m-polar fuzzy graph representation of concept lattice

- A method is introduced to represent the data with m-polar information in the formal context.
- An elicit link between m-polar fuzzy set, m-polar fuzzy graph and concept lattice has been established for knowledge processing tasks.
- An algorithm is proposed for generating the m-polar formal fuzzy concepts using their subset.
- Another algorithm is proposed to analyze the m-polar formal fuzzy concepts based on their object set and attribute set using projection.
- One application of the proposed algorithms is also discussed with an illustrative example.

Recently, the calculus of fuzzy concept lattice is studied beyond the three-way fuzzy space ([0,1]3) for precise representation of uncertainty and vagueness in the attributes. However, to dovetail the uncertainty in case of voxel, multi-index or multi-polar information the properties of lattice theory need to be explored in component wise m-polar fuzzy space ([0,1]m). In this case, another problem arises while finding some of the hidden or interested pattern from the given m-polar fuzzy context for the knowledge processing tasks. To conquer this problem, current paper generalizes the mathematical background of concept lattice with m-polar fuzzy sets and its graphical properties. To elicit this objective, two methods are introduced for providing a unified framework based on discovered m-polar formal fuzzy concepts and their projection.

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