A fuzzy logic system is composed of four principal components: a fuzzifier, a fuzzy rule base, a fuzzy inference engine and a defuzzifier (Mendel, J. M., 1995). It is an information processing system. Fig. 2 depicts a fuzzy logic system that is widely used in fuzzy logic controllers and signal processing applications. The crisp inputs s, are first converted into fuzzy quantities u. This process is known as fuzzification, where a fuzzifier transforms crisp input values into linguistic values. Input values are translated into linguistic concepts, which are represented by fuzzy sets. Rules may be provided by experts or can be extracted from numerical data. In either case, engineering rules are expressed as a collection of IF-THEN statements. The inference engine Open Access Database www.intechweb.org temperature regulator that uses a fan. Fig. 3 shows the fuzzy sets and the membership functions for the input temperature.
Fig. 3. Fuzzy sets of a simple temperature regulator that use a fanA membership function x , for x∈ X, quantifies the grade of membership of the elements x to the fundamental set Χ. An element mapping to the value 0 means that the member is not included in the given set, 1 describes a fully included member. Values strictly between 0 and 1 characterize the fuzzy members. Membership functions are applied to the measurement and the degree of truth in each determined premise. According to Fig.3, if the input temperature s is 33ºC, after fuzzification, the membership value that s belongs to warm and hot temperature are The fuzzy rules may be provided by a human expert, or can be extracted from numerical input-output data pairs. In either case, engineering rules are expressed as a collection of IF-THEN statements, i.e., "IF temperature is very hot THEN speed maximum fan." "IF temperature is hot THEN speed medium high fan." "IF temperature is warm THEN maintain medium fan." "IF temperature is cold THEN turn down medium low fan." "IF temperature is very cold THEN stop fan." These rules reveal that we will need an understanding of (Mendel, J.M., 1995): 1. Linguistic variables versus numerical values of the variable, e.g., very hot versus 45ºC. 2. Quantifying linguistic variables. E.g., u may have a finite number of linguistic terms associated with it, ranging from very hot to very cold, which is fuzzifying using fuzzy membership functions. There is no unique membership function in a situation and it is primarily subjective in nature. But this does not mean that membership function can be assigned arbitrarily, it is rather on the basis of application-specific criteria. Some of the commonly used membership functions are shown in Fig. 1 (Chen, S., 1990). 3. Implications, which is the relationship between two statements where the truth of one suggests the truth of the other, e.g., "IF temperature is warm THEN maintain medium www.intechopen.comKalman Filter: Recent Advances and Applications 90 fan." Here, the truth of temperature is warm suggests the fan to maintain in medium speed. 4. Logical connections for li...