An efficient method to represent and process imprecise knowledge

We are primarily concerned with the problem of representing imprecise statements and knowledge as well as drawing conclusions based on this type of knowledge. Our particular interest is to establish an efficient method, capable to represent and apply (i.e. reason with) imprecise knowledge within real problems. In the present paper we first introduce an axiomatic framework and discuss it with illustrative examples. One suggestion for an application-oriented specialization is given by scalar fuzzy control (SFC), which is presented in the second part of this paper. After the introduction of the SFC theory, it is proofed that it is a member of the axiomatic framework. Its usage is finally illustrated by applying it to the well known inverted pendulum problem.