Vector retrieval, fuzzy retrieval and the universal fuzzy IR surface for IR evaluation

Abstract

It is shown that vector information retrieval (IR) and general fuzzy IR uses two types of fuzzy set operations: the original "Zadeh min–max operations" and the so-called "probabilistic sum and algebraic product operations". The universal IR surface, valid for classical 0–1 IR (i.e. where ordinary sets are used) and used in IR evaluation, is extended to and reproved for vector IR, using the probabilistic sum and algebraic product model. We also show (by counterexample) that, using the "Zadeh min–max" fuzzy model, yields a breakdown of this IR surface.