Download or read book Partial ordering of hyper powersets and matrix representation of belief functions within DSmT written by Jean Dezert and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we examine several issues for ordering or partially ordering elements of hyperpowertsets involved in the recent theory of plausible, uncertain and paradoxical reasoning (DSmT) developed by the authors. We will show the benefit of some of these issues to obtain a nice and useful matrix representation of belief functions.
Download or read book Partial ordering on hyper power sets written by Jean Dezert and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we examine several issues for ordering or partially or dering elements of hyper-power sets involved in the DSmT. We will show the benefit of some of these issues to obtain a nice and interesting structure of matrix represen tation of belief functions.
Download or read book Advances and Applications of DSmT for Information Fusion Collected works second volume written by Florentin Smarandache and published by Infinite Study. This book was released on 2006-01-01 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence. Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm and N-conorm (hence using neutrosophic logic and neutrosophic set in information fusion), and an attempt to unify the fusion rules and fusion theories. The known fusion rules are extended from the power set to the hyper-power set and comparison between rules are made on many examples. One defines the degree of intersection of two sets, degree of union of two sets, and degree of inclusion of two sets which all help in improving the all existing fusion rules as well as the credibility, plausibility, and communality functions. The book chapters are written by Frederic Dambreville, Milan Daniel, Jean Dezert, Pascal Djiknavorian, Dominic Grenier, Xinhan Huang, Pavlina Dimitrova Konstantinova, Xinde Li, Arnaud Martin, Christophe Osswald, Andrew Schumann, Tzvetan Atanasov Semerdjiev, Florentin Smarandache, Albena Tchamova, and Min Wang.
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 Advances and Applications of DSmT for Information Fusion Collected works written by Florentin Smarandache and published by Infinite Study. This book was released on 2004 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers collected from researchers in fusion information, such as: Florentin Smarandache, Jean Dezert, Hongshe Dang, Chongzhao Han, Frederic Dambreville, Milan Daniel, Mohammad Khoshnevisan, Sukanto Bhattacharya, Albena Tchamova, Tzvetan Semerdjiev, Pavlina Konstantinova, Hongyan Sun, Mohammad Farooq, John J. Sudano, Samuel Corgne, Gregoire Mercier, Laurence Hubert-Moy, Anne-Laure Jousselme, Patrick Maupin and others on Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning (DSmT).. The principal theories available until now for data fusion are the probability theory, the fuzzy set theory, the possibility theory, the hint theory and the theory of evidence. Since last two years J. Dezert and F. Smarandache are actively developing a new theory of plausible and paradoxical reasoning, called DSmT (acronym for Dezert-Smarandache Theory), for information fusion of uncertain and highly conflicting sources of information. The DSmT can be interpreted as a generalization of the Dempster-Shafer Theory (DST) but goes far beyond the DST. The free-DSmT model, which assumes that the ultimate refinement of the frame of discernment of the fusion problem is not accessible due to the intrinsic nature of its elements, is opposite to the Shafer's model (on which is based the DST) assuming the exhaustivity and exclusivity of all elements of the frame of discernment. The DSmT proposes a new theoretical framework for data fusion based on definition of hyper-power sets and a new simple commutative and associative rule of combination. Recently, it has been discovered, through a new DSm hybrid rule of combination, that DSmT can be also extended to problems involving hybrid-models (models including some exclusivity and/or non-existentially constraints). This new important theoretical result offers now to the DSmT a wider class of fusion applications and allows potentially to attack the next generation of complex dynamical/temporal fusion problems. DSmT can also provide a theoretical issue for the fusion of neutrosophic information (extension of fuzzy information proposed by F. Smarandache in nineties - see http://www.gallup.unm.edu/~smarandache/FirstNeutConf.htm for details about the neutrosophy logic and neutrosophy set theory).
