Download or read book A new generalization of the proportional con ict redistribution rule stable in terms of decision written by Arnaud Martin and published by Infinite Study. This book was released on with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we present and discuss a new generalized proportional conflict redistribution rule. The Dezert-Smarandache extension of the DempsterShafer theory has relaunched the studies on the combination rules especially for the management of the conflict. Many combination rules have been proposed in the last few years. We study here different combination rules and compare them in terms of decision on didactic example and on generated data. Indeed, in real applications, we need a reliable decision and it is the final results that matter. This chapter shows that a fine proportional conflict redistribution rule must be preferred for the combination in the belief function theory.
Download or read book Generalized proportional con ict redistribution rule applied to Sonar imagery and Radar targets classi cation written by Arnaud Martin and published by Infinite Study. This book was released on with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we present two applications in information fusion in order to evaluate the generalized proportional conflict redistribution rule presented in chapter [7]. Most of the time the combination rules are evaluated only on simple examples. We study here different combination rules and compare them in terms of decision on real data. Indeed, in real applications, we need a reliable decision and it is the final results that matter. Two applications are presented here: a fusion of human experts opinions on the kind of underwater sediments depicted on a sonar image and a classifier fusion for radar targets recognition.
Download or read book Proportional Con ict Redistribution Rules for Information Fusion written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter we propose five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with several examples.
Download or read book Probabilistic PCR6 fusion rule written by Frederic Dambreville and published by Infinite Study. This book was released on with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This chapter defines and implements a non-Bayesian fusion rule for combining densities of probabilities, derived from imprecise knowledge. This rule is the restriction to a strict probabilistic paradigm of the Proportional Conflict Redistribution rule no 6 (PCR6) developed in the DSmT framework for fusing basic belief assignments.
Download or read book Non numeric labels and constrained focal elements written by Christophe Osswald and published by Infinite Study. This book was released on with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of belief functions allows to build a large family of combination operators, based mostly on intersections and unions between the focal elements expressed by the experts, and multiplications and additions on the masses affected to these focal elements.
Download or read book Advances and Applications of DSmT for Information Fusion Collected Works Volume 5 written by Florentin Smarandache and published by Infinite Study. This book was released on 2023-12-27 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 (available at fs.unm.edu/DSmT-book4.pdf or www.onera.fr/sites/default/files/297/2015-DSmT-Book4.pdf) in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. We want to thank all the contributors of this fifth volume for their research works and their interests in the development of DSmT, and the belief functions. We are grateful as well to other colleagues for encouraging us to edit this fifth volume, and for sharing with us several ideas and for their questions and comments on DSmT through the years. We thank the International Society of Information Fusion (www.isif.org) for diffusing main research works related to information fusion (including DSmT) in the international fusion conferences series over the years. Florentin Smarandache is grateful to The University of New Mexico, U.S.A., that many times partially sponsored him to attend international conferences, workshops and seminars on Information Fusion. Jean Dezert is grateful to the Department of Information Processing and Systems (DTIS) of the French Aerospace Lab (Office National d’E´tudes et de Recherches Ae´rospatiales), Palaiseau, France, for encouraging him to carry on this research and for its financial support. Albena Tchamova is first of all grateful to Dr. Jean Dezert for the opportunity to be involved during more than 20 years to follow and share his smart and beautiful visions and ideas in the development of the powerful Dezert-Smarandache Theory for data fusion. She is also grateful to the Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, for sponsoring her to attend international conferences on Information Fusion.
Download or read book General Combination Rules for Qualitative and Quantitative Beliefs written by ARNAUD MARTIN and published by Infinite Study. This book was released on with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martin and Osswald have recently proposed many generalizations of combination rules on quantitative beliefs in order to manage the conflict and to consider the specificity of the responses of the experts. Since the experts express themselves usually in natural language with linguistic labels, Smarandache and Dezert have introduced a mathematical framework for dealing directly also with qualitative beliefs. In this paper we recall some element of our previous works and propose the new combination rules, developed for the fusion of both qualitative or quantitative beliefs.
