Fuzzy logic was developed by Lotfi A. Zadeh in the 1960s in order to provide mathematical
rules and functions which permitted natural language queries. Fuzzy logic provides a means
of calculating intermediate values between absolute true and absolute false with resulting
values ranging between 0.0 and 1.0. With fuzzy logic, it is possible to calculate the degree
to which an item is a member. For example, if a person is .83 of tallness, they are "
rather tall. " Fuzzy logic calculates the shades of gray between black/white and true/false.
Fuzzy logic is a super set of conventional (or Boolean) logic and contains similarities and
differences with Boolean logic. Fuzzy logic is similar to Boolean logic, in that Boolean logic
results are returned by fuzzy logic operations when all fuzzy memberships are restricted to 0
and 1. Fuzzy logic differs from Boolean logic in that it is permissive of natural language
queries and is more like human thinking; it is based on degrees of truth.
The graphical representation of fuzzy and boolean sets are different as well. Place your mouse over the words below to view the respective graphs.
Fuzzy logic may appear similar to probability and statistics as well. Although, fuzzy logic is
different then probability even though the results appear similar. The probability statement,
" There is a 70% chance that Bill is tall" supposes that Bill is either tall or he is
not. There is a 70% chance that we know which set Bill belongs. The fuzzy logic statement,
" Bill's degree of membership in the set of tall people is .80 " supposes that Bill
is rather tall. The fuzzy logic answer determines not only the set which Bill belongs, but
also to what degree he is a member. There are no probability statements that pertain to fuzzy
logic. Fuzzy logic deals with the degree of membership.
Fuzzy logic has been applied in many areas; it is used in a variety of ways. Household
appliances such as dishwashers and washing machines use fuzzy logic to determine the optimal
amount of soap and the correct water pressure for dishes and clothes. Fuzzy logic is even used
in self-focusing cameras. Expert systems, such as decision-support and meteorological systems,
use fuzzy logic. Fuzzy logic has many varied applications.
The application of fuzzy logic is being debated. Formal logicians argue the usefulness of fuzzy logic while others
maintain its practical applications are very successful.
For more information, check out #2, #3, #5, #7 on our References page.
What do you think?
The History of Fuzzy Logic provides information on how it all began.
