Abstract
In this article, bipolar fuzzy algebra and bipolar fuzzy relation are defined, and then, the bipolar fuzzy matrix is introduced. Also, an order relation ( $$\le $$ ) is defined and it is proved that the bipolar fuzzy set is a poset and a lattice. Some results on transitive closure and power-convergent of bipolar fuzzy matrices are investigated. Some applications of bipolar fuzzy sets and bipolar fuzzy matrix are included in this study.
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