Fuzzy Logic
- PDF / 180,813 Bytes
- 7 Pages / 504.567 x 720 pts Page_size
- 70 Downloads / 233 Views
Fuzzy Logic
Theory and Application
Alessandra Caggiano Department of Industrial Engineering, Fraunhofer Joint Laboratory of Excellence on Advanced Production Technology (Fh-J_LEAPT Naples), University of Naples Federico II, Naples, Italy
Introduction The concept of fuzzy logic emerged in 1965 within the development of the theory of fuzzy sets by Lotfi A. Zadeh, professor of computer science at the University of California in Berkeley (Zadeh 1965). Later, in 1972, Michio Sugeno of the Tokyo Institute of Technology introduced the concepts of fuzzy measure and fuzzy integral (Sugeno 1972). One of the first control systems built using fuzzy set theory was proposed in 1975 by Ebrahim Mamdani of the University of London to control a steam engine and boiler combination by synthesizing a set of linguistic control rules obtained from skilled human operators (Mamdani and Assilian 1975). It is known as Mamdani fuzzy inference method, and it is the most commonly seen fuzzy methodology. The basic concept underlying FL is that of a linguistic variable, that is, a variable whose values are words rather than numbers. In effect, much of FL may be viewed as a methodology for computing with words rather than numbers. Although words are inherently less precise than numbers, their use is closer to human intuition. Furthermore, computing with words exploits the tolerance for imprecision and thereby lowers the cost of solution. Fuzzy logic effectively deals with the trade-off between significance and precision. FL provides the opportunity for modeling conditions
Synonyms Multivalued logic
Definition The term fuzzy logic has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FLw, is almost synonymous with the theory of fuzzy sets (Zadeh 1975). Extended Definition Basically, fuzzy logic (FL) is a multivalued logic, which allows intermediate values to be defined between conventional evaluations like true/false, yes/no, and high/low. Fuzzy logic is an extension of the traditional logic to intermediate and approximate values.
# CIRP 2016 The International Academy for Production Engineering et al. (eds.), CIRP Encyclopedia of Production Engineering, DOI 10.1007/978-3-642-35950-7_6555-3
2
that are inherently imprecisely defined (Russell and Norvig 2003). Fuzzy Sets and Membership Functions Fuzzy logic starts with the concept of fuzzy set. A fuzzy set is a set without a crisp, clearly defined boundary that can contain elements with only a partial degree of membership. A fuzzy set defines a mapping between elements in the input space (usually referred to as the universe of discourse) and values in the interval [0, 1] (Teti and Kumara 1997). The basic concept of the theory is that of membership function, which specifies to what degree an element belongs to a fuzzy set. Let X be a space of points (objects), with a generic element of X indicated by x. Thus, X = {x}. A fuzzy set A
Data Loading...
