The generation of hyper-power sets


Book Description

The development of DSmT is based on the notion of Dedekind’s lattice, called also hyper-power set in the DSmT framework, on which is defined the general basic belief assignments to be combined. In this chapter, we explain the structure of the hyper-power set, give some examples of hyper-power sets and show how they can be generated from isotone Boolean functions. We also show the interest to work with the hyper-power set rather than the power set of the refined frame of discernment in terms of complexity.




On the generation of hyper-powersets for the DSmT


Book Description

The recent theory of plausible and paradoxical reasoning (DSmT) developed by the authors appears to be a nice promising theoretical tools to solve many information fusion problems where the Shafer’s model cannot be used due to the intrinsic paradoxical nature of the elements of the frame of discernment and where a strong internal conflict between sources arises.




Partial ordering on hyper-power sets


Book Description

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.




Partial ordering of hyper-powersets and matrix representation of belief functions within DSmT


Book Description

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.




An introduction to DSmT


Book Description

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or highly conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning.




A Comparison of the Generalized minC Combination and the Hybrid DSm Combination Rules


Book Description

A generalization of the minC combination to DSm hyper-power sets is presented. Both the special formulas for static fusion or dynamic fusion without non-existential constraints and the quite general formulas for dynamic fusion with non-existential constraints are included. Examples of the minC combination on several different hybrid DSm models are presented. A comparison of the generalized minC combination with the hybrid DSm rule is discussed and explained on examples.




Satellite image fusion using Dezert-Smarandache theory


Book Description

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.




A Generalized Pignistic Transformation


Book Description

This chapter introduces a generalized pignistic transformation (GPT) developed in the DSmT framework as a tool for decision-making at the pignistic level. The GPT allows to construct quite easily a subjective probability measure from any generalized basic belief assignment provided by any corpus of evidence. We focus our presentation on the 3D case and we provide the full result obtained by the proposed GPT and its validation drawn from the probability theory.







Advances and Applications of DSmT for Information Fusion (Collected works)


Book Description

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).