Interval-Valued Neutrosophic Graph Representation of Concept Lattice and Its ( $$\alpha ,\beta ,\gamma $$ α , β , γ )-Decomposition

Abstract

Recently, three-way representation of fuzzy concept lattice is introduced to characterize the uncertainty and vagueness in the given data set based on its acceptation, rejection and uncertain regions, by a well-defined single-valued neutrosophic set. This paper put forward effort to deal with partial ignorance in the given three-way fuzzy context using the properties of interval-valued neutrosophic set and its graphical properties. The objective is to discover some of the important hidden patterns (i.e. formal concepts) in the interval-valued neutrosophic context, and visualize their super–sub-concept hierarchical-order reflection in the concept lattice. To achieve this goal, a method is proposed to generate the interval-valued neutrosophic formal concepts based on properties of interval-valued neutrosophic set, interval-valued neutrosophic graph and concept lattice. Another method is proposed to refine some of the important patterns (i.e. interval-valued neutrosophic formal concepts) at user-defined ( $$\alpha , \beta , \gamma $$ )-cut for their truth (i.e. $$\alpha $$ -cut), indeterminacy (i.e. $$\beta $$ -cut) and falsity (i.e. $$\gamma $$ -cut) membership value, independently. In addition to that, both of the proposed methods are demonstrated with an illustrative example.