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Author: Yuan-Wei Du Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 40
Book Description
The Dempster–Shafer (DS) theory of evidence can combine evidence with one parameter. The evidential reasoning (ER) approach is an extension of DS theory that can combine evidence with two parameters (weights and reliabilities). However, it has three infeasible aspects: reliability dependence, unreliability effectiveness, and intergeneration inconsistency.
Author: Yuan-Wei Du Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 40
Book Description
The Dempster–Shafer (DS) theory of evidence can combine evidence with one parameter. The evidential reasoning (ER) approach is an extension of DS theory that can combine evidence with two parameters (weights and reliabilities). However, it has three infeasible aspects: reliability dependence, unreliability effectiveness, and intergeneration inconsistency.
Author: Glenn Shafer Publisher: Princeton University Press ISBN: 0691214697 Category : Mathematics Languages : en Pages :
Book Description
Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental. The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds to develop an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions. This rule, together with the idea of "weights of evidence," leads to both an extensive new theory and a better understanding of the Bayesian theory. The book concludes with a brief treatment of statistical inference and a discussion of the limitations of epistemic probability. Appendices contain mathematical proofs, which are relatively elementary and seldom depend on mathematics more advanced that the binomial theorem.
Author: Xiangjun Mi Publisher: Infinite Study ISBN: Category : Mathematics Languages : en Pages : 30
Book Description
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Author: Zhan Deng Publisher: Infinite Study ISBN: Category : Education Languages : en Pages : 11
Book Description
In Dempster–Shafer evidence theory, the basic probability assignment (BPA) can effectively represent and process uncertain information. How to transform the BPA of uncertain information into a decision probability remains a problem to be solved. In the light of this issue, we develop a novel decision probability transformation method to realize the transition from the belief decision to the probability decision in the framework of Dempster–Shafer evidence theory. The newly proposed method considers the transformation of BPA with multi-subset focal elements from the perspective of the belief interval, and applies the continuous interval argument ordered weighted average operator to quantify the data information contained in the belief interval for each singleton. Afterward, we present an approach to calculate the support degree of the singleton based on quantitative data information. According to the support degree of the singleton, the BPA of multi-subset focal elements is allocated reasonably. Furthermore, we introduce the concepts of probabilistic information content in this paper, which is utilized to evaluate the performance of the decision probability transformation method. Eventually, a few numerical examples and a practical application are given to demonstrate the rationality and accuracy of our proposed method.
Author: Kari Sentz Publisher: ISBN: Category : Dempster-Shafer theory Languages : en Pages : 100
Book Description
Dempster-Shafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. The significant innovation of this framework is that it allows for the allocation of a probability mass to sets or intervals. Dempster-Shafer theory does not require an assumption regarding the probability of the individual constituents of the set or interval. This is a potentially valuable tool for the evaluation of risk and reliability in engineering applications when it is not possible to obtain a precise measurement from experiments, or when knowledge is obtained from expert elicitation. An important aspect of this theory is the combination of evidence obtained from multiple sources and the modeling of conflict between them. This report surveys a number of possible combination rules for Dempster-Shafer structures and provides examples of the implementation of these rules for discrete and interval-valued data.
Author: Ronald R. Yager Publisher: Springer ISBN: 354044792X Category : Technology & Engineering Languages : en Pages : 813
Book Description
This is a collection of classic research papers on the Dempster-Shafer theory of belief functions. The book is the authoritative reference in the field of evidential reasoning and an important archival reference in a wide range of areas including uncertainty reasoning in artificial intelligence and decision making in economics, engineering, and management. The book includes a foreword reflecting the development of the theory in the last forty years.
Author: David Hall Publisher: CRC Press ISBN: 1420038540 Category : Technology & Engineering Languages : en Pages : 564
Book Description
The emerging technology of multisensor data fusion has a wide range of applications, both in Department of Defense (DoD) areas and in the civilian arena. The techniques of multisensor data fusion draw from an equally broad range of disciplines, including artificial intelligence, pattern recognition, and statistical estimation. With the rapid evolut
Author: Weiru Liu Publisher: Physica ISBN: 3790818119 Category : Computers Languages : en Pages : 279
Book Description
How to draw plausible conclusions from uncertain and conflicting sources of evidence is one of the major intellectual challenges of Artificial Intelligence. It is a prerequisite of the smart technology needed to help humans cope with the information explosion of the modern world. In addition, computational modelling of uncertain reasoning is a key to understanding human rationality. Previous computational accounts of uncertain reasoning have fallen into two camps: purely symbolic and numeric. This book represents a major advance by presenting a unifying framework which unites these opposing camps. The Incidence Calculus can be viewed as both a symbolic and a numeric mechanism. Numeric values are assigned indirectly to evidence via the possible worlds in which that evidence is true. This facilitates purely symbolic reasoning using the possible worlds and numeric reasoning via the probabilities of those possible worlds. Moreover, the indirect assignment solves some difficult technical problems, like the combinat ion of dependent sources of evidcence, which had defeated earlier mechanisms. Weiru Liu generalises the Incidence Calculus and then compares it to a succes sion of earlier computational mechanisms for uncertain reasoning: Dempster-Shafer Theory, Assumption-Based Truth Maintenance, Probabilis tic Logic, Rough Sets, etc. She shows how each of them is represented and interpreted in Incidence Calculus. The consequence is a unified mechanism which includes both symbolic and numeric mechanisms as special cases. It provides a bridge between symbolic and numeric approaches, retaining the advantages of both and overcoming some of their disadvantages.
Author: Yuan-Wei Du
Author: Yuan-Wei Du
Author: Glenn Shafer
Author: Xiangjun Mi
Author: Zhan Deng
Author: Kari Sentz
Author: Ronald R. Yager
Author: University of California, Berkeley. Cognitive Science Program
Author: Lotfi Asker Zadeh
Author: David Hall
Author: Weiru Liu