Galois Connections in Data Analysis: Contributions from the Soviet Era and Modern Russian Research

Abstract

A retrospective survey of several research directions at the All-Soviet (now All-Russia) Institute for Scientific and Technical Information (VINITI), as well as research represented in several VINITI editions, is proposed. In a number of papers of the 1970-1980s, taxonomies (classifications) were naturally considered as lattices. Several problems of classification required consideration of tolerance relations as a model of similarity of objects. Such relations define symmetric formal contexts. A JSM-method of inductive plausible reasoning, which has been developed at VINITI since the early 1980s, is considered in terms of Galois connections and concept lattices. Mathematical research around the JSM-method and its applications is discussed.