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Data fusion - Coggle Diagram
Data fusion
Fuzzy logic
permits representing imprecisions and incertitudes
introduce semantics
combine variations of info types
Fuzzy sets theory
$$\mathcal{X} (x)$$
$$1\ if\ x\ \in\ A$$
$$0\ if\ x\ \notin\ A$$
Subjective neighboring notion
Noyau
$$ Noy(A)\ ={x \in A : \mu_A (x) = 1 } $$
$$Normalised\ sub-set : Noy(A) != \emptyset $$
Support
$$ {x \in A : \mu_A (x) > 0 } $$
Height
$$sup_{x \in A}(x) $$
Cardinal
$$|A| = \Sigma_{s \in S} \mu_A (x)$$
$$Coupe\ \alpha$$
$$A_{\alpha} = { X\in S : \mu _A (x) \geq \alpha }$$
for defuzzifying
Fuzzy number
approximately tolerable interval
fuzzifying
needs
univers de discours
partition classifying of that universe
belonging functions
Possibility theory
Evidential theory
Modeling
Mass function
Can represent imprecisions
Plausibility function
Affaiblissement
αj=0 : total ignorance
Belief function
Focality
Estimation
Simple support functions
Fonction de croyance complémentaire
Fonction sur singletons
Combinaison
Mass modification based
Conflict redistribution based
Dempster Shafer rule
Synopsis
+Certainty convergence
---Total certainty to minor opinion
--- Loss of majority opinion
---unearned mass
Calcul du consensus
+Disappearing ignorance
$$m_{DS}(X)=\frac{m_{12}(H)}{1-m_{12}(\emptyset)}$$ $$m_{12}(H)= \Sigma m_1(H_1) m_2 (H_2)$$
Corrective strategy of body evidence
Total/partial conflict redistribution strategy
Décision
Max de plausibilité
Max de croyance
Vote decisional method
Combination
$$\mathcal{M}_{k}^{E}(x)\ = \Sigma_{j=1}^{m} M^{j}_k (x) \ $$
is associative
is commutative
Problems
if sources are pair
total incertitude
Source ponderation
$$\mathcal{M}_{k}^{E}(x)\ = \Sigma_{j=1}^{m} \alpha _{j}M^{j}_k (x) \ $$
non idempotent
needs learning
success criterions : accuracy...
$$\mathcal{M}_{k}^{E}(x)\ = \Sigma_{j=1}^{m} \alpha _{jk}M^{j}_k (x) \ $$
Decision
majority voting
absolute majority voting
if $$M^{E}_{k} (x) > m/2$$
Simple, naturlisch
no prior knowledge
Modèle probabiliste
Approche objectiviste
Approche subjective (Bayésienne)
Combinaisons
Bayesian
$$ p(d_{i}|S_1,...,S_m) = \frac{p(S_1,S_2,...,S_m|d_i)p(d_i)}{p(S_1,...,S_m)} $$
$$ p(d_{i}|S_1,...,S_m) = \frac{p(S_1|d_i)p(S_2|S_1,d_i) ... p(S_m|S_1,...,S_{m-1} ,d_i ) p(d_i) }{ p(S_1) p(S_2|S_1) ... p(S_m|S_1,...,S_{m-1}) } $$
$$Using\ Independence\ hypothesis\ : \frac{\Pi ^m_{j=1} p(S_j|d_i) p(d_i) }{\Pi ^m_{j=1} p(S_j) } $$
Posterior
$$ p(H_i /x) = \frac{v_x (H_i) p(H_i) }{ \Sigma_{H_j \in \Omega} v_x (H_j) p(H_j) } $$
Likelihood
$$ v_{x_{1,2} }(H_i) = \frac{v_{x_1} (H_i) v_{x_2} (H_i) }{ \Sigma_{H_j \in \Omega} v_{x_1} (H_j) v_{x2} (H_j) } $$
Conflict
No available conflict notion
total conflict, no possible likelihood calculation
other operators
Decision
posterior max : MAP
Max likelihood : MV
confusion between ignorance and equiprobability
good for rich knowledges
no coflict modelisation
closed world exclusivity, exhaustivity
continuous distribution
Representing ignorance
Principe de raison insuffiante
if information is absent, take uniform law
ignorance : uniform law => maximum entropy
Goal
get a more
sure
and
precise
decision