A fuzzy system is basically a control system based on fuzzy logic, which is a mathematical system that analyzes input values in terms of logical variables that take on continuous values between 0 and 1 instead of belongingness or non-belongingness to any set, as in crisp set theory or classical or digital logic, which operates either in 1 or in 0 for a logic to be true or false respectively. Fuzzy systems have become extremely popular in recent times for their various business applications.
Fuzzy logic on the other hand is the mathematical theory based on set theory, from which fuzzy systems have been developed. Essentially, fuzzy logic is based on fuzzy set theory which proposes that logical variables can take on continuous values between 0 and 1 instead of crisp belongingness or non-belongingness to any set, as in crisp set theory which operates either in 1 or in 0 for a logic to be true or false respectively.
Typically, a response in real life situation is not crisp, i.e. its not in black and white. Say one is asked to judge the performance of a technology application, typically the person (judge) will think that for every specification of feature there is a degree of acceptability in performance while in certain dimensions, the performance is not acceptable. This is precisely what fuzzy logic or fuzzy sets attempts to capture. Here, every item of a set may belong to multiple sets by a degree of belongingness and not by absolution of belongingness or non-belongingness to any set.
Today, Fuzzy sets and systems have taken a major interest from both the academia and the industry for its numerous and unlimited applicability and the scope. The first wave of application of these systems were primarily in process control and electronics, while slowly, these have made their impact felt in information systems development and deployment in business processes and activities. The largest applications are in the area of decision sciences in business intelligence and decision making, and is being thought of as one of the biggest change creating mathematical tool.