Fuzzy Logic
11) It is a form of multivalued logic derived from set theory to deal with reasoning that is approximate rather than premise.
22) It is a form of mathematical logic in which truth can assume a values in between 0 and 1.
33) It can be implemented in hardware, software or a combination of both.
44) It is a superset of conventional or Boolean logic that has been extended to handle the concept of partial truth values between complement true and completely false.
55) In a fuzzy logic, everything is a matter of degree.
66) Any logic system can be fuzzified.
77) In fuzzy logic, knowledge is interpreted as a collection of fuzzy constraint on a collection of variables.
Fuzzy Set
A fuzzy set A in U where U={u1,u2,u3,......, up to n times} be the universe of discourse, is defined as the set of ordered pairs
A={ (u1.µA(u) : u belongs to U) },
where µA(u) is grade of membership of element u in the set.
The greater µA(u), the greater is the truth of statement that the element u belongs to the set.
The membership function for fuzzy system sets can take values from the closed interval [0,1]
Fuzzy logic is a convenient way to map an input space to an output space. Mapping input to output is starting point for everything.
Diagram:
A black box contains any number of things fuzzy systems, linear systems, expert systems, neural networks, etc.
