The Seven Truths Of Fuzzy Logic
The Seven Truths of Fuzzy Logic: There is nothing fuzzy about Fuzzy Logic. Fuzzy Logic is different from Probability. Designing the Fuzzy Sets is very easy. Fuzzy systems are stable, easily tuned, and can be conventionally validated. Fuzzy systems are different from and complementary to neural networks. Fuzzy Logic "ain't just process control anymore". Fuzzy Logic is a representation and reasoning process.
An excerpt from Computer Design that recently appeared in comp.ai.fuzzy. Reprinted with permission.
By Earl Cox (earlcoxreports.com), April 1992.
The idea that fuzzy logic is fuzzy or intrinsically imprecise is one of the most commonly expressed fables in the fuzzy logic mythos. This wide-spread belief comes in two flavors, the first holds that fuzzy logic violates common sense and the well proven laws of logic, and the second, perhaps inspired by its name, holds that fuzzy systems produce answers that are somehow ad-hoc, fuzzy, or vague. The feeling persists that fuzzy logic systems somehow, through their handling of imprecise and approximate concepts, produce results that are approximations of the answer we would get if we had access to a model that worked on hard facts and crisp information. Nothing could be further from fact.
There is nothing fuzzy about fuzzy logic, Fuzzy Sets differ from classical or crisp sets in that they allow partial or gradual degrees of membership. We can see the difference easily by looking at the difference between a conventional (or "crisp") set and a fuzzy set. Thus someone 34 years, eleven months, and twenty eight days old is not middle aged. In the Fuzzy representation, however, we see that as a person grows older he or she acquires a partial membership in the set of Middle Aged people, with total membership at forty years old.
But there is nothing ambiguous about the fuzzy set itself. If we know a value from the domain, say an age of 35 years old, then we can find its exact and unambiguous membership In the set, say 82%. This precision at the set level allows us to write fuzzy rules at a rather high level of abstraction. Thus we can say, if age is middle-aged, then weight is usually quite heavy; and means that, to the degree that the individual's age is considered middle aged, their weight should be considered somewhat heavy. A weight estimating function, following this (very simple) rule might infer a weight from age through the following fuzzy implication process.
Much of the discomfort with fuzzy logic stems from the implicit assumption that a single ``right'' logical system exists and to the degree that another system deviates from this right and correct logic it is in error. This ``correct'' logic, of course, is Aristotelian or Boolean logic. But as a logic of continuous and partial memberships, Fuzzy Logic has a deep and impressive pedigree. Using the metaphor of the river, Heraclitus aptly points out that a continuous reasoning system more correctly maps nature's logical ambiguities. From his dictum that all is flux, nothing is stationary, he developed a rudimentary multi-valued logic two hundred years before Aristotle. Recently, Bart Kosko, one of the most profound thinkers in fuzzy logic, has shown that Boolean logic is, in fact, a special case of fuzzy logic.
The difference between probability and fuzzy logic is clear when we consider the underlying concept that each attempts to model. Probability is concerned with the undecidability in the outcome of clearly defined and randomly occurring events, while fuzzy logic is concerned with the ambiguity or undecidability inherent in the description of the event itself. Fuzziness is often expressed as ambiguity rather than imprecision or uncertainty and remains a characteristic of perception as well as concept.
Not only are fuzzy sets easy to conceptualize and represent, but they reflect, in a general "one-to-one" mapping, the way experts actually think about a problem. Experts can quickly sketch out the approximate shape of a fuzzy set. Later, after we have run the model or examined the process, the precise characteristics of the fuzzy vocabulary can be adjusted if necessary.
Creating fuzzy sets and building a fuzzy system is faster and quicker than conventional knowledge-based systems using "crisp" constructs. These fuzzy systems routinely show a one or two order of magnitude reduction in rules since fuzzy logic simultaneously handles all the interlocking degrees of freedom. Fuzzy systems are very robust since the over-lapping of the fuzzy regions, representing the continuous domain of each control and solution variable, contributes to a well-behaved and predictable system operation. These systems are validated in the same manner as conventional system. The tuning of fuzzy systems, however, is usually much simpler since there are fewer rules; representation if visually centered around fuzzy sets, and operations act simultaneously on the output areas.
There is a close relationship between fuzzy logic and neural systems. A fuzzy system attempts to find a region that represents the space defined by the intersection, union, or complement of the fuzzy control variables. This has analogies to both neural network classifiers and linear programming models. Yet fuzzy systems approach the problem differently with a deeper and more robust epistemology. In a fuzzy system, the classification and bounding process is much more open to the developer and user with capabilities for explanations, rule and fuzzy set calibration, performance measurements, and controls over the way the solution is ultimately derived.
Historically we have come to view fuzzy logic as a process control and signal analysis technique, but fuzzy logic is really a way of logically representing and analyzing information, independent of particular applications. The information management field in particular has, until recently, ignored fuzzy logic, delaying its introduction into expert system and decision support technology. Recently, however, new types of knowledge base construction tools have emerged. Such tools will make it easier for experts who are not computer experts to intuitively represent and manipulate information.
Not the "Magic Bullet" for all AI's current problems - Fuzzy Logic is a tool for representing imprecise, ambiguous, and vague information. Its power lies in its ability to perform meaningful and reasonable operations on concepts that are outside the definitions available in conventional Boolean logic. We have used fuzzy logic in such applications as project management, product pricing models, health care provider fraud detection, sales forecasting, market share demographic analysis, criminal identification, capital budgeting, and company acquisition analysis. Although fuzzy logic is a powerful and versatile tool, it is not a solution to all problems. Nevertheless, it opens the door for the modeling of problems that have generally been extremely difficult or intractable.