Decision validation and emotional layers on Fuzzy Boolean Networks

Abstract

Fuzzy Boolean Networks are capable of learning and reasoning. However, the reasoning result must be validated by an emotional layer, which ensures the acting rules are meaningful and that no contradictory rules are giving a wrong, "averaged", defuzzified result. Here the problem is addressed and an emotional layer is developed to deal with it.

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Decision Validation and Emotional Layers on
Fuzzy Boolean Networks• •

José A. B. Tomé
Instituto Superior Técnico/ INESC-ID
Rua Alves Redol nº9, 1000 Lisboa, Portugal
jose.tome@inesc-id.pt
João P. Carvalho
Instituto Superior Técnico/ INESC-ID
Rua Alves Redol nº9, 1000 Lisboa, Portugal
joao.carvalho@inesc-id.pt

and reasoning. However, the reasoning result must be validated
by an emotional layer, which ensures the acting rules are
meaningful and that no contradictory rules are giving a wrong,
“averaged”, defuzzified result. Here the problem is addressed
and an emotional layer is developed to deal with it.

Abstract. Fuzzy Boolean Networks are capable of learning
I. INTRODUCTION

and they are capable to perform qualitative reasoning based on
their internal memories, which are set during the learning
phase [8]. These nets can be considered a neural fuzzy model
where the fuzziness is an inherent emerging property in
contrast with other known models where fuzziness is
artificially introduced on neural nets or where neural
components are inserted on the fuzzy systems [2, 3, 4, 5, 7].
Moreover, it has been proved [9] that they are Universal
Approximators (they are equivalent to Parzen Windows
estimators [6]) and that they are capable to distinguish
between different rules, provided a relationship between the
number of rules and the number of inputs per neuron is
obeyed [10].
Based on this theoretical background some applications have
been implemented [12], but there are interesting questions yet
to be developed, such as the one here treated.
Since the learnt rules are distributed among a network of
neurons, two important questions arise:
1. The first one is: how can the network, itself, know that it
has learnt enough from the real world, in order to trust its
output on a future application experiment (or, in other words,
is the performed reasoning trustable, based on the teaching)?
2. The second question is related with situations where
different activated rules provide different outputs from the
same input data of a given experiment, in a dangerously way.
This situation tends to set the system output on a kind of
“average” of the different rule decisions. This problem arises
also on the traditional fuzzy systems, where the process of
deffuzification gets the “responsibility” of solving it. It is the
known case of the automobile control when this “sees” one
obstacle ahead, just in front. If some of the rules drive the
automobile to the left, in order to avoid the eminent disaster,
Fuzzy Boolean Nets can learn from real experiments

• This work is partially supported by FCT project
POSI/SRI/33741/2000
and some other rules drive it to the right the result may be
catastrophic!
On Fuzzy Boolean Nets the network is by itself and must
decide what to do, without any external, artificial or
algorithmic help. It is the purpose of this paper to present a
natural (embedded on the network) solution to these problems.
The first problem is easily solved if one uses, in addition to
the internal activation ratios of the neurons, the non-taught
ratio. That is, the output of the system (which is represented
by the ratio of “ones” among every output neuron) is provided
together with a “credibility” output (also a ratio of activated
neurons), which gives an indication about the trust one can put
on the output.
The second problem is more interesting and is dealt with
another layer of neurons, which inputs do not come from the
external variables but from the internal states of the reasoning
layer of neurons. This is possible because when reasoning
takes place, and due to the internal structure of the binary
neurons, the network disposes of all necessary information
about how every rule is firing, about the output activation ratio
and thus about any incoherence.
That is, one uses a meta-network that interprets the work of
the network itself and validates its decisions. Reasoning may
be performed but decisions not taken at all, if the meta-
network is not satisfied with the process. In a certain way this
can be viewed as a neural network that provides “emotion” to
the reasoning process itself. It is known that on animals,
humans particularly, real decisions can not be achieved
without the work of the emotional layers [1], even if reasoning
has been performed.
II. EMBEDDING LEARNING KNOWLEDGE
The values taken by the linguistic terms on a given experiment
are expressed by the binary memories activation ratios and
these determine the consequent area activation ratio (which
represents the consequent deffuzification). Then, any initial
activation ratios (or corresponding to antecedent rule areas not
taught enough) have no meaning but wrongly affect the
consequent. In order to deal with this situation it is necessary
to memorize, for each joint antecedent area of each neuron
(corresponding to a given rule antecedent), not only the
Boolean value (“0” if that joint antecedent has not been
addressed or “1” if it has) but also extra binary information
specifying if any thing at all has or not been taught. In
hardware terms this would mean two bits of memory per