Download or read book The Geometry of Uncertainty written by Fabio Cuzzolin and published by Springer Nature. This book was released on 2020-12-17 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to introduce to the widest possible audience an original view of belief calculus and uncertainty theory. In this geometric approach to uncertainty, uncertainty measures can be seen as points of a suitably complex geometric space, and manipulated in that space, for example, combined or conditioned. In the chapters in Part I, Theories of Uncertainty, the author offers an extensive recapitulation of the state of the art in the mathematics of uncertainty. This part of the book contains the most comprehensive summary to date of the whole of belief theory, with Chap. 4 outlining for the first time, and in a logical order, all the steps of the reasoning chain associated with modelling uncertainty using belief functions, in an attempt to provide a self-contained manual for the working scientist. In addition, the book proposes in Chap. 5 what is possibly the most detailed compendium available of all theories of uncertainty. Part II, The Geometry of Uncertainty, is the core of this book, as it introduces the author’s own geometric approach to uncertainty theory, starting with the geometry of belief functions: Chap. 7 studies the geometry of the space of belief functions, or belief space, both in terms of a simplex and in terms of its recursive bundle structure; Chap. 8 extends the analysis to Dempster’s rule of combination, introducing the notion of a conditional subspace and outlining a simple geometric construction for Dempster’s sum; Chap. 9 delves into the combinatorial properties of plausibility and commonality functions, as equivalent representations of the evidence carried by a belief function; then Chap. 10 starts extending the applicability of the geometric approach to other uncertainty measures, focusing in particular on possibility measures (consonant belief functions) and the related notion of a consistent belief function. The chapters in Part III, Geometric Interplays, are concerned with the interplay of uncertainty measures of different kinds, and the geometry of their relationship, with a particular focus on the approximation problem. Part IV, Geometric Reasoning, examines the application of the geometric approach to the various elements of the reasoning chain illustrated in Chap. 4, in particular conditioning and decision making. Part V concludes the book by outlining a future, complete statistical theory of random sets, future extensions of the geometric approach, and identifying high-impact applications to climate change, machine learning and artificial intelligence. The book is suitable for researchers in artificial intelligence, statistics, and applied science engaged with theories of uncertainty. The book is supported with the most comprehensive bibliography on belief and uncertainty theory.
Download or read book An In Depth Look at Quantitative Information Fusion Rules written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This chapter may look like a glossary of the fusion rules and we also introduce new ones presenting their formulas and examples.
Download or read book De nition of evidence fusion rules based on referee functions written by Frederic Dambreville and published by Infinite Study. This book was released on with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This chapter defines a new concept and framework for constructing fusion rules for evidences. This framework is based on a referee function, which does a decisional arbitrament conditionally to basic decisions provided by the several sources of information.
Download or read book A class of fusion rules based on the belief redistribution to subsets or complements written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter we present a class of fusion rules based on the redistribution of the conflicting or even non-conflicting masses to the subsets or to the complements of the elements involved in the conflict proportionally with respect to their masses or/and cardinals. At the end, these rules are presented in a more general theoretical way including explicitly the reliability of each source of evidence. Some examples are also provided.
Download or read book Implementing general belief function framework with a practical codi cation for low complexity written by Arnaud Martin and published by Infinite Study. This book was released on with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we propose a new practical codification of the elements of the Venn diagram in order to easily manipulate the focal elements. In order to reduce the complexity, the eventual constraints must be integrated in the codification at the beginning.
Download or read book Target Type Tracking with Di erent Fusion Rules A Comparative Analysis written by J. Dezert and published by Infinite Study. This book was released on with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze the behavior of several combinational rules for temporal/sequential attribute data fusion for target type estimation. Our comparative analysis is based on: Dempster’s fusion rule, Proportional Conflict Redistribution rule no. 5 (PCR5), Symmetric Adaptive Combination (SAC) rule and a new fusion rule, based on fuzzy T-conorm and T-norm operators (TCN).
