By editors F. Smarandache & J. Dezert

This quantity has approximately 760 pages, cut up into 25 chapters, from forty-one individuals. First a part of this publication provides advances of Dezert-Smarandache conception (DSmT) that's turning into probably the most finished and versatile fusion concept in line with trust capabilities. it could paintings in all fusion areas: strength set, hyper-power set, and super-power set, and has a variety of fusion and conditioning principles that may be utilized counting on each one software. a few new generalized ideas are brought during this quantity with codes for imposing a few of them. For the qualitative fusion, the DSm box and Linear Algebra of sophisticated Labels (FLARL) is proposed which may convert any numerical fusion rule to a qualitative fusion rule. while one must paintings on a elegant body of discernment, the refinement is finished utilizing Smarandache s algebraic codification. New interpretations and implementations of the fusion principles in line with sampling ideas and referee services are proposed, together with the probabilistic proportional clash redistribution rule. a brand new probabilistic transformation of mass of trust is usually awarded which outperforms the classical pignistic transformation in time period of probabilistic details content material. the second one a part of the booklet offers purposes of DSmT in goal monitoring, in satellite tv for pc photo fusion, in snow-avalanche danger overview, in multi-biometric fit rating fusion, in overview of an characteristic info retrieved in accordance with the sensor info or human originated details, in sensor administration, in automated target allocation for a planetary rover, in computer-aided clinical analysis, in a number of digicam fusion for monitoring items on flooring aircraft, in item identity, in fusion of digital help Measures allegiance document, in map regenerating wooded area stands, and so on.

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**Example text**

94 which is less than 1. Therefore Dubois & Prade’s rule of combination does not work when a singleton, or an union of singletons, becomes empty (in a dynamic fusion problem). 5) which transfers these products to the total or partial ignorances. 41 = mDP (θ1 ∪ θ2 ) We can easily verify that mDSmH (θ1 ) + mDSmH (θ2 ) + mDSmH (θ1 ∪ θ2 ) = 1. 41. Clearly, DSmH rule doesn’t provide the same result as Dubois and Prade’s rule, but only when working on static frames of discernment (restricted cases). 7 Fusion of imprecise beliefs In many fusion problems, it seems very diﬃcult (if not impossible) to have precise sources of evidence generating precise basic belief assignments (especially when belief functions are provided by human experts), and a more ﬂexible plausible and paradoxical theory supporting imprecise information becomes necessary.

1 12 ... 2 ... ... . . ... . . ... . . . ... ... ... .. ... ... ... ... ... . . . ... .. ... ... .... .... ..... ..... ...... ..... ...... . . . . . . ....... ......... ............................ ... 1: Venn diagram of a free DSm model for a 2D frame. θ1 = A ∪ C, θ2 = B ∪ C, θ1 ∩ θ2 = C Then the classical power set of Θref is given by 2Θ ref = {∅, A, B, C, A ∪ B, A ∪ C, B ∪ C, A ∪ B ∪ C} We see that we can deﬁne easily a one-to-one correspondence, written ∼, between all the elements of the super-power set S Θ and the elements of the power ref as follows: set 2Θ ∅ ∼ ∅, (θ1 ∩θ2 ) ∼ C, θ1 ∼ (A∪C), c(θ1 ∩ θ2 ) ∼ (A ∪ B), θ2 ∼ (B ∪C), c(θ1 ) ∼ B, (θ1 ∪θ2 ) ∼ (A∪B ∪C) c(θ2 ) ∼ A ref Such one-to-one correspondence between the elements of S Θ and 2Θ can be deﬁned for any cardinality |Θ| ≥ 2 of the frame Θ and thus one can consider ref S Θ as the mathematical construction of the power set 2Θ of the minimal reﬁnement of the frame Θ.

1: Venn diagram of a free DSm model for a 2D frame. θ1 = A ∪ C, θ2 = B ∪ C, θ1 ∩ θ2 = C Then the classical power set of Θref is given by 2Θ ref = {∅, A, B, C, A ∪ B, A ∪ C, B ∪ C, A ∪ B ∪ C} We see that we can deﬁne easily a one-to-one correspondence, written ∼, between all the elements of the super-power set S Θ and the elements of the power ref as follows: set 2Θ ∅ ∼ ∅, (θ1 ∩θ2 ) ∼ C, θ1 ∼ (A∪C), c(θ1 ∩ θ2 ) ∼ (A ∪ B), θ2 ∼ (B ∪C), c(θ1 ) ∼ B, (θ1 ∪θ2 ) ∼ (A∪B ∪C) c(θ2 ) ∼ A ref Such one-to-one correspondence between the elements of S Θ and 2Θ can be deﬁned for any cardinality |Θ| ≥ 2 of the frame Θ and thus one can consider ref S Θ as the mathematical construction of the power set 2Θ of the minimal reﬁnement of the frame Θ.