Bipolar fuzzy concepts reduction using granular-based weighted entropy

The bipolar fuzzy concept lattice has given a way to analyze the uncertainty in soft data set beyond the unipolar space. In this process, a problem is addressed while dealing with large number of bipolar fuzzy concepts and its importance for adequate decision-making process. It may create randomness in the decision due to bipolarity and its existence in customer feedback, or expert opinion. To overcome from this issue, the current paper tried to measure the randomness in bipolar fuzzy concepts using the properties of Shannon entropy. The importance of bipolar fuzzy concept is decided based on defined window of granulation (α1,α2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _1, \alpha _2$$\end{document}) for its computed weight with an illustrative example. The obtained results are also compared with recently available approaches on data with bipolar fuzzy attributes for validation.