Fuzzy logic neural network modular architecture

The invention relates to a modular architecture of a cellular network for improved large-scale integration, of the type which comprises a plurality of fuzzy cellular elements (C.sub.m,n) interconnected to form a matrix of elements having at least m rows and n columns, the row and column numbers describing the location of each element. Each fuzzy processor is adapted for connection to other processors of the same type such that a parallel architecture of the modular type can be implemented. The management of the architecture is facilitated by each submatrix being controlled by an individually dedicated fuzzy processor device.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to a modular architecture of a cellular network for 
integration on semiconductor circuits using large-scale integration 
technology. A cellular network includes a plurality of cellular elements 
(C.sub.m,n) interconnected together to form a matrix of elements having at 
least m rows and n columns, the row and column numbers describing the 
location of each element in the matrix. 
The invention also relates to a device for processing fuzzy logics rules to 
control the temporal dynamic evolution of the state of such cellular 
elements. 
The invention relates to, in particular, an architecture for cellular 
networks which is based on fuzzy logic and refers to a bi-dimensional 
plane on which said network is assumed to lie. The description to follow 
will cover this field of application for convenience of illustration only. 
2. Discussion of Related Art 
As pointed out by certain articles that have appeared in the scientific 
literature, such as COLLECTIVE BEHAVIOUR OF CELLULAR FUZZY SYSTEM FOR NEW 
ADIGM OF COMPUTATION by S. Baglio, L. Fortuna, G. Giudice, and G. 
Manganaro, architectures which are based on fuzzy cellular elements 
identical with one another have a wide field of potential applications. 
Such architectures can process data in real time with high efficiency, and 
facilitate integration on semiconductor circuits intended for large volume 
production. 
A first exemplary application of these architectures is represented by the 
solution of such hard mathematical problems as differential equations, or 
image processing. These first applications were originally based on the 
so-called "cellular automata" philosophy by Tofoli and Margolous, 1987, 
and subsequently on a philosophy set forth by Chua and Yang in an article 
"Cellular Neural Networks" (CNN's), 1988. 
While both of the above philosophies point to the use of a cellular 
network, there still exists the problem of how to configure these 
architectures by the determination of a set of parameters, in order for 
them to serve their intended function. 
Heretofore they have been designed, and the set of parameters determined, 
by assigning certain estimated starting values to the parameter of the 
cellular network, and using supporting simulators in order to determine 
any errors from the trials made. 
This approach took into consideration the possibility of extending to 
cellular neural networks self-taught algorithms that could determine the 
optimum values of such parameters. 
In the above-referenced scientific article, a novel approach to the use of 
cellular network-based architectures is proposed, wherein the duty of each 
cell in the cellular architecture is described by suitable language 
constructions or "fuzzy logic rules". 
With this novel philosophy, a given problem is solved simultaneously as it 
is defined, because the behaviors of the fuzzy-type cells can be defined 
in language. 
Purely as an example, consider the instance of a fuzzy cellular network 
consisting of a fuzzy cell matrix of m rows and n columns, all identical 
and interacting with one another. 
Suppose that such a matrix is in biunivocal correspondence to a video image 
comprising a number of pixels equal to the number of cells in the matrix, 
so that a state variable can be associated with each cell which would take 
into consideration the brilliance of the individual pixel, for example. 
The dynamic evolution of these state variables is defined by first R.sub.1 
and second R.sub.2 sets of fuzzy logic rules defining the cell 
interactions within a given range. 
It is indeed possible to define, for each cell C.sub.m,n in the fuzzy 
cellular network, a set of cells N.sub.2 (m,n)={C.sub.k,1 
:max(.vertline.k-m.vertline.,.vertline.l-n.vertline.).ltoreq.r}, which 
include the adjacent cells to the base cell within a range of radius r. 
In the function that defines the range N.sub.2 (m.n), max is an operator 
which gives back the largest of the values between brackets, while l and k 
are indexes identifying a generic cellular element. 
The second set R.sub.2 of rules applies to the state variables of the cells 
within the range of radius r. 
The dynamic evolution of the individual cell is determined by a set of 
rules formed by the first and second sets (R.sub.1 U R.sub.2) combined, 
while the overall dynamic evolution of the fuzzy cellular network, as 
resulting from the mutual interactions of the m*n cells, is fixed by the 
second set R.sub.2 alone. 
For example, the state of a generic base cell C.sub.m,n can be described by 
the exemplary set of rules here below, either through fuzzy logics 
language constructions or algorithms which can be represented graphically 
by flow diagrams. 
