9. Read and discuss the article. Do you believe that the future is fuzzy? Explain your opinion, referring to scientific journals.

SMART MACHINES

Pop a snack into a fuzzy microwave oven, leave the room and just forget about it. No, your treat won't come out half raw or burnt to a crisp. .Fuzzy microwaves cook foods perfectly all by themselves. And no, they're not covered with fuzz. Fuzzy refers to the fuzzy logic computer chip inside the oven. This chip turns an ordinarily dumb machine into one smart cookie.

Not Just Microwaves Fuzzy logic is spiffy technology that can make almost any machine work better.

Fuzzy washing machines automatically know how much soap and water to add to a load of laundry. They stop washing as soon as the clothes are clean.

Fuzzy, automobiles adjust themselves to fit driving conditions. This saves gas and gives a better ride.

Fuzzy cameras adjust themselves so even a beginner can take good pictures, with every photograph in focus. Fuzzy video cameras remove the jiggle.

It's a technology that will change forever the way we deal with machines.

FUZZY LOGIC

"When Theseus returned from slaying the Minotaur, says Plutarch, the Athenians preserved his ship, and as planks rotted, replaced them with new ones. When the first plank was replaced, everyone agreed it was still the same ship. Adding a second plank made no difference either. At some point, the Athenians may have replaced every plank in the ship. Was it a different ship? At what point did it become one?"

Questions of the above nature, bothered people acquainted with a classical logic for ages. The Aristotelian concept of the excluded middle, where every logical preposition has to either be completely true or false, does not seem to fulfill expectations of nowadays very technical and logic dependent world. Nevertheless, most computer, control system engineers and many other people involved in modeling and programing behavior still rely on the True/False conditions and differential equations. There were several people who tried to adjust classical logic to accept a broader concept of something being true or false. In the early 1900's, Lukasiewicz presented his three-valued logic, where the third value proposed could be described as "possible", and had a numeric value between True and False. His efforts were followed by Knuth, but none of the notions gained a wide acceptance. It was not until 1965, when Lotfi Zadeh published his works on fuzzy sets and math accompanying them. The theory quickly was branded fuzzy logic. It created a lot of new possibilities along with controversy and misunderstandings. This paper attempts to give a general description of the concepts of fuzzy logic and applications that might benefit from it.

The classical logic relies on something being either True or False. A True element is usually assigned a value of 1, while False has a value of 0. Thus, something either completely belongs to a set or it is completely excluded from it. The fuzzy logic broadens this definition of membership. The basis of the logic are fuzzy sets. Unlike in "crisp" sets, where membership is full or none, an object is allowed to belong only partly to one set. The membership of an object to a particular set is described by a real value from the range between 0 and 1. Thus, for instance, an element can have a membership value 0.5, which describes a 50% membership in a given set. Such logic allows a much easier application of many problems that cannot be easily implemented using classical approach.

For example, considering a set of tall people in the classical logic, one has to decide where is the border between the tall people and people that are not tall. If the border is set to ex. 6 feet, than, if the person is 6 feet and 1 inch tall, it belongs to the set of tall people. If the person is 5 feet 11 inches tall it does not belong to the set. In this case such a representation of reality leaves much to be desired. On the other hand, using the fuzzy logic, the person being 6-1 tall can still have a full membership of the set of tall people, but the person that is 5-11 tall, can have 90% membership of the set. The 5-11 person thus can have, what can be described as a "quite tall" representation in a model.

Such a classification certainly allows a single object to be a member of two mutually exclusive in the "crisp" sense sets. For example a person 5 feet and 5 inches tall can be classified as 0.5 tall and also 0.3 short, thus it could be described as "rather tall" and at the same time "sort of short". A single element membership to different sets does not have to add up to any particular value. Although, a membership to a negative set (ex. a set of not tall people) has to equal to 1 minus membership to the positive set (a set of tall people).

Because of the above alterations, some logical operations had to be also modified. For the union of two sets, it was found, the result is the higher membership value out of the two. For example if an element is a person that is 0.6 member of a set of smart people and 0.7 member of a set of pretty people, it makes logical sense to state that such person has 0.7 membership in a set of smart or pretty people. The intersection of the two sets is the minimal element of the operators. Thus, referring to the above example, the person would be only 0.6 member of a set of smart and pretty people.

It is worth noting that such a representation operates on different principles than probabilistic theory, which relies on the same set of values, and is often confused with the fuzzy set manipulation. Unlike as in the fuzzy sets, where an element is partly a member of a set, the probability value describes a chance of the whole element belonging to a particular set. The union and the intersection are the most obvious differences between these two representations. In the case of the fuzzy logic adding memberships for the union of sets or multiplying memberships for the intersection makes no logical sense (ex. a person from the example being 1.3 member of a set of smart or pretty people or 0.42 member of a set of smart and pretty people).

Fuzzy logic since its beginnings stirred a lot of controversy in the United States. Although it is a reliable and consistent source of modeling reality, it is not easily representable in the form of differential equations, most control engineers nowadays have learned to rely on. The name itself became a controversy on the American market. Some people argued that it is too "fuzzy" and too unpredictable. While the States stalled in the controversy, there were thousands of successful fuzzy logic implementations performed in Japan. It is suspected that Japanese culture, which bases on the philosophy that there is no absolute good or absolute evil, had no objections to the concept of partial memberships to different groups. Thus, a lot of Japanese firms applied fuzzy logic concepts to factory and industry control systems, medical and navigational equipment, home electronics, and many more.

One of the most successful fuzzy logic implementations is the control of subway in Sendai, Japan. The fuzzy system controls acceleration, deceleration, and breaking of the train. Since its introduction, it not only reduced energy consumption by 10%, but the passengers hardly notice «now when the train is changing its velocity. In the past neither conventional, nor human control could have achieved such performance.

Generally the fuzzy logic is recommended for the implementation of a very complex processes, where a simple mathematical model cannot be obtained. Fuzzy logic can also be successfully applied to a highly nonlinear processes, where it is observed to greatly simplify the modeling. It is not recommended to employ fuzzy logic into systems where a simple and adequate mathematical model already exists or where the conventional control theory yields a satisfying result. Fuzzy logic seems to be a general case for the classical logic and as such it does not present any better solutions for problems that might be easily solved using the "crisp" sets.

The most obvious implementation for the fuzzy logic is the field of artificial intelligence. In the examples stated at the beginning of this paper it was shown how one can easily relate logic to ambiguous linguistics in form of "very", "little", "sort of, and so on. Such flexibility allows for a rapid advancements and easier implementation of projects in the field of natural language recognition. Although, fuzzy logic not only brings logic closer to natural language, but also closer to human or "natural" reasoning. Many times knowledge engineers have to deal with very vague and common sense descriptions of the reasoning leading to a desired solution. The power of fuzzy logic is to perform reasonable and meaningful operations on concepts that cannot be easily codified using a classical approach. Implementing the logic will not only make the knowledge systems more user friendly, but it also will allow programs to justify better the obtained results.

Fuzzy logic seems to be a general case for the classical logic. It modifies the rules for a set membership and defines operations on modified sets. It allows an element to belong only partly to a given set. Such modification allows for a much more flexible and wide spread use of reliable and consistent logic in a variety of applications. So far, the most common use of the fuzzy logic was encountered in the field of control systems, although the theory seems to have a big potential in the different fields of artificial intelligence. The logic stirred a lot of controversy since its introduction, but as it is successfully implemented into more and more applications, it becomes a more accepted way of modeling reality.