals of Gaussian distribution. Figure 1 is a flowchart of generating BPA with the proposed method. The specific steps are as follows.
Visualization of basic probability assignment
Applying geometry to the analysis and interpretation of basic probability assignment (BPA) is a unique research direction in evidence theory. Among them, the visualization of BPA helps to intuitively analyze the geometric properties and characteristics of BPA, which is an important research content in this direction, but there are currently few related studies. In response to this problem, we ...
A new classification method based on the negation of a basic
The body of evidence (BOE), also known as basic probability assignment (BPA) or basic belief assignment (BBA), is defined as the focal sets and the corresponding mass functions: (3) ℜ, m = A, m A: A ∈ 2 Ω, m A > 0. where ℜ is a subset of the power set 2 Ω. Definition 3.4
A new approach for generation of generalized basic probability
A new method is proposed to generate the generalized basic probability assignment (GBPA) based on the triangular fuzzy number model under the open-world assumption. First, the maximum, minimum, and mean values for the triangular membership function of each attribute in classification problem can be obtained to construct a triangular fuzzy ...
Basic Probability Assignment Using Intuitive Fuzzy Cloud Model for
The Dempster-Shafer (DS) evidence theory is the most popular information fusion method, which takes Basic Probability Assignments (BPAs) as its fusion elements. The precision of BPAs directly affects the decision results; however, it is still a challenging issue to obtain reliable BPAs. This article proposes a novel approach for generating ...
4.1 Introduction to Probability and Random Variables
Random Variables. Random variables (RVs) are probability models quantifying situations. A random variable describes the outcomes of a statistical experiment in words or as a function that assigns each element of a sample space a unique real number. Uppercase letters such as X or Y typically denote a random variable. Lowercase letters like x or y denote a specific value of that random variable.
Fractal-based basic probability assignment: A transient mass function
Belief information measure. Fractal-based basic probability assignment. 1. Introduction. Dempster-Shafer theory, a generalization of probability theory, is based on upper and lower probabilities through multivalued mapping [1], [2]. Also known as evidence theory or belief function theory, it is adept at expressing stochastic uncertainty, as ...
The Negation of a Basic Probability Assignment
The Negation of a Basic Probability Assignment. Abstract: In the field of information science, how to represent the uncertain information is still an open issue. The negation is an important way to represent the information. However, existing negation method has the limitations since it can only be applied to the probability distributions.
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COMMENTS
In the application of Dempster-Shafer (D-S) evidence theory, the determination of basic probability assignment (BPA) is a key step. How to determine BPA is an open issue. To solve this problem, a new method to determine BPA based on probability distribution is proposed in this paper. First, the approximate distribution of training set is constructed. Next, the distance is proposed according to ...
However, how to determine the basic probability assignment (BPA), which is the main and first step in D-S theory, is still an open issue. In this paper, based on the normal distribution, a method to obtain BPA is proposed. The training data are used to build a normal distribution-based model for each attribute of the data.
A basic probability assignment is a mapping m from the set of all subsets of a universal finite nonempty set X to the interval [0, 1], but it need not meet all the probability measure requirements. From: North-Holland Series in Applied Mathematics and Mechanics, 2004
Moreover, the proposed basic probability assignment generation method is extended by K-nearest neighbor (K-NN) algorithm. The detailed implementation of the proposed method is demonstrated by several numerical examples. As an extension, a classifier called KKC is constructed according to the developed approach, and its classification effect ...
In the Dempster-Shafer (D-S) evidence theory, how to transform the objective data in reality into the basic probability assignment (BPA) is still an open issue. Based on this problem, a new method of generating BPA based on interval number distance model and reliability is proposed. First, construct the interval number model under each attribute. Second, calculate the interval number ...
ω∈Ω. P({ω}) = 1 • The probability of any other event A(by the additivity axiom) is simply P(A) = X. ω∈A. P({ω}) EE 178/278A: Basic Probability Page 1-15. • Examples: For the coin flipping experiment, assign P({H}) = pand P({T}) = 1 −p, for 0 ≤ p≤ 1 Note: pis the bias of the coin, and a coin is fair if p=1 2.
Finally, Dempster's combination rule is used to combine multiple basic probability assignments to get the final basic probability assignment. The experiments on Iris data set that is widely used in classification problem illustrated that the proposed method is effective in determining basic probability assignment and classification problem ...
Dempster-Shafer evidence theory(D-S theory) is a widely used method in information fusion fields. The significant step in applying D-S theory is to determine the basic probability assignment(BPA). But how to determine BPA appropriately is still a problem to be solved. In this paper, we propose a new formula for calculating the similarity of interval numbers and introduce attribute weights ...
Dempster-Shafer evidence theory is an important technique to fuse uncertain information and make decisions. As the first step of applying the evidence theory in practical applications, the generation of basic probability assignment(BPA) directly affects the subsequent fusion and decision-making. However, it is still a difficult and open issue. This paper proposed a new method to generate BPA ...
The determination of basic probability assignment (BPA) is a crucial issue in the application of Dempster-Shafer evidence theory. Classification is a process of determining the class label that a sample belongs to. In classification problem, the construction of BPA based on the confusion matrix has been studied. However, the existing methods ...
called basic probability assignment (BPA) or mass function. This probability assigns evidence to a proposition (hypothesis). The derivation of the BPA is the most crucial step since it represents the knowledge about the application as well as the uncertainty incorporates in the selected information source. BPA definition remains
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 ...
Generation of basic probability assignment will be based on two methods: (1) using the function value of Gaussian distribution, and (2) using the probability intervals of Gaussian distribution. Figure 1 is a flowchart of generating BPA with the proposed method. The specific steps are as follows.
Applying geometry to the analysis and interpretation of basic probability assignment (BPA) is a unique research direction in evidence theory. Among them, the visualization of BPA helps to intuitively analyze the geometric properties and characteristics of BPA, which is an important research content in this direction, but there are currently few related studies. In response to this problem, we ...
The body of evidence (BOE), also known as basic probability assignment (BPA) or basic belief assignment (BBA), is defined as the focal sets and the corresponding mass functions: (3) ℜ, m = A, m A: A ∈ 2 Ω, m A > 0. where ℜ is a subset of the power set 2 Ω. Definition 3.4
A new method is proposed to generate the generalized basic probability assignment (GBPA) based on the triangular fuzzy number model under the open-world assumption. First, the maximum, minimum, and mean values for the triangular membership function of each attribute in classification problem can be obtained to construct a triangular fuzzy ...
The Dempster-Shafer (DS) evidence theory is the most popular information fusion method, which takes Basic Probability Assignments (BPAs) as its fusion elements. The precision of BPAs directly affects the decision results; however, it is still a challenging issue to obtain reliable BPAs. This article proposes a novel approach for generating ...
Random Variables. Random variables (RVs) are probability models quantifying situations. A random variable describes the outcomes of a statistical experiment in words or as a function that assigns each element of a sample space a unique real number. Uppercase letters such as X or Y typically denote a random variable. Lowercase letters like x or y denote a specific value of that random variable.
Belief information measure. Fractal-based basic probability assignment. 1. Introduction. Dempster-Shafer theory, a generalization of probability theory, is based on upper and lower probabilities through multivalued mapping [1], [2]. Also known as evidence theory or belief function theory, it is adept at expressing stochastic uncertainty, as ...
The Negation of a Basic Probability Assignment. Abstract: In the field of information science, how to represent the uncertain information is still an open issue. The negation is an important way to represent the information. However, existing negation method has the limitations since it can only be applied to the probability distributions.