In the sets R.sub.1 and R.sub.2, the quantities subject to conditioning are 
the state variables X.sub.m,n (t), X.sub.k1 (t).epsilon.N.sub.2 and 
Range.sub.-- of.sub.-- X.sub.m,n (t). 
The first state variable X.sub.m,n (t) defines the condition of the generic 
cell C.sub.m,n at a time t, while the state variable Range.sub.-- 
of.sub.-- X.sub.m,n (t) is dependent on the state X.sub.k1 (t) of the 
adjacent cells to the base cell C.sub.m,n in a range of radius r. 
Subsequently, said state variables are compared with the pre-selected 
membership functions of the set "universe of discourse", following their 
conversion to fuzzy quantities by the fuzzyfying process. 
In the following example, "Low", "Medium" and "High" are the respective 
membership functions associated with the input variables, and 
"Small-positive" is one of the membership functions associated with the 
output variables. 
SET R.sub.1 . . . 
IF X.sub.m,n (t) IS Low AND Range.sub.-- of.sub.-- X.sub.m,n (t) IS High 
THEN X.sub.m,n (t+1) IS Small-positive . . . 
SET R.sub.2 . . . 
IF X.sub.(m--1),n (t) IS Low AND X.sub.m,(n+1) IS Medium AND THEN 
Range.sub.-- of.sub.-- X.sub.m,n IS High 
If the set of rules that describes the dynamic evolution of the cellular 
network is known, the value of the single state variable associated with 
the individual cell is updated in the manner expressed by a flow diagram 
shown in FIG. 3. 
The flow diagram has five functional blocks therein which are cascade 
connected to one another, with feedback provided between an end block and 
a second block. 
An initial block effects the acquisition of the state variables X.sub.m,n 
and Range.sub.-- of.sub.-- X.sub.m,n associated with the condition of the 
single network cell at the initial point in time. 
These values are transferred to a second block, connected downstream from 
the initial block, which effects the conversion of these state variables 
to fuzzy logic quantities for subsequent processing by the sets of rules 
R.sub.1 and R.sub.2. 
A third block, connected downstream from the second block, will receive the 
value of the output fuzzy quantity delta X.sub.m,n that results from the 
second block processing. 
The third block effects a necessary defuzzyfying operation to obtain the 
corresponding true value of that fuzzy quantity. 
The value from the third block is used by a fourth block to decide, in the 
event that the defuzzyfied quantity delta X.sub.m,n is zero or below a 
predetermined threshold, that the processing of the value of the state 
variable X.sub.m,n associated with the individual cell should be 
terminated. 
Where the value of delta X.sub.m,n is non-zero, the end block will receive 
said value delta X.sub.m,n from the fourth block, and add it algebraically 
to the initial value of the state variable X.sub.m,n to yield the new 
value of X.sub.m,n at a subsequent point in time. 
The end block will also place the updated value of X.sub.m,n on the second 
block input, so that the future values of X.sub.m,n at later points in 
time can be determined. 
The control of the dynamic evolution of the generic cellular network by the 
above series of operations can be performed by a fuzzy rule processor, as 
suggested in the scientific article COLLECTIVE BEHAVIOUR OF CELLULAR FUZZY 
SYSTEM FOR NEW ADIGM OF COMPUTATION, page 2, FIG. 2. 
In particular, the above-referenced article suggests that the W.A.R.P. 
fuzzy processor manufactured by SGS-Thomson S.r.1. may be used. 
While achieving its objective, this proposal is not devoid of shortcomings. 
For example, where the number of the state variables associated with the 
number of fuzzy cells that make up the generic cellular network is large, 
the processor will be unable to simultaneously determine the states of all 
the cells, because all of them cannot be processed in parallel. 
Therefore, the processor operates separately on different subsets of cells 
in the cellular network in a sequential manner. This causes its processing 
rate to be slower. 
A fast response is essential where these architectures are to be 
implemented in image processing applications. 
For example, the use of a general-purpose fuzzy processor of the W.A.R.P. 
type for such processing defines an upper limit of two hundred and fifty 
six processable rules, which is regarded as insufficient to process images 
by simple fuzzy procedures, and a respective number of input terminals and 
output terminals of sixteen and four, associable with the states of their 
respective cells. 
Thus, specific modular structures which are identical with one another are 
desirable, to facilitate integration on semiconductor circuits for large 
volume manufacture. In this manner, the numbers of the processor inputs 
and outputs are not tied to that of the cellular network dimensions. 