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neuron and per joint antecedent area, instead of one. Let us
designate these two bits by value and credit, respectively.
With this, the learnt knowledge of each rule, after the teaching
phase, should now be interpreted not only by the active
consequent activation ratio of that rule/joint antecedent area
(defined as the ratio between the number of “ones” among
every value bit of that rule on every consequent neuron and
the number of “ones” among the respective credit bits), but
also by the teaching ratio of the same rule (defined as the ratio
of credit bits of that rule on every consequent neuron and the
total number of consequent neurons, since each consequent
neuron has one and only one credit bit per rule). Thus after the
teaching phase one knows which rules have been taught or
not, just by evaluating the teaching ratios of those rules. On
the reasoning phase (when antecedent values are applied and
one wants to get the consequent value) a similar attitude can
be taken. Since each neuron output is just the “ORING” of
every value bit of that neuron, if it has been addressed by the
particular joint antecedent sampled configuration, and since
just one value bit is addressed per neuron, the credit bit
corresponding to that value bit can also be furnished as an
extra output. Thus one gets two output areas – the active
output area and the credit output area – and the output
activation ratio of the first may be interpreted with the credit
given by the activation ratio of the second. For example, if the
net has not been taught at all one could obtain any active
output activation ratio (say 80%) without any meaning,
because the credit activation ratio was 0%. This can be a
valuable improvement to validate or not the reasoning output
or to take consciousness of which rules have been or not
taught.
On fig.1 one may have an idea of a possible neuron with n
antecedents each one with 3 inputs to the neuron. Four
different internal rule memories (each one corresponding to a
different joint antecedent linguistic term) and each one with 2
bits – value and credit. In such a case (if each antecedent
provides 3 inputs to the neuron) one should get 3n sets of two
bit internal memories. It is supposed that the addressed
internal rule is Rj (upper right), meaning that the neuron
output is “0” and it has been taught (credit “1”). To obtain the
output activation ratio one should look to every neuron output.
In the same way one could obtain each rule consequent value
and the respective credit looking to the internal memories of
that rule throughout every neuron.

For example, in fig.2, only two rules (rule A-Above and rule
B-Below) are shown in six neurons, as well as their active and
credit outputs.
It is supposed that Rule A has been addressed on neurons
N11, N1i, N21 and N2k, and Rule B on neurons N1k and N2i.
If the activation ratios were to be maintained globally among
every neuron, this would mean (since only 5 neurons have
credit “1” for that rule and, of those one has the value at “0”)
that the consequent of Rule A was learnt with a value of 4/5 –
probably a linguistic term of High or Very High, depending on
the number of membership functions used, and Rule B 1/4.
The result of the network (the defuzzication of the results
obtained by the 2 rules), on the shown experiment, would be
of 3/4 with a credibility of 6/8.
To address the second problem, that is antagonic results from
different rules with the same input data, an emotional layer
(based on relational operators already developed for these nets
[11]) is developed.
III. THE EMOTIONAL LAYER
From the point one has arrived at in the last section, it is
known that inside each neuron one has two bits per antecedent
rule and that they are established by the teaching process: one,
Vi, that gives the “value” of the consequent on what that
neuron is concerned, and another, Ci, that assures, if at “1”,
that the neuron has indeed learnt that rule. In addition, when a
real experiment of reasoning happens, each neuron will “see”
a joint sample of the inputs coming from the antecedent areas
and one and only one of the bit rules of the neuron will be
Fig. 1 Internal structure of a Neuron-Value and Credit bits
……
…..
……
v
c
v
c
v
cv
c
R1 Rj
Ri
Rk
value credit
A1
A2
An
N11
N1i N1k
……
……
N21
N2k
N2i
Fig. 2 Example

