Reliable Computing 4: 99–101, 1998.
1998 Kluwer Academic Publishers. Printed in the Netherlands.
A New Application of Local Minima of Interval
Functions: Interval-Valued Fuzzy Control
Department of Computer Science, University of Houston, Houston, TX 77204-3350, USA,
(Received: 10 March 1996; accepted: 8 February 1997)
Abstract. A new application is proposed for the algorithms of ﬁnding local minima of an interval-
valued function: computing control in intelligent control systems.
1. The Main Idea of Fuzzy (Intelligent) Control
Fuzzy control (see, e.g., –) isamethodologythat transforms (rule-based fuzzy)
knowledge of a skilled human operator into the design of an automated controller.
This methodology has many successful applications, ranging from the temperature
control of the Space Shuttle to appliances like washing machines .
A similar problem of formalizing expert knowledge is solved in expert systems;
the main difference is as follows:
An expert system produces advise for the human decision-maker (just as an
expert would). For example, a medical expert system can conclude that a patient
has cancer with degree of belief 60% and TB with a degree of belief 30%, and
that probably further tests are needed before we can choose the appropriate cure.
A fuzzy control system must function automatically, and therefore, it must make
a control decision even if we do not have complete information.
In other words, for a fuzzy control system, it is not sufﬁcient to describe which
control values are reasonable with what degree of belief (as an expert system would
do), but we must also use this information about different control values to generate
a single control value that will be actually applied.
In mathematical terms, an expert-system like methodology enables us to compute,
for different possible control values u, the degree of belief (denoted usually by
that u is an appropriate control value; we must transform the resulting function
into a single value
u. This transformation must transform the uncertain (“fuzzy”)
decision about control (as expressed by the function
(u)) into a precise one (as
described by a single number
u), and is, therefore, called a defuzziﬁcation.