Title :
Investigating approximate reasoning and fuzzy control by concepts of functional analysis
Author_Institution :
Dept. of Comput. Sci., Dortmund Univ., Germany
Abstract :
We investigate the input-output behaviour of the inference machine of a fuzzy controller, which is interpreted as a functional operator operating on the set of all fuzzy sets defined on a given universe. The concepts of fixed point, eigen function, eigen value and linearity are suitably translated into the fuzzy approach presented. Classical fixed point theorems (Birkhoff, Zorn, Banach) are applied in order to investigate the behaviour of inference machines. The concept of linearity is studied for Mamdani interpretations
Keywords :
digital arithmetic; eigenvalues and eigenfunctions; functional analysis; fuzzy control; fuzzy set theory; inference mechanisms; uncertainty handling; Mamdani interpretations; approximate reasoning; classical fixed point theorems; eigen function; eigen value; fixed point; functional analysis; functional operator; fuzzy approach; fuzzy control; fuzzy controller; fuzzy sets; inference machine; input-output behaviour; linearity; Circuits; Computer science; Control systems; Equations; Feeds; Functional analysis; Fuzzy control; Fuzzy reasoning; Fuzzy sets; Linearity;
Conference_Titel :
Knowledge-Based Intelligent Electronic Systems, 1997. KES '97. Proceedings., 1997 First International Conference on
Conference_Location :
Adelaide, SA
Print_ISBN :
0-7803-3755-7
DOI :
10.1109/KES.1997.619428