Download or read book Advances and Applications of DSmT for Information Fusion Vol 3 written by Florentin Smarandache and published by Infinite Study. This book was released on 2004 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume has about 760 pages, split into 25 chapters, from 41 contributors. First part of this book presents advances of Dezert-Smarandache Theory (DSmT) which is becoming one of the most comprehensive and flexible fusion theory based on belief functions. It can work in all fusion spaces: power set, hyper-power set, and super-power set, and has various fusion and conditioning rules that can be applied depending on each application. Some new generalized rules are introduced in this volume with codes for implementing some of them. For the qualitative fusion, the DSm Field and Linear Algebra of Refined Labels (FLARL) is proposed which can convert any numerical fusion rule to a qualitative fusion rule. When one needs to work on a refined frame of discernment, the refinement is done using Smarandache¿s algebraic codification. New interpretations and implementations of the fusion rules based on sampling techniques and referee functions are proposed, including the probabilistic proportional conflict redistribution rule. A new probabilistic transformation of mass of belief is also presented which outperforms the classical pignistic transformation in term of probabilistic information content. The second part of the book presents applications of DSmT in target tracking, in satellite image fusion, in snow-avalanche risk assessment, in multi-biometric match score fusion, in assessment of an attribute information retrieved based on the sensor data or human originated information, in sensor management, in automatic goal allocation for a planetary rover, in computer-aided medical diagnosis, in multiple camera fusion for tracking objects on ground plane, in object identification, in fusion of Electronic Support Measures allegiance report, in map regenerating forest stands, etc.
Download or read book Information Processing and Management of Uncertainty in Knowledge Based Systems written by Marie-Jeanne Lesot and published by Springer Nature. This book was released on 2020-06-05 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three volume set (CCIS 1237-1239) constitutes the proceedings of the 18th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2020, in June 2020. The conference was scheduled to take place in Lisbon, Portugal, at University of Lisbon, but due to COVID-19 pandemic it was held virtually. The 173 papers were carefully reviewed and selected from 213 submissions. The papers are organized in topical sections: homage to Enrique Ruspini; invited talks; foundations and mathematics; decision making, preferences and votes; optimization and uncertainty; games; real world applications; knowledge processing and creation; machine learning I; machine learning II; XAI; image processing; temporal data processing; text analysis and processing; fuzzy interval analysis; theoretical and applied aspects of imprecise probabilities; similarities in artificial intelligence; belief function theory and its applications; aggregation: theory and practice; aggregation: pre-aggregation functions and other generalizations of monotonicity; aggregation: aggregation of different data structures; fuzzy methods in data mining and knowledge discovery; computational intelligence for logistics and transportation problems; fuzzy implication functions; soft methods in statistics and data analysis; image understanding and explainable AI; fuzzy and generalized quantifier theory; mathematical methods towards dealing with uncertainty in applied sciences; statistical image processing and analysis, with applications in neuroimaging; interval uncertainty; discrete models and computational intelligence; current techniques to model, process and describe time series; mathematical fuzzy logic and graded reasoning models; formal concept analysis, rough sets, general operators and related topics; computational intelligence methods in information modelling, representation and processing.
Download or read book A DSmT based Fusion Machine for Robot s Map Reconstruction written by Xinhan Huang and published by Infinite Study. This book was released on with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Characteristics of uncertainty and imprecision, even imperfection is presented from knowledge acquisition in map reconstruction of autonomous mobile robots. Especially in the course of building grid map using sonar, this characteristic of uncertainty is especially servere.
Download or read book Fusion of qualitative beliefs written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: This chapter introduces the notion of qualitative belief assignment to model beliefs of human experts expressed in natural language (with linguistic labels). We show how qualitative beliefs can be efficiently combined using an extension of Dezert-Smarandache Theory (DSmT) of plausible and paradoxical quantitative reasoning to qualitative reasoning.
