Multi-Granulation-Based Graphical Analytics of Three-Way Bipolar Neutrosophic Contexts

Abstract

Recently, a three-way fuzzy concept lattice and its graphical structure analytics has given a mathematical way to deal with cognitive concept learning based on its truth, false, and uncertain regions, independently. In this process, a major problem was addressed while existence of bipolar information in a three-way decision space. To address this problem, the current paper aimed at introducing bipolar neutrosophic graph representation of concept lattice and its granular-based processing for cognitive concept learning. In addition, the proposed method is illustrated with an example for better understanding. Cognitive computing provides a way to mimic with human brain and its uncertainty beyond the binary values. To characterize these types of bipolar attributes based on its acceptation, rejection, and uncertain part, the three-way bipolar neutrosophic context and its concept lattice is introduced in this paper. In addition, another method is proposed to extract some of the bipolar cognitive concepts based on user required bipolar truth, bipolar indeterminacy, and falsity membership values, independently. This paper provides a graphical structure visualization of the three-way bipolar information at user defined granules. It is also shown that the extracted information from both of the proposed methods are concordant with each other. It is also shown that, the proposed method provides an adequate way to model the three-way bipolar cognitive concepts when compared to other available approaches. This paper introduces a method to model the three-way bipolar cognitive context using the properties of bipolar neutrosophic graph and its lattice structure. The line diagram is drawn based on their lower neighbors within O(|C| n2 m3) time complexity. In addition, another method is proposed to refine the three-way bipolar neutrosophic cognitive concepts at user defined granulation within O(n6) or O(m6) time complexity with an illustrative example. However, the proposed method is unable to measure the changes in the three-way bipolar neutrosophic cognitive concepts at the given phase of time. Due to that, the author will focus on resolving this issue of bipolar neutrosophic context in near future.