Determining the Rules for Computing Fixpoints and Introduction of Min-generated Fuzzy Concepts from a Fuzzy Context

Abstract

In theory of fuzzy concept lattice, generating fuzzy concepts from a given data with fuzzy attributes is one of the fundamental problem. Since fuzzy concepts are the fixpoints of a particular fuzzy operator that is associated with input data, the problem of generating fuzzy concepts turn out to be the problem of computing all fixpoints of this operator. In this article, we have established ten rules for generating fixpoints of two fuzzy closure operators, \(\uparrow\downarrow\) and \(\downarrow\uparrow\). Then unifying all the proposed rules, we present a new method and algorithm for computing fixpoints (fuzzy concepts) which are defined as min-generated fuzzy concepts.