The underlying technical problem is to provide an architecture of a 
cellular network, as well as a related cellular network processor, which 
has such constructional and functional features as to allow fuzzy logics 
rules to be processed in the manner outlined above, thereby overcoming the 
limitations and shortcomings previously mentioned in connection with the 
background art. 
SUMMARY OF THE INVENTION 
The primary idea on which the present invention is based is one having the 
cellular network divided into a plurality of subareas, each leading an 
independent life of the others through the dynamic evolution of the 
system. 
These subareas interact with one another to exchange information on the 
states of those cells which, by lying close to or within a range of radius 
r from a subarea boundary, or at the outward periphery of the subarea, are 
bound to affect the dynamic evolution of adjacent subareas with respect to 
the subarea in which they belong. 
On the grounds of this idea, the technical problem is solved by a modular 
architecture of a cellular network being of the type indicated above and 
in which at least one of the cellular elements includes a submatrix of 
cellular elements. 
In this way, the cellular architecture is given a modular configuration 
that facilitates both its integration on semiconductors in the form of 
integrated electronic circuits for large volume manufacture, and the 
integration on boards of several processors of the same type working in 
parallel. 
Another advantage which is obtained is related to the architecture 
management, which is facilitated by each submatrix being controlled by an 
individually dedicated device. 
The last-mentioned device is a fuzzy logic processor adapted for 
communication to other processors of the same type. In essence, each fuzzy 
processor can be connected to other processors of the same type to 
implement a parallel architecture of the modular type. 
Furthermore, in accordance with the invention, the cellular network 
architecture is adapted for application to a three-dimensional field 
wherein a cellular element is identified by three coordinates. 
By further expansion of the inventive principle, a cellular network may be 
thought of which can be applied to a multi-dimensional field wherein a 
cellular element is identified by an n-th number of co-ordinates N. 
An application for a multi-dimensional cellular network could be related, 
for instance, to the processing of color images, with each image pixel 
being associated cell vectors instead of a single fuzzy cell. 
This is specially advantageous in that the three fundamental components of 
a pixel color (red, green, blue) can be processed concurrently with the 
pixel brilliance. 
The features and advantages of an architecture and a cellular network 
processor according to the invention will be apparent from the following 
description of embodiments thereof, given by way of non-limitative example 
with reference to the accompanying drawings.

DETAILED DESCRIPTION 
Referring to the drawing figures, 
FIG. 1 is a schematic representation of a prior art cellular network. FIG. 
2 illustrates possible connections and interactions of a generic cell in a 
fuzzy cellular network. 
Generally and schematically shown at 4 is a cellular network architecture 
embodying this invention and featuring simplified control of its dynamic 
evolution, as well as allowing for easier integration on semiconductors in 
the form of integrated circuits for large volume manufacture. 
FIG. 4 illustrates a specific case of a cellular network of the 
nine-by-nine (9*9) type, where a subset of cells in a matrix-like 
structure called submatrix is identified by thicker-outlined squares in 
the figure. 
Each submatrix comprises a three-by-three (3*3) matrix of cellular 
elements, such that all of the fuzzy cells which form the network are 
enclosed within said submatrices. Thus, the cellular network shown in FIG. 
4 has been divided into a three-by-three (3*3) matrix composed of 
submatrices of cellular elements which interact with one another to 
exchange information. 
The dynamic evolution of each submatrix is governed by a set of rules which 
can be expressed as fuzzy logic constructions. 
These rules are similar to those previously described in connection with 
the prior art, wherein the state of a single cell in a given submatrix is 
made to depend on a set of rules (R.sub.1 U R.sub.2) being the combination 
of a first set R.sub.1 and a second set R.sub.2. 
The determination of the value of the future state variable, that is at a 
subsequent time to the initialization time, of a generic cell is effected 
by processing said set of rules on the basis of given input values. 
These values are respectively dependent on the state variable of the cell 
whose future state is to be revealed, and on the other state variables of 
adjacent cells to said base cell within a range of radius r. 
The application of these rules becomes more complicated where the reference 
cell, namely the cell whose future state is to be determined, and its 
adjacent cells within a range of radius r are formed by cells which belong 
to different submatrices. 
A typical case is that of a cell being located at the outward periphery or 
the boundary of a first submatrix, and cells within the range of radius r 
located outside said submatrix. 
