Proto-fuzzy Concepts, their Retrieval and Usage

The aim of this paper is to define so-called proto-fuzzy con- cepts, as a base for generating dierent types of one-sided fuzzy concept lattices. Fuzzy formal context is a triple of a set of objects, a set of at- tributes and a fuzzy binary relation over a complete residuated lattice, which determines the degree of membership of each attribute to each object. A proto-fuzzy concept is a triple of a subset of objects, a subset of attributes and a value as the best common degree of membership of all pairs of objects and attributes from the above-mentioned sets to the fuzzy binary relation. Then the proto-fuzzy concepts will be found with a help of cuts and projections to the object-values or attribute-values plains of our fuzzy-context. 1 Introduction and motivation Let us have a group of schoolmates of a secondary grammar school and their studying results of ten subjects as it is shown in the table below. Names of subjects are in the table as abbreviations (Ma - Math, Sl - Slovak language, Ph - Physics, Ge - Geography, Bi - Biology, Gr - German, En - English, Ch - Chemistry, Ae - Aesthetics, Hi - History). Abbreviations of names of students are in the table.