Data processing: artificial intelligence – Fuzzy logic hardware – Fuzzy inference processing
Reexamination Certificate
1997-09-26
2002-07-23
Shah, Sanjiv (Department: 2172)
Data processing: artificial intelligence
Fuzzy logic hardware
Fuzzy inference processing
C706S004000
Reexamination Certificate
active
06424957
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for calculation in parallel of multiple fuzzy logic inference rules. The present invention concerns also a circuit architecture for implementation of the parallel calculation.
Specifically the present invention relates to a method for parallel processing of multiple fuzzy logic inference rules organized in fuzzy sets or logical functions of multiple fuzzy sets including membership functions defined in a so-called discourse universe and said rules being configured essentially as IF-THEN rules with at least one antecedent preposition and at least one consequent implication and said prepositions including at least one term of comparison between the membership functions and a plurality of input data and the terms being separated by logical operators.
2. Discussion of the Related Art
Fuzzy logic has now been established as a technique capable of supplying solutions for broad classes of control problems for which conventional techniques, e.g. those based on Boolean logic, have proven unsuited, and for providing acceptable performance at acceptable cost.
Fuzzy logic supplies a method of modelling the ‘inaccurate’ modes of reasoning typical of the human mind and which play an essential role in the human ability to make decisions under conditions of uncertainty.
Fuzzy logic operates on a linguistic description of reality using a particular class of variables termed ‘linguistic variables’. The values of said variables include words or phrases of any natural or artificial language. Basically, to each variable is assigned a corresponding semantic meaning of the words or phrases which are used in the modelling of a given problem.
In addition, to each variable can be syntactically joined a set of values dependent upon it which can take on different meanings depending on the context in which they are employed. Said values are found starting from a primary term which represents the variable, from one of its contraries, and from a series of so-called modifiers of the primary term, as described in European patent application no. 92830095.3.
Each value assigned to a linguistic variable is represented furthermore by a so-called fuzzy set, a possibilistic distribution function which links each value of the variable corresponding definition domain known as the universe of discourse.
The functions which identify a fuzzy set in the universe of discourse of a variable are called membership functions FA. For example, a value FA=0 indicates the non-membership of the point in the fuzzy set identified by the function, while a value FA=1 indicates the certainty of membership of the point in the fuzzy set. The assembly of all the fuzzy sets of a linguistic variable is called a ‘term set’.
Membership functions are defined by means of a sample representation obtained by dividing the definition domain in m points and the interval [0, 1] in 1 levels.
At present, definition or storage in a fuzzy logic based electronic controller of the membership functions which identify the fuzzy sets represents one of the major constraints on development of new fuzzy logic applications and thus limits the theoretical potential of this methodology.
Indeed, if it is desired to implement the membership functions in hardware to reflect the semantics of the fuzzy concept and to obtain a correct incidence of a term in a rule, one is forced to use considerable memory space. This makes fuzzy logic advantageous only for those applications where the term set of the linguistic variable consists of a reduced number of membership functions.
The data for a membership function are normally stored in a memory word. In known devices the memory area occupied is thus negatively influenced by the number of data necessary for defining these membership functions.
In many cases it has proven sufficient to store triangular membership functions, generally not symmetrical, or trapezoid membership functions so as to reduce the amount of data necessary for their storage.
With these triangular or trapezoid membership functions, it is not at all necessary to store the values of the function at all points of the universe of discourse. It is sufficient to store only the points where the curve changes slope and the value of this slope.
Appropriate logical operations—termed ‘inferential’—which allow description of the behavior of a system with the change in input parameters are performable among the membership functions. These operations are performed by fuzzy rules which have generally a syntax of the following type:
IF
X
IS
A
, THEN
Y
IS
B
where 1 is the input value, A and B are membership functions FA which represent system knowledge, and Y is the output value.
The part of the rule preceding the term THEN is called the ‘left’ or ‘antecedent’ part while the following part is called ‘right’ or ‘consequent’ part of the inference rule.
The implication between the antecedent part and the consequent part of a fuzzy rule is governed by two laws:
modus ponens: in it the truth of the implication (Th), i.e. of the consequent part of the rule, depends on that of the premise (Hp), i.e. the antecedent part of the rule;
modus tollens: in it occurrence of the implication (Th) which ensures correctness of the premise (Hp).
Adopting the modus ponens as the rule, the degree of truth of the entire rule cannot be greater than that of the antecedent part.
Since the antecedent part can be made up of one or more terms T corresponding to hypotheses of the type (F is F′) on the data F and on the membership functions F′ its overall degree of truth which we shall indicate by the symbol W in the following description depends on the inference operations on these same terms T.
In addition the overall degree of truth W takes on a determinate value by applying to these terms T the logical operators AND, OR and NOT.
Electronic data processing tools which allow performance of this type of operation require a particular architecture expressly dedicated to the set of inference operations which constitute the fuzzy logic computational model.
With reference to triangular or trapezoid membership functions FA such as those set forth in
FIG. 1
, a weight ∝ of a set of data I for an antecedent part term represented in the universe of discourse U by means of a membership function I′ means the greatest value of the intersection between the input data set I and the membership function I′ corresponding to said term T.
In a processor operating with fuzzy logic procedures there must be room for a circuit capable of calculating the overall degree of truth W regardless of the logical operators present.
Heretofore multivalue fuzzy logic inferences were calculated in different ways.
In a project developed at OMRON by T. Yamakawa et al. the inference processing circuit can operate analogically in parallel only on four rules whose antecedent part can have at most three terms.
In addition to this initial limitation, for design simplicity other constraints were imposed:
the terms T of the antecedent part of the rules can be separated only by logical operators AND;
the membership functions I′ of the term sets of the input variables I can only have an S, Z, trapezoid or triangular shape;
the inputs are deterministic, i.e. they correspond to an individual point P in the universe of discourse U.
An architecture of H. Watanabe et al. performs in parallel all the rules for the same output variable. The user is however limited in his choice of the variables with which he can work. These can be only four input variables and two output variables out of fifty-one rules, or two input variables and one output out of one hundred two rules.
A plurality of Watanabe circuits can be connected in cascade under control of a software program in such a manner as to process more than one hundred two rules. In this case moreover it is possible to introduce a feedback of the output signal on the input of one of the components.
In like manner circuits of this type can be conne
Abruzzese Massimo
Giacalone Biagio
Matranga Vincenzo
Consorzio per la Ricerca sulla Microelettronica nel Mezzogiorno
Morris James H.
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