Accordingly, there is a need for adjacent submatrices to be able to 
exchange information with one another in order that each of them can, 
within the aforementioned rules governing the dynamic evolution of each 
submatrix, be supplied the necessary data to determine the future state of 
each of the cells therein. 
The dynamic evolution of each submatrix and the exchange of data between 
submatrices are controlled by a number of cellular network processors, 
identical with one another, as described hereinafter. 
As for the diagram of FIG. 4, special attention is to be given to the cells 
located at the outermost periphery of the cellular network which do not 
fill the condition for a range of radius r. 
Two different kind of solutions can be adopted to extend the rules, binding 
the dynamic evolution of the cellular network, to the above cells, namely: 
application of a particular set of rules (other than the set R.sub.1 U 
R.sub.2 which is ruling the system general evolution) where a cell whose 
future state is to be determined, locates at the boundary of the cellular 
network; 
creation of a virtual auxiliary boundary, whereby the cells located at the 
outermost periphery of the cellular network also can have a range of 
radius r. 
This auxiliary boundary is achieved by storing the values of state 
variables associated with dummy cells into suitable supports, such that 
they can be made available whenever the future state of a cell located at 
the network boundary requires to be computed. 
With the latter solution, a modularity of approach is ensured which is 
uniform for all the cells in the network, although additional processing 
is involved in creating the auxiliary boundary. 
The processing of the fuzzy cellular network can be provided by connecting 
a plurality of functional blocks to one another by control, data, and 
address buses. 
These buses serve a transmission function for electronic control, address, 
and data signals through the above functional blocks. 
The processor is shown schematically in FIG. 5 to comprise: a plurality of 
functional blocks called FUZZY CORE, LOCAL MEMORY UNIT (LMU), EXT. MEMORY 
INTERFACE, COMMUNICATION INTERFACE, and CLOCK GENERATOR; a backbone formed 
of data, control, and address buses; and a plurality of input/outputs. 
A first block, designated Fuzzy CORE, functions essentially as the 
processing unit. This block mainly operates to compute, in conformity with 
the general rules R.sub.1 and R.sub.2 enforced for each cell in the 
three-by-three (3*3) submatrix, the respective future state at a 
subsequent time t+1, once the values of the state variables of the 
adjacent cells within a range of radius one are known at a given prior 
time t. This block Fuzzy CORE is, therefore, to acquire the values by 
carrying out read and write operations on the functional blocks LMU and 
EXT.MEM.INT which are managed by the plurality of buses and suitable 
synchronization signals denoted by WR and RD. The other information about 
the parameters of the fuzzy rules needed to determine the dynamic 
evolution of the submatrix being controlled by the processor is acquired 
by read operations from a storage block outside the processor, being of 
the EPROM, FLASH or an equivalent type. All of the operations mentioned 
this far can be reset by suitably driving a signal, designated RS, which 
is an input to the block FUZZY CORE. 
EPROM is a storage block connected externally to a first set of 
input/output terminals of the processor matching the plurality of buses. 
This block is enabled by FUZZY CORE for a read operation, through the 
synchronization signal RD and the plural buses, in order to supply the 
fuzzy core with the parameters of the fuzzy rules to be used in computing 
the future state. 
LOCAL MEMORY UNIT (LMU) is an internal memory block which is used for 
storing the end and intermediate values of the fuzzy cell state variables 
during the dynamic evolution of the cellular network. This block's 
read/write operation is enabled by FUZZY CORE through the read/write 
synchronization signals (RD, WR). The exchange of information with the 
other blocks in FIG. 5 takes place over data, address, and control buses. 
EXT. MEMORY INTERFACE is a block arranged to manage all of the input/output 
operations related to data being processed. Each input data or information 
item is presented in digital form with an appropriate number of bits, 
preferably eight bits, to allow of the use of ordinary banks of memories 
set up as cells of one byte. In a specific application, e.g. image 
processing, the above choice allows the brilliance of an individual pixel 
to be represented as two hundred and fifty six levels of gray. 
COMMUNICATION INTERFACE is a block which is enabled by the block FUZZY CORE 
through a synchronization signal CS. It manages the communications between 
identical processors controlling adjacent submatrices, so as to receive 
the information (values of the state variables of cells within a range of 
radius with respect to a base cell) and define the range of radius of all 
the cells in the submatrix. 
CLOCK GENERATOR is a block generating a clock signal which is distributed 
to the inputs of the blocks EPROM, LOCAL MEMORY UNIT, EXT. MEMORY 
INTERFACE, and COMMUNICATION INTERFACE for the purpose of synchronizing 
the write/read operations of FUZZY CORE into/from these blocks. 
