Sinopsis
In the literature sources, we can find different kinds of justification for fuzzy systems theory. Human knowledge nowadays becomes increasingly important – we gain it from experiencing the world within which we live and use our ability to reason to create order in the mass of information (i.e., to formulate human knowledge in a systematic manner). Since we are all limited in our ability to perceive the world and to profound reasoning, we find ourselves everywhere confronted by uncertainty which is a result of lack of information (lexical impression, incompleteness), in particular, inaccuracy of measurements. The other limitation factor in our desire for precision is a natural language used for describing/sharing knowledge, communication, etc. We understand core meanings of word and are able to communicate accurately to an acceptable degree, but generally we cannot precisely agree among ourselves on the single word or terms of common sense meaning. In short, natural languages are vague.
Our perception of the real world is pervaded by concepts which do not have sharply defined boundaries – for example, many, tall, much larger than, young, etc. are true only to some degree and they are false to some degree as well. These concepts (facts) can be called fuzzy or gray (vague) concepts – a human brain works with them, while computers may not do it (they reason with strings of 0s and 1s). Natural languages, which are much higher in level than programming languages, are fuzzy whereas programming languages are not. The door to the development of fuzzy computers was opened in 1985 by the design of the first logic chip by Masaki Togai and Hiroyuki Watanabe at Bell Telephone Laboratories. In the years to come fuzzy computers will employ both fuzzy hardware and fuzzy software, and they will be much closer in structure to the human brain than the present-day computers are. The entire real world is complex; it is found that the complexity arises from uncertainty in the form of ambiguity. According to Dr. Lotfi Zadeh, Principle of Compatability, the complexity, and the imprecision are correlated and adds, The closer one looks at a real world problem, the fuzzier becomes its solution (Zadeh 1973).
The Fuzzy Logic tool was introduced in 1965, also by Lotfi Zadeh, and is a mathematical tool for dealing with uncertainty. It offers to a soft computing partnership the important concept of computing with words’. It provides a technique to deal with imprecision and information granularity. The fuzzy theory provides a mechanism for representing linguistic constructs such as “many,” “low,” “medium,” “often,” “few.” In general, the fuzzy logic provides an inference structure that enables appropriate human reasoning capabilities. On the contrary, the traditional binary set theory describes crisp events, events that either do or do not occur. It uses probability theory to explain if an event will occur, measuring the chance with which a given event is expected to occur. The theory of fuzzy logic is based upon the notion of relative graded membership and so are the functions of mentation and cognitive processes. The utility of fuzzy sets lies in their ability to model uncertain or ambiguous data, Fig. 1.1, so often encountered in real life.
It is important to observe that there is an intimate connection between Fuzziness and Complexity. As the complexity of a task (problem), or of a system for performing that task, exceeds a certain threshold, the system must necessarily become fuzzy in nature. Zadeh, originally an engineer and systems scientist, was concerned with the rapid decline in information afforded by traditional mathematical models as the complexity of the target system increased. As he stressed, with the increasing of complexity our ability to make precise and yet significant statements about its behavior diminishes. Realworld problems (situations) are too complex, and the complexity involves the degree of uncertainty – as uncertainty increases, so does the complexity of the problem. Traditional system modeling and analysis techniques are too precise for such problems (systems), and in order to make complexity less daunting we introduce appropriate simplifications, assumptions, etc. (i.e., degree of uncertainty or Fuzziness) to achieve a satisfactory compromise between the information we have and the amount of uncertainty we are willing to accept. In this aspect, fuzzy systems theory is similar to other engineering theories, because almost all of them characterize the real world in an approximate manner.
Fuzzy sets provide means to model the uncertainty associated with vagueness, imprecision, and lack of information regarding a problem or a plant, etc. Consider the meaning of a “short person.” For an individual X, the short person may be one whose height is below 4 25 . For other individual Y, the short person may be one whose height is below or equal to 3 90 . This “short” is called as a linguistic descriptor. The term “short” informs the same meaning to the individuals X and Y, but it is found that they both do not provide a unique definition. The term “short” would be conveyed effectively, only when a computer compares the given height value with the preassigned value of “short.” This variable “short” is called as linguistic variable, which representsthe imprecision existing in the system.
The uncertainty is found to arise from ignorance, from chance and randomness, due to lack of knowledge, from vagueness (unclear), like the fuzziness existing in our natural language. Lotfi Zadeh proposed the set membership idea to make suitable decisions when uncertainty occurs. Consider the “short” example discussed previously. If we take “short” as a height equal to or less than 4 feet, then 3 90 would easily become the member of the set “short” and 4 25 will not be a member of the set “short.” The membership value is “1” if it belongs to the set or “0” if it is not a member of the set. Thus membership in a set is found to be binary i.e., the element is a member of a set or not.
Content
- Introduction
- Classical Sets and Fuzzy Sets
- Classical and Fuzzy Relations
- Membership Functions
- Defuzzification
- Fuzzy Rule-Based System
- Fuzzy Decision Making
- Applications of Fuzzy Logic
- Fuzzy Logic Projects with Matlab
,+A+-+Stroustrup,+Bjarne.jpg)
.jpg){kind=spacer}
0 komentar:
Posting Komentar