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addressed; let one name Di ∈{0,1}, with i being the rule
index, the binary variable which is “1” for the addressed rule
and “0” for the other rules.
Now, if, during the teaching phase, similar input antecedent
values have provided very different outputs different
consequent have been learnt by the network for the same
antecedents. If the actual reasoning experiment is not far (in
linguistic terms of the antecedents) from those, this situation
tends to set the system output on a kind of “average” of the
different rule decisions. This problem arises also on the
traditional fuzzy systems, where the process of defuzzification
gets the “responsibility” of solving it. It is the known case of
the automobile control when this “sees” one obstacle ahead,
just in front. If some of the rules drive the automobile to the
left, in order to avoid the eminent disaster, and some other
rules drive it to the right the result may be catastrophic.
A possible solution for this problem is the use of another
neural layer that monitors the internal activity of the other
neurons, through the values Vi, Ci and Di. Its responsibility is
to determine if two or more rules are been “reasonably”
activated and if the outputs of those rules are “quite” different
and validated by credit bits. The final decision of the network
depends on this layer, and it will not be taken unless
permission is granted by it. Another possibility is this
“monitoring” layer to decide for one of the two contradictory
outputs, based on the relative credits, for example. The kind of
behavior of that layer, recalls for what the emotional layers are
supposed to do [1], and thus one names it as the emotional
layer.
Although the layer can implement more sophisticated
differentiations, since one wants to separate rules with “quite”
different activations it is enough to use the “low” and “high”
activations.
The input “areas” for this layer are composed with the bits of
the same rule from every neuron of the reasoning layer. For
instance, in fig. 2, the lower bits VB and CB together with DB
(the last one not shown but implicit because the output bits of
each neuron are those addressed by the antecedent rule
present) from neuron N11 to neuron N2k are used to form
input area 2.
The logic equation corresponding to the conditions for
forming one input (from one consequent neuron) of the
emotional input area, corresponding to any rule i, is then:
Biti=AND(Di,Ci,Vi), and since the two output bits are given
by Vo=∑iAND(Di,Vi) and Co=∑iAND(Di,Ci), it comes
Biti=AND(Vo,Co,Di) because only one Di is “1”. This
information can be provided in a more useful way if bit Vi is
separated from the AND of Di with Ci as it is shown in fig. 3,
with two pairs of these bits (the same should be repeated for
every neuron), from rule B input area to the emotional layer
(in fig. 3 they are denoted by BitV and BitCD, respectively).
The set of these bits, for an area/rule i are named as areas Vi
and CDi.
The “emotional” layer can be constructed with a generalized
relational operator made of the same kind of neurons [11], or
it can be decomposed on a series of more simple relational
operators, each of them just comparing a pair of rules. In the
first case the inputs for that layer come from every pair of
areas CDi and Vi. Taking the second possibility, the inputs for
each of the sub-networks/relational operators can be the same,
but using only the CD and V of the two involved rules. The
logical operation such a net must implement is:

IF (AND (Vi “quite different” from Vj, CDi is “activated a
lot”, CDj is “activated a lot”)) Then Block

This kind of reasoning ensures that blocking the output of the
reasoning only occurs if both rules have been taught and are
being activated on the present experiment (CDi AND CDj)
and the consequent activations are quite different. Notice that
Area1
Area2
AreaN

CDi
CDj
Vi
Vj
REASONING
LAYER
Emotional
Layer
Output
Validation
Fig. 4 Global Network
N11
N1i
……
N21
N2i
BitCD
BitCD
Fig. 3 Bits for Rule B area
BitV
BitV
N1k
N2k

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the output of this layer is to be interpreted again as the
activation ratio of its neuron outputs. Then, the result of the
reasoning layer is validated by the activation ratio of the
emotional layer. On fig. 4 the overall topology of the network
is depicted.

IV CONCLUSIONS

The capability of fuzzy neural networks to perform relational
operations, in addition to the qualitative reasoning, is here
used to implement an emotional layer, which function is to
validate the output of the reasoning layer. This means that no
consequence is taken from the antecedent inputs if not enabled
by the emotional layer. Another possibility is to impose a
consequent obtained from some rules, discarding (on the
implicit defuzzification process) the results obtained from
other rules. In this paper the first option has been taken.

Two different problems (although linked between themselves)
may arise, in order to make necessary the extra layer: there is
not enough learning about some rules, or, a real experiment
may simultaneously activate (with relatively high intensity)
different rules with contradictory consequent results – which
may originate an undesirable and dangerous “averaging”
effect.
Since each reasoning layer neuron gets its own information
about each individual rule, specifically: one bit stating if there
has been or not teaching of that rule and the other bit
indicating the taught value. Using each and every neuron
addressed rule information (one and only one rule per neuron
is addressed) it has been developed an emotional layer that
uses that information as inputs and gives an output activation
ratio that inhibits or not the consequent result of the reasoning
layer.
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