method [10] as depicted by boxed-dashed-red line in Table 1. The A3S method equations are given in Equation 1 and Equation 2.
1
m i
j
j i
t
P P
m
ϑϑϑϑ ψ
ψψ ψ
====
====
∑ ∑
∑ ∑
... 1
1,...,
max
i t
estimate i
n
P P
ψ ψ
ψ ψ
ψ ψ
ψ ψ
====
====
... 2
with
i t
P
ψ ψψ
ψ
is New-Knowledge Probability Distribution NKPD at time t where
1 2 t
, , ...,
ττττ
====
.
i j
P
ϑϑϑϑ
means hypothesis i at indication j. The
i t
P
ψ ψψ
ψ
is the representation of “fused probabilities” of all posterior probabilities from the same hypothesis at a certain t, while “estimated” means the selected
hypothesis is the most likely hypothesis from all available hypotheses given indications at a certain t.
estimate
P
ψ ψψ
ψ
is the largest value of
i t
P
ψ ψψ
ψ
that we call it as DoC of the selected hypothesis at a certain t that becomes new knowledge at time t.
Table 1 : The Illustration of the MMEO technique with A3S information-inferencing fusion method
i
A
Multi-Hypothesis,
i
A
j
B
1 …
i ...
n
Multi-Indication
j
B
1
1 1
P
ϑϑϑϑ
…
1
i
P
ϑϑϑϑ
…
1
n
P
ϑϑϑϑ
2
1 2
P
ϑϑϑϑ
…
2
i
P
ϑϑϑϑ
…
2
n
P
ϑϑϑϑ
… …
… …
… …
j
1
j
P
ϑϑϑϑ
…
i j
P
ϑϑϑϑ
…
n j
P
ϑϑϑϑ
… …
… …
… …
m
1
m
P
ϑϑϑϑ
…
i m
P
ϑϑϑϑ
…
n m
P
ϑϑϑϑ
A3S JPD
i t
P
ψ ψψ
ψ
1 1
m j
j
P m
ϑϑϑϑ
====
∑ ∑
∑ ∑
1
m i
j
j
P m
ϑϑϑϑ
====
∑ ∑
∑ ∑
1
m n
j
j
P m
ϑϑϑϑ
====
∑ ∑
∑ ∑
A3S + Maximum Score
estimate
P
ψ ψψ
ψ
1 1
m i
j
j i
,...,n
P max
m
ϑϑϑϑ
==== ====
∑ ∑
∑ ∑
4. Knowledge-Growing with the Extension of A3S Information-Inferencing Fusion Method –
OMA3S
The essential matter of KGS is time parameter as the indicator of the growing of the knowledge in KGS. Therefore we extended A3S method by involving this parameter and formed a new method called
as Observation Multi-time A3S OMA3S [2, 3] as depicted in Figure 7. The OMA3S method can be obtained as follows. We define a new term called New-Knowledge
Probability Distribution over Time NKPDT,
P Θ
Θ Θ
Θ
with
{{{{ }}}}
1 2
, ,...,
λλλλ
θ θ θ
θ θ θ
θ θ θ
θ θ θ
Θ = Θ =
Θ = Θ =
, as the collection of DoCs of the fused knowledge-inferencing obtained from OMA3S, which is the extension of A3S with the
involvement of the time parameter. Equation 3 and Equation 4 present the OMA3S method as well as the mechanism to obtain the highest DoC as the most likely hypothesis that describes the observed
phenomenon to become new knowledge.
1
t i
t t
P P
ττττ
θθθθ θθθθ
ττττ
====
====
∑ ∑
∑ ∑
... 3
1,...,
max
i t
estimate i
P P
λλλλ
θ θ
θ θ
θ θ
θ θ
====
==== ... 4
with
i t
P
θθθθ
is NKPDT,
i t
P
θθθθ
means new knowledge i at time t. The
i t
P
θθθθ
is the representation of “fused probabilities” of all probabilities of the information-inferencing at each t from the same knowledge
hypothesis, while “estimated” means the selected knowledge hypothesis is the most likely knowledge from all available knowledge hypotheses given a sequence of time.
estimate
P
θθθθ
is the largest value of
i t
P
θθθθ
that we call it as the DoC of the selected knowledge hypothesis.
Figure 7 : The model of knowledge-growing mechanism in KGS [3, 11].
APPLICATIONS EXAMPLES
Up to now we have applied KGS to two problems, one is in military field [6, 12] and another is in non-military field [2, 6]. In this section we only present one of our achievements in estimating the genes
behavior in a Genetic Regulatory System GRS by utilizing KGS. The term ”genes behavior” in this paper is the behavior of genes extracted from genes interaction over a series of time. We will show how
to extract the knowledge from the genes behavior in order to estimate the GRS behavior in the future. The analysis will be viewed in two perspectives. The first one is viewed from all genes interaction
over time and the second one is viewed from the contribution of individual gene over a time interval. In this paper we only present examples of the first perspective’s analysis. For this purpose, we use secondary
data i.e. genes’ interaction values database for yeast25-cdc28 taken from [13] as depicted in Table 2. In this database, there are 25 genes from ACE2 to SIC1 as listed in column A with a time interval from t-1
to t-17 or 17t times as shown in line 1.
Table 2 : Genes’ interaction values for yeast25-cdc28
1. Extracting Knowledge of the Genes Behavior
The knowledge in this case is the GRS behavior viewed from genes interactions over time that will be used as the basis for making an estimation regarding their interactions in the future. The ultimate aim
of this effort is by apprehending the GRS behavior we can suppress the genes that cause poor offspring quality and support the genes that produce good offspring quality. For examples we will deliver
knowledge extracted by KGS for 13 and all the 25 genes in 17t time of interactions. We also present the original data as the comparisons for the results obtained by KGS.
