Extensionality based approximate reasoning

Abstract

The aim of this paper is to analyze Approximate Reasoning (AR) through extensionality with respect to the natural T-indistinguishability operator, by considering the indistinguishability level between fuzzy sets as a formal measure of its degree of similarity, resemblance or closeness, having in all these terms an intuitive meaning.Postprint (published version

Mathematical Fuzzy Logics

“…Additionally there have been diverse papers, e.g., [17,18,21,22,35,49], which treated generalized inferences as graded inference relations, often intending applications in the field of approximate reasoning. However, there was not always a nice correspondence between graded inference relations and graded closure operators.…”

On approximate reasoning with graded rules

“…Inference rules were also intensively studied from the algebraical point of view as special operations called compositions (see, e.g. [17,13,3,5]). …”

Extensionality with Respect to Indistinguishability Operators

“…• Given a mapping f : X → Y and E, F fuzzy equivalence relations (indistinguishability operators) on X and Y respectively, f is (E, F )extensional, or simply extensional, with respect to E and F when E(x, y) ≤ F (f (x), f (y)) i.e., when the images of the objects x and y are more similar than the objects themselves. This is essential in fuzzy systems and in Approximate Reasoning, since it means that the consequences are closer than the antecedents [2] [7].…”