A fuzzy soft matrix is a type of mathematical matrix that combines the principles of fuzzy set theory and soft set theory. It is used to handle uncertainty and vagueness in decision-making problems. Fuzzy soft matrix theory cannot handle negative information. To overcome this difficulty, we define the notion of bipolar fuzzy soft (BFS) matrices and study their fundamental properties. We define products of BFS matrices and investigate some useful properties and results. We also give an application of bipolar fuzzy soft matrices to decision-making problems. We propose a decision-making algorithm based on computer programs under the environment of the bipolar fuzzy soft sets.
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