Download or read book The Generalized Pignistic Transformation written by Jean Dezert and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents in detail the generalized pignistic transformation (GPT)succinctly developed in the Dezert-Smarandache Theory (DSmT) framework as a tool for decision process. The GPT allows to provide a subjective probability measure from any generalized basic belief assignment given by any corpus of evidence. We mainly focus our presentation on the 3D case and provide the complete result obtained by the GPT and its validation drawn from the probability theory.
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 Combining uncertain and paradoxical evidences for DSm hybrid models written by Jean Dezert and published by Infinite Study. This book was released on with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a general method for combining uncertain and paradoxical source of evidences for a wide class of fusion problems.
Download or read book On the Tweety Penguin Triangle Problem written by Jean Dezert and published by Infinite Study. This book was released on with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, one studies the famous well-known and challenging Tweety Penguin Triangle Problem (TPTP or TP2) pointed out by Judea Pearl in one of his books.
Download or read book On the Blackman s Association Problem written by Jean Dezert and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern multitarget-multisensor tracking systems involve the development of reliable methods for the data association and the fusion of multiple sensor information, and more specifically the partioning of observations into tracks. This paper discusses and compares the application of Dempster-Shafer Theory (DST) and the Dezert-Smarandache Theory (DSmT) methods to the fusion of multiple sensor attributes for target identification purpose. We focus our attention on the paradoxical Blackman’s association problem and propose several approaches to outperfom Blackman’s solution. We clarify some preconceived ideas about the use of degree of conflict between sources as potential criterion for partitioning evidences.
Download or read book Modeling and Characterization of Vegetation Aquatic and Mineral Surfaces Using the Theory of Plausible and Paradoxical Reasoning from Satellite Images Case of the Toumodi Yamoussoukro Ti bissou Zone in V Baoul C te d Ivoire written by Jean-Claude Okaingni 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 paper, the theory of plausible and paradoxical reasoning of Dezert- Smarandache (DSmT) is used to take into account the paradoxical character through the intersections of vegetation, aquatic and mineral surfaces. In order to do this, we developed a classification model of pixels by aggregating information using the DSmT theory based on the PCR5 rule using the NDVI, MNDWI and NDBaI spectral indices obtained from the ASTER satellite images.
Download or read book DSm models and Non Archimedean Reasoning written by Andrew Schumann and published by Infinite Study. This book was released on with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dezert-Smarandache theory of plausible and paradoxical reasoning is based on the premise that some elements θi of a frame Θ have a non-empty intersection.
Download or read book Neutrosophic logics on Non Archimedean Structures written by Andrew Schumann and published by Infinite Study. This book was released on with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom.
Download or read book FUSION written by and published by . This book was released on 2003 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Satellite image fusion using Dezert Smarandache theory written by Abdenour Bouakache and published by Infinite Study. This book was released on with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free and hybrid models of multisource satellite images fusion are developed using the plausible and paradoxical reasoning theory of Dezert-Smarandache. The aim of this work is to show the contribution of these fusion models for improving the thematic classification and the quantification of change.
Download or read book In nite classes of counter examples to the Dempster s rule of combination written by Jean Dezert and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents several classes of fusion problems which cannot be directly attacked by the classical mathematical theory of evidence, also known as the Dempster-Shafer Theory (DST) either because the Shafer’s model for the frame of discernment is impossible to obtain or just because the Dempster’s rule of combination fails to provide coherent results (or no result at all). We present and discuss the potentiality of the DSmT combined with its classical (or hybrid) rule of combination to attack these infinite classes of fusion problems.
Download or read book Advances and Applications of DSmT for Information Fusion Collected Works Volume 4 written by Florentin Smarandache and published by Infinite Study. This book was released on 2015-07-01 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth volume on Advances and Applications of Dezert-Smarandache Theory (DSmT) for information fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics. The contributions have been published or presented after disseminating the third volume (2009, http://fs.gallup.unm.edu/DSmT-book3.pdf) in international conferences, seminars, workshops and journals.
