Fuzzy Application Library/What is Fuzzy Logic?
This introduction is kept brief. You find introductory
literature in the Fuzzy Logic Literature section. Complete
introductory literature is also contained with all fuzzyTECH products.
What is Fuzzy Logic?
How can a logic which is "fuzzy" be useful?
Professor Lotfi Zadeh, the inventor of fuzzy logic, contends that a computer cannot solve
problems as well as human experts unless it is able to think in the characteristic manner
of a human being.
As humans, we often rely on imprecise expressions like
"usually", "expensive", or "far". But the comprehension of a
computer is limited to a black-white, everything-or-nothing, or true-false mode of
thinking. In this context, Lotfi Zadeh emphasizes the fact that we easily let ourselves be
dragged along by a desire to attain the highest possible precision without paying
attention to the imprecise character of reality.
There are many subjects which do not fit into the precise
categories of the conventional set theory: The set of "all triangles" or
"all the guys named John" is easy to handle with conventional theory. Either
somebody's name is John or it is not. There is no other status in between. The set of
"all intelligent researchers" or "all the people with an expensive
car", however, is much more complicated and cannot be handled easily by a
"digital" mode of thinking. This is because of the fact that there is no way to
define a precise threshold to represent a vague and blurry boundary: there are some
obviously expensive cars, like the Rolls-Royce, but many others could be fit into this
category as well, depending on how much money you have, where you live, and how you feel!
Why use fuzzyTECH ?
As mentioned before, within conventional logic, terms can
be only "true" or "false". Fuzzy logic allows a generalization of
conventional logic. It provides for terms between "true" and "false"
like "almost true" or "partially false". Therefore, fuzzy logic cannot
be directly processed on computers but must be emulated by special code.
This what what fuzzyTECH brings to the party. fuzzyTECH
on one hand provides you with all the tools to design and test a fuzzy logic system. Once
designed, fuzzyTECH stores your work as an FTL format file. FTL stands for
"Fuzzy Technology Language", and can be considered "the programming
language of fuzzy logic". Because fuzzyTECH provides an all-graphical user
interface, however, you never need to program a single line of code in FTL. Rather, fuzzyTECH
on the other hand converts this FTL description to code that can be used on your target
hardware that is, the hardware where your fuzzy logic solution finally shall run on.
Designing a fuzzy logic system is different from
conventional coding. To give you the most efficient start, fuzzyTECH features three
"Fuzzy Design Wizards" that guides you step-by-step. As a beginner, this insures
that you have covered all design steps thouroughly, as an experienced developer you will
be able to design the prototype of a complex system in just a few minutes.
Integrating Neural Net Technology
There are many applications where it is easier to define
the desired system behavior (or part of it) through examples rather than through manual
creation of the rules or the linguistic variables. In such cases, you may use the
NeuroFuzzy Module which is entirely integrated in fuzzyTECH.
The NeuroFuzzy module automatically generates and optimizes
not only the fuzzy logic rules and their weights but also the membership functions from
available data which represent sample cases. The NeuroFuzzy Module integrates neural
network technologies in order to train fuzzy logic systems. In contrast to conventional
neural network solutions, the entire training process and the resulting fuzzy logic system
remains completely self-explanatory.
The employed training technology is based on a fuzzy logic
inference component of fuzzyTECH: the use of Fuzzy Associative Maps (FAM). FAMs
allow fuzzy logic rules with an inherent 'fuzzy' character. Such FAM rules can be viewed
as generalized neurons ("Approximate Reasoning") whose plausibility is
calculated through Competitive Learning. A fuzzy logic system generator optionally sets up
appropriate membership functions and rule blocks prior to the actual training phase based
on the data sets.
The NeuroFuzzy Module can also be used to optimize existing
fuzzy logic systems. Starting with an existing system, the NeuroFuzzy Module interactively
tunes rule weights and membership function definitions such that the system converges to
the behavior represented by the data sets. The optimization process allows specified rules
and membership functions to be locked or opened for learning. The entire learning process
is visualized, and any fuzzy logic system generated by the NeuroFuzzy module can be
further optimized and verified manually.
You find more information in the NeuroFuzzy Module section.
Advanced Fuzzy Technologies
In addition to the common methods of fuzzy logic, there are
various expanded fuzzy technologies which have proven to be very useful. Most fuzzyTECH
products support such Advanced Fuzzy Technologies:
Support of normalized rule sets
If you have complex applications, you can easily cause confusing rules using different
operators, a chaos of parentheses and complicated "if-then-else" statements.
Such constructs destroy the actual advantages of fuzzy logic systems, like clarity and
easy expansion. fuzzyTECH uses a different approach by providing normalized rule
sets and graphical structure editors. Even the most complex compositions, which must be
handled within the rule syntax by other fuzzy logic tools, can be easily developed
graphically with fuzzyTECH. Applying normalized rule sets has the additional
advantage that the rules can be transformed automatically and developed easily in matrix
form, which is often more readable than text or table form in the case of huge and complex
systems.fuzzyTECH provides all three presentation forms (text, table, and matrix),
while also allowing for switching between them or using them in mixed formats.
Inference methods
Aside from the standard fuzzy inference methods (MAX-MIN, MAX-PROD), most fuzzyTECH
products support the advanced Fuzzy Associative Map inference. FAM is an extension of
fuzzy inference which was developed out of the combination of neural technology and fuzzy
logic. It allows more accurate tuning of the rule bases according to the prerequisites,
and as a result, it reduces the often necessary selection procedures of the rules. fuzzyTECH
supports not only the maximum operator for result aggregation, but also the BSUM operator
(Bounded-Sum). This operator also considers the so-called "support rules" which
support the current firing rule.
The fuzzy inference of fuzzyTECH represents a combination of forward/backward
chaining which is totally transparent for the user. fuzzyTECH automatically decides
the best processing method appropriate to the current fuzzy logic system.
Fuzzy operators
Most fuzzyTECH products provide families of generalized operators for fuzzy
inference, from which you can create a desired operator through free parameterization of
the available operators. There are three operator families available: Min-Max, Avg-Max,
and Gamma. The Min-Max family represents a generalization of the "traditional"
fuzzy operators that can also be created as a special case of Min-Max. Through broad
empirical research, we now know that the Gamma families are able to represent the human
characteristics of decision behavior the best. Through free parameterization you can
individually modify your Gamma operators to achieve the optimum of your desired system.
The Avg-Max family is an approximation of the Gamma operator family, optimized with
regards to computing efficiency. Especially in cases requiring the processing of huge
amounts of data in a short time, you may choose the Avg-Max operators, thereby giving up
some of the higher accuracy provided by the Gamma operators.