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An $m-$polar fuzzy set and soft sets are two different tools for representing uncertainty and vagueness. An $m-$polar soft fuzzy set is a mapping from parameter set to the $m-$polar fuzzy subsets of the universe. An $m-$polar soft fuzzy set theory provides a parameterized point of view for uncertainty modeling and soft computing model. In this paper, we have introduced the notions of $m-$polar soft fuzzy bipartite graph, size and degree of $m-$polar soft fuzzy bi-partite graph as well as an investigation on buying of residence by considering various parameters. People, while buying residence, have many options. So, to choose the best one, they have to consider many parameters. $m-$polar soft fuzzy graph is one of the major areas of graph theory, which finds a solution to this problem