Approximate Reasoning

Definition

Approximate reasoning is a deduction method which makes it possible to derive a conclusion on the basis of imprecisely characterized situation (quite often using linguistically specified fuzzy IF-THEN rules) and a new information that can also be imprecise. The basic scheme of approximate reasoning is the following:

$$ \begin{array}{ll}\mathrm{Condition}:& \mathrm{IF}X\mathrm{is}{A}_1\mathrm{THEN}Y\mathrm{is}{B}_1\\ &\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \\ &\mathrm{IF}X\mathrm{is}{A}_m\mathrm{THEN}Y\mathrm{is}{B}_m\\ &\mathrm{Premise}:X\mathrm{is}{A}^{\prime}\\ &\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \\ &\mathrm{Conclusion}:Y\mathrm{is}{B}^{\prime}\end{array} $$

(1)

where “Condition” is a linguistic description consisting of a set of fuzzy/linguistic IF-THEN rules and A^′ is a possible modification of antecedent of some of the former rules. For example, “X is small” can be replaced by “X is very small.”

Key Points

The mathematical...