## (2004)

### BibTeX

@MISC{Dezert04,

author = {Jean Dezert and Florentin Smarandache},

title = {},

year = {2004}

}

### OpenURL

### Abstract

Fusion of imprecise, uncertain and conflicting beliefs with DSm rules of combination

### Citations

2249 |
A mathematical theory of evidence
- Shafer
- 1976
(Show Context)
Citation Context ... propose new rules of combination which appear to be more attractive than the classical Dempster’s rule of combination proposed by G. Shafer within the development of the Dempster-Shafer Theory (DST) =-=[13]-=-, specially when one has to deal with high conflicting sources of information and/or dynamical fusion problems, where the frame of discernment changes with time. The DSmT allows the fusion of sources,... |

878 |
Interval analysis
- Moore
- 1966
(Show Context)
Citation Context ...To manipulate imprecise information and for the paper to be self-contained, we need to introduce operations on sets as follows (detailed presentations on Interval Analysis and Methods can be found in =-=[7, 8, 10, 11, 12]-=-). The interval operations defined here about imprecision are similar to the rational interval extension through the interval arithmetics [14], but they are different from Modal Interval Analysis whic... |

529 |
Methods and Applications of Interval Analysis
- Moore
- 1979
(Show Context)
Citation Context ...To manipulate imprecise information and for the paper to be self-contained, we need to introduce operations on sets as follows (detailed presentations on Interval Analysis and Methods can be found in =-=[7, 8, 10, 11, 12]-=-). The interval operations defined here about imprecision are similar to the rational interval extension through the interval arithmetics [14], but they are different from Modal Interval Analysis whic... |

508 |
Interval Methods for Systems of Equations
- Neumaier
- 1990
(Show Context)
Citation Context ...To manipulate imprecise information and for the paper to be self-contained, we need to introduce operations on sets as follows (detailed presentations on Interval Analysis and Methods can be found in =-=[7, 8, 10, 11, 12]-=-). The interval operations defined here about imprecision are similar to the rational interval extension through the interval arithmetics [14], but they are different from Modal Interval Analysis whic... |

367 | The transferable belief model - Smets, Kennes - 1994 |

34 | Foundations for a new theory of a plausible and paradoxical reasoning
- Dezert
(Show Context)
Citation Context ...A17, 68T40. 1 Introduction During the last two years, we have developed a new mathematical theory, the DSmT (Dezert Smarandache Theory), for combining uncertain and conflicting sources of information =-=[1, 4, 16, 15]-=-. The DSmT is based on a new modeling of the fusion problem and propose new rules of combination which appear to be more attractive than the classical Dempster’s rule of combination proposed by G. Sha... |

15 | Smarandache F., Partial ordering of hyper-power sets and matrix representation of belief functions within DSmT
- Dezert
- 2003
(Show Context)
Citation Context ... | is the dimension of the hyper-power set, and mij ∈ [0, 1] for all 1 ≤ i ≤ k and 1 ≤ j ≤ d, is the mass assigned by source Bi to the element Aj ∈ DΘ . We use the DSm ordering procedure presented in =-=[5, 16]-=- for enumerating the elements A1, A2, . . . , Ad of the hyper-power set DΘ . The matrix M characterizes all information available which has to be combined to solve the fusion problem under considerati... |

13 | A lucid interval
- Hayes
(Show Context)
Citation Context |

12 | F.Smarandache, On the generation of Hyper-Powersets for the DSmT
- Dezert
- 2003
(Show Context)
Citation Context ...mbination Let’s consider a frame of discernment of a fusion problem Θ = {θ1, θ2, . . .,θn}, its hyper-power set DΘ (i.e. the set of all propositions built from elements θi of Θ with ∩ and ∪ operators =-=[6, 16]-=-, and k independent (precise) sources of information B1, B2, . . ., Bk with their associated generalized basic belief assignments (gbba) m1(.), m2(.), . . ., mk(.) defined over DΘ . Let M be the mass ... |

12 |
Advances and applications of DSmT for information fusion (Collected works), Vols
- Smarandache, Dezert
(Show Context)
Citation Context ...A17, 68T40. 1 Introduction During the last two years, we have developed a new mathematical theory, the DSmT (Dezert Smarandache Theory), for combining uncertain and conflicting sources of information =-=[1, 4, 16, 15]-=-. The DSmT is based on a new modeling of the fusion problem and propose new rules of combination which appear to be more attractive than the classical Dempster’s rule of combination proposed by G. Sha... |

11 |
Calculus with linguistic probabilities and beliefs, Chap. 7
- Lamata, Moral
- 1994
(Show Context)
Citation Context ...ructures represented by real subset intervals of [0, 1] is not new and we strongly encourage the reader to examine previous Lamata & Moral’s together with Denœux’s works for instance on this topic in =-=[9, 2, 3]-=- and references therein. The proposed works available in the literature, upon our knowledge were limited only to sub-unitary interval combination in the framework of Transferable Belief Model (TBM) de... |

8 |
Data Fusion in the Transferable Belief Model
- PH
- 2000
(Show Context)
Citation Context ...herein. The proposed works available in the literature, upon our knowledge were limited only to sub-unitary interval combination in the framework of Transferable Belief Model (TBM) developed by Smets =-=[17, 18]-=-. We extend Lamata & Moral’s together with Denœux’s subunitary interval-valued masses to subunitary set-valued masses; therefore the closed intervals used by Denoeux to denote imprecise masses are gen... |

7 | Reasoning with imprecise belief structures
- Denœux
- 1999
(Show Context)
Citation Context ...{k} � S2) = +∞ One has also as some particular case for k ̸= 0, S2 � {k} = {x | x = s2/k, where s2 ∈ S2} with { inf(S2 � {k}) = inf(S2)/k sup(S2 � {k}) = sup(S2)/k Examples: [0.4, 0.6] � [0.1, 0.2] = =-=[2, 6]-=- because 0.4/0.2 = 2 and 0.6/0.1 = 6; [0.4, 0.6] � {0.4} = [1, 1.5] because 0.4/0.4 = 1 and 0.6/0.4 = 1.5; {0.8} � [0.2, 0.5] = [1.6, 4] because 0.8/0.2 = 4 and 0.8/0.5 = 1.6; [0, 0.5] � [0.1, 0.2] = ... |

6 |
Fondations pour une nouvelle thorie du raisonnement plausible et paradoxal
- Dezert
- 2003
(Show Context)
Citation Context ...A17, 68T40. 1 Introduction During the last two years, we have developed a new mathematical theory, the DSmT (Dezert Smarandache Theory), for combining uncertain and conflicting sources of information =-=[1, 4, 16, 15]-=-. The DSmT is based on a new modeling of the fusion problem and propose new rules of combination which appear to be more attractive than the classical Dempster’s rule of combination proposed by G. Sha... |

1 |
Modal Interval Analysis: An Introduction, http://ima.udg.es/SIGLA/X/mod_interval
- Group
(Show Context)
Citation Context ...terval Analysis and Methods can be found in [7, 8, 10, 11, 12]). The interval operations defined here about imprecision are similar to the rational interval extension through the interval arithmetics =-=[14]-=-, but they are different from Modal Interval Analysis which doesn’t serve our fusion needs. We are not interested in a dual of an interval [a, b], used in the Modal Interval Analysis, because we alway... |