Analysis of composed fuzzy contexts through projection

Formal concept analysis (FCA) is a mathematical model for data analysis and processing tasks. Recently, FCA has received significant attention for the analysis of data with fuzzy attributes by representing them as a matter of degree in the formal context. In this paper, we concentrated on the analysis of fuzzy contexts (X, Y, R<SUB align="right"><SMALL>1</SMALL></SUB>) and (Z, Y, R<SUB align="right"><SMALL>2</SMALL></SUB>) which share same attribute set (Y). We can observe that, these two contexts can be connected through composition as (X, Z, R<SUB align="right"><SMALL>3</SMALL></SUB> = R<SUB align="right"><SMALL>1</SMALL></SUB> * R<SUB align="right"><SMALL>2</SMALL></SUB>), which contains objects set from one context and attribute set from another. In this case, the problem is how to analyse the composed contexts with regard to its object and attribute set with less number of formal concepts using FCA. For this purpose, a method is proposed in this study which provides one context with regard to its object set and another with regard to its attribute set.composition; formal concept analysis; FCA; fuzzy formal concepts; fuzzy concept lattice; projection; mathematical modelling; data analysis; data processing