Logical Interpretation of Fuzzy Control
In spite of the appearance there are several difficulties to give a rigorous logical interpretation of the IF-THEN rules. As an example, interpret a rule as IF (temperature is "cold") THEN (heater is "high") by the first order formula Cold(x)→High(y) and assume that r is an input such that Cold(r) is false. Then the formula Cold(r)→High(t) is true for any t and therefore any t gives a correct control given r. A rigorous logical justification of fuzzy control is given in Hájek's book (see Chapter 7) where fuzzy control is represented as a theory of Hájek's basic logic. Also in Gerla 2005 a logical approach to fuzzy control is proposed based on fuzzy logic programming. Indeed, denote by f the fuzzy function arising of a IF-THEN systems of rules. Then we can translate this system into fuzzy program in such a way that f is the interpretation of a vague predicate Good(x,y) in the least fuzzy Herbrand model of this program. This gives further useful tools to fuzzy control.
Read more about this topic: Fuzzy Control System
Famous quotes containing the words logical, fuzzy and/or control:
“Opera, next to Gothic architecture, is one of the strangest inventions of Western man. It could not have been foreseen by any logical process.”
—Kenneth MacKenzie Clark, Baron of Saltwood (19031983)
“Even their song is not a sure thing.
It is not a language;
it is a kind of breathing.
They are two asthmatics
whose breath sobs in and out
through a small fuzzy pipe.”
—Anne Sexton (19281974)
“In view of the fact that the number of people living too long has risen catastrophically and still continues to rise.... Question: Must we live as long as modern medicine enables us to?... We control our entry into life, it is time we began to control our exit.”
—Max Frisch (19111991)