Fuzzy Logic Systems
Fuzzy Logic is a new generation of expert systems developed in the late sixties and early seventies by Lotfi Zadeh of the University of California at Berkeley.It is designed to simulate human thinking to intellectualize computer programs and microprocessor chips operations in decision making and control applications. The idea behind fuzzy logic is to capture human experience which is available in the form of linguistic terms and rules to intellectualize computer software technology. Humans perceive world events not only as black and white, but with a large gray area extending between these two limits. Many adjectives and descriptions used are quite vague. For example, people may be described as being tall, short, fat, thin etc., and even though these labels are vague in the sense that they do not give exact measurements, they are understood. Fuzzy logic refers to this human ability to perform logical reasoning using such usual facts and previous experience (knowledge). Examples of the facts which are fuzzy in nature and contain imprecise statements and descriptions are:
- The temperature is high
- The motor speed is normal
The experience is captured as human rules in the form of “IF … THEN” statements such as:
- IF the flow is low THEN open the valve moderately
- IF car speed is high THEN press brake firmly
Fuzzy logic handles VAGUE situations to provide as PRECISE decisions as possible.
Fuzzy logic has two strong features:
- It accepts imprecise, human-like (fuzzy) knowledge, compared to knowledge-based systems with precise knowledge such as traditional expert systems.
- It employs powerful adaptive reasoning mechanism to deduce results from facts (e.g. measurements) and fuzzy (human) knowledge (e.g. rules).
Fuzzy logic is:
- A new way of developing and implementing control systems;
- A method for handling control systems which are:
- too complex,
- highly nonlinear,
- uncertain using traditional techniques and methods.
- Used for complex systems which cannot be modeled mathematically;
- Not in conflict with conventional methods and can be added or integrated to them;
- Solves the question of uncertainty;
- Provides a systematic framework for dealing with linguistic quantifiers such as most, many, few, somewhat, almost etc.
To see what is meant by saying fuzzy logic accepts imprecise knowledge, consider the conventional set theory on which the Boolean logic operates. An object is either a member of a given set of objects or not. In fuzzy set theory, however, an object has a degree of membership in a given set of objects. This degree can be anywhere between 0 (not a member of the set) and 1 (completely in the set). So if we say John is short, Boolean logic would require John to belong to the set of short people and the statement would be either TRUE or FALSE. Fuzzy logic, on the other hand, would not have such a stringent requirement. Instead, it would assign a degree of membership for John in the set of short people, say 0.4 . This allows fuzzy logic to handle human concepts in a natural and simple way.
Fuzzy logic defines operators on the values of membership functions which are analogous to Boolean logic operators. These are AND, OR and NOT and used as shown in the table below: