Generation of proto-fuzzy concepts from fixpoints of fuzzy closure operators

Abstract

It is well known in Formal Concept Analysis that computation of all formal concepts from data table with graded attributes can be reduced to the problem of computing fixpoints of two fuzzy closure operators, ↑↓ and ↓↑. It is also true that as the size of datasets grows, the fuzzy concepts generated from fuzzy context become larger in number. Therefore for large and complex datasets, it is very hard to deal with such a large number of fuzzy concepts. To handle large and complex datasets, several alternative approaches were proposed to the fuzzy concept lattice theory by researchers. The fuzzy concepts introduced by Kridlo et al (2008) are known as proto-fuzzy concepts. In point of view of applications in different domain, significance of proto-fuzzy concepts is very much effective. But as far as our knowledge is concerned, there is no general method to generate proto-fuzzy concepts. In this paper, we present an algorithm for finding proto-fuzzy concepts directly from the input data. The algorithm we present generates proto-fuzzy concepts form the fixpoints of the fuzzy closure operators, ↑↓ and ↓↑.