Abstract
B-algebra is an algebraic structure related to BCI/BCK-algebra. Many researchers have studied fuzzy B-ideal on B-algebra, m-polar fuzzy set on BCI-algebra and B-algebra, m-polar fuzzy subalgebra on BCI-algebra and B-algebra, m-polar fuzzy ideal on BCI-algebra, m-polar (∈,∈)-fuzzy p-ideal on BCI-algebra, m-polar (∈,∈)-fuzzy q-ideal on BCI-algebra, and m-polar (∈,∈)-fuzzy a-ideal on BCI-algebra. We build a new structure, namely m-polar (∈,∈)-fuzzy B-ideal on B-algebra. This research aims to extend the knowledge of m-polar fuzzy sets, which can be combined with other algebraic structures, besides BCI-algebra. In this study, we investigate and describe the properties of m-polar (∈,∈)-fuzzy B-ideal of B-algebra. We also investigate the connection among m-polar (∈,∈)-fuzzy B-ideal, m-polar fuzzy subalgebra, and m-polar fuzzy ideal. We serve a condition that causes an m-polar fuzzy ideal to become an m-polar (∈,∈)-fuzzy B-ideal. We also serve expansion properties of an m-polar (∈,∈)-fuzzy B-ideal. Futhermore, examples showing the modification of π_i formula are added. The properties of m-polar (∈,∈)-fuzzy B-ideal of B-algebra are obtained by combining and modifying the properties of m-polar (∈,∈)-fuzzy p-ideal, m-polar (∈,∈)-fuzzy q-ideal, and m-polar (∈,∈)-fuzzy a-ideal of BCI-algebra
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