A possible use for the cellular architecture in the field of image 
processing, with particular reference to a black/white image which is 
affected by gaussian noise as shown in FIG. 6, will now be described. By 
associating a cell from the fuzzy network with each image pixel, the image 
can be re-processed to suppress the noise that is detracting from the 
image quality. Accordingly, it is necessary to define which are the input 
variables, the output variables, and their membership functions in the 
universe set. The universe set is represented by the plus-one-minus-one 
[+1;-1] interval, with the value plus-one being associated to the pixel of 
black and the value minus-one with the pixel of white. 
The input variables are the state variables associated with each pixel and 
denoted by the symbol X.sub.i,j (k), where the indexes i and j determine 
the position of the generic pixel within the image, and k designates the 
k-th iteration (or processing). The output variables are equal in number 
to the input variables and denoted by the symbol delta(x).sub.i,j. The 
value delta(x).sub.i,j is the variation associated with the generic state 
variable X.sub.i,j needed to determine its dynamic evolution in the manner 
represented by the flow diagram of FIG. 3. 
The membership functions of the input variables are shown in FIG. 9, as 
denoted by the symbols W and B making explicit reference to the possible 
black and white hues of the generic pixel. Shown in FIG. 10 are the four 
output membership functions, respectively referenced N, P, SP, SN, which 
identify the four possible values that can be attributed to the generic 
output variable delta(x).sub.i,j. 
To complete the picture of the parameters required to determine (bind) the 
dynamic evolution of the cellular network system, the set of rules 
R.sub.1, R.sub.2 should be defined such that it expresses suitable bonds 
to suppress the noise affecting the image to be processed. 
In the specific case under consideration, wherein FIG. 7 is obtained from 
the image in FIG. 6, the decision has been made to use a range of radius 
of one defining the distance of interaction between adjacent cells. Sets 
of rules, R.sub.1, R.sub.2, can be defined as follows: 
SET R.sub.1 
IF X.sub.i,k (k) IS W AND n.sub.i,j IS W THEN delta(x).sub.i,j IS N 
IF X.sub.i,k (k) IS B AND n.sub.i,j IS B THEN delta(x).sub.i,j IS P 
IF X.sub.i,k (k) IS W AND n.sub.i,j IS B THEN delta(x).sub.i,j IS SP 
IF X.sub.i,k (k) IS B AND n.sub.i,j IS W THEN delta(x).sub.i,j IS SN 
SET R.sub.2 
EQU n.sub.i,j (x)=(x.sub.i-1,j (k)+x.sub.i+1,j (k)+x.sub.i,j-1 (k)+x.sub.i,j+1 
(k)) 
For simplicity, the interactions between adjacent cells with range one, as 
described by the set of rules R.sub.2, have been synthesized into an 
algebraic formula rather than the constructions of fuzzy logic. 
FIG. 8 shows the original image of FIG. 6, with the gaussian noise removed. 
The good results obtained so far point to the use of these fuzzy cellular 
architectures for image processing to suppress noise, as well as for image 
segmenting and compressing. 
The architecture proposed herein can also be used for other applications, 
such as to modularize complex physical phenomena involving interaction 
mechanisms between identical individuals on which the overall dynamic 
evolution is based. For example, the architecture can be applied to 
partial derivative equations, reaction-diffusion equations, cellular 
automata, fractal geometries including their applications to fluid 
dynamics, meteorology, and artificial life. 
In conclusion, the architecture and device according to the invention have 
obvious advantages of modularity and structural simplicity, as well as 
good computational capabilities, to be obtained through the use of fuzzy 
logics in integrated form. Although two dimensional matrices have been 
illustrated, three or more dimensions can be implemented with the modular 
cellular structure. For three dimensions, each cellular element 
C.sub.m,n,o is represented by three coordinates m, n, and o. For multiple 
dimensions, each cellular element C.sub.m,n,o,p . . . z represented 
multiple elements m, n, o. P . . . z. 
Having thus described at least one illustrative embodiment of the 
invention, various alterations, modifications, and improvements will 
readily occur to those skilled in the art. Such alterations, 
modifications, and improvements are intended to be within the spirit and 
scope of the invention. Accordingly, the foregoing description is by way 
of example only and is not intended as limiting. The invention is limited 
only as defined in the following claims and the equivalents thereto.