Introduction To Fuzzy System

Introduction

As the complexity of a system enhance, our ability to make precise and until now significant statements about its behavior diminishes till a threshold is reached beyond which significance and precision become almost mutually exclusive characteristics. Zadeh's principle of incapability suggests ambiguity and complexity are correlated: "The closer one seems at a real-world problem, and fuzzier becomes its solution". For such system with little complexity, thus little uncertainty, closed from mathematical expressions provides precise descriptions of the system. Systems are little more complex, however significant data exist, are modeled by methods as like artificial neural networks. At last, for the most complex systems here few numerical data exist and here only imprecise or ambiguous information may be available, fuzzy reasoning gives a way to know system behavior by permitting us to interpolate approximately among observed input and output conditions. Therefore the imprecision in fuzzy models is generally quite high. Fuzzy systems can implement crisp outputs and inputs, and in this case produce a nonlinear functional mapping just as algorithms do. Fuzzy set theory gives a means for modeling the kind of uncertainty associated with a lack of information, with imprecision, and or with vagueness regarding a particular element of the problem on hand. The underlying power of fuzzy set theory is that this uses linguistic variables, quite than quantitative variables, to represent imprecise concept. The incorporation of fuzzy logic and fuzzy set theory into computer models has displayed tremendous payoff in areas where judgment and intuition still play major roles in the model. Control applications, as like process control in computer traffic control, integrated manufacturing, temperature control, are the most prevalent of current fuzzy logic applications. The notion of set membership is central to the presentation of objects inside a universe by sets explained on the universe. Classical set have objects that satisfy precise properties of membership; fuzzy sets have objects that satisfy imprecise properties of membership that is membership of an object in a fuzzy sets can be approximate. To elaborate, assume we have an exhaustive collection of individual elements x, which make up a universe of information X. Further different combinations of these individual elements make up sets, say A, on universe.        

For crisp sets an element x in universe X is either a member of several crisp set A or this is not. This binary issue of membership can be presented mathematically along with the indicator function. Zadeh extended the notion of binary membership to accommodate different degrees of membership in a real continuous interval [0, 1], here the endpoints of 0 and 1 confirm to no membership and full membership, respectively, while indicator function does for crisp sets, however where the infinite number of values among the endpoints can represent different degrees of membership for an element x in some set on the universe. There are different methods name are: Intuition, Rank ordering, Inference, Angular fuzzy sets, Genetic algorithms, neural networks, Meta rules; that are being utilized to enhance membership function.

In the field of machine intelligence there are several ways to represent knowledge. Possibly the most usual way to represent human knowledge is to form this into natural language expression of the type.

                                       IF premise, THEN conclusion  . . . Eqn(1)

This form is usually referred to as the IF-THEN rule-based form. The subjectivity such exists in fuzzy modeling is a blessing quite than a curse. The vagueness present in the definition of terms is consistent along with the information contained in the conditional rules developed by the practitioner here observing some complex process. Although the set of linguistic variables and their meanings is compatible and consistent along with the set of conditional rules utilized, the overall outcome of the qualitative process is translated into objective and quantifiable results. Fuzzy calculus and the mathematical tools of fuzzy IF- THEN rules give a most helpful paradigm for the implementation and automation of an extensive body of human knowledge consequently not embodied in the quantitative modeling process. These mathematical tools provide a means of transferring, communicating, and sharing this human subjective knowledge of processes and system. The rule based system is distinguished from classical expert systems in the sense that the rule containing a rule based system might derive from sources other than human expert, and in such context are distinguished from expert system.