The Duality of Good Diagnostic Tests

The Duality of Good Diagnostic Tests

Xenia Naidenova (Military Medical Academy, Russia)
DOI: 10.4018/978-1-60566-810-9.ch008
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Abstract

The concept of good classification test is redefined in this chapter as a dual element of interconnected algebraic lattices. The operations of lattice generation take their interpretations in human mental acts. Inferring the chains of dual lattice elements ordered by the inclusion relation lies in the foundation of generating good classification tests. The concept of an inductive transition from one element of a chain to its nearest element in the lattice is determined. The special reasoning rules for realizing inductive transitions are formed. The concepts of admissible and essential values (objects) are introduced. Searching for admissible or essential values (objects) as a part of reasoning is based on the inductive diagnostic rules. In this chapter, we also propose a non-incremental learning algorithm NIAGaRa based on a reasoning process realizing one of the ways of lattice generation. Next, we discuss the relations between the good test construction and the Formal Concept Analysis (FCA).
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Correspondence Of Galois For Good Classification Test Definition

Let S = {1, 2,…, N} be the set of objects’ indices (objects, for short) and T = {A1, A2, …, Aj, …Am} be the set of attributes’ values (values, for short). Each object is described by a collection of values from T.

The definition of good tests is based on correspondences of Galois G on S×T and two relations ST, TS (Ore, 1944; Riguet, 1948; Everett, 1944). Let sS, tT. Denote by ti, tiT, i = 1,…, N the description of object with index i. We define the relations ST, TS as follows:

ST: t = val(s) = {intersection of all ti: tiT, i ∈ s} and TS: s = obj(t) = {i: iS, tti}.

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