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Bipolar Fuzzy Set Theory Applied to the Certain Ideals in BCI-Algebras
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The study of symmetry is one of the most important and beautiful themes uniting various areas of contemporary arithmetic. Algebraic structures are useful structures in pure mathematics for learning a geometrical object’s symmetries. In this paper, we introduce new concepts in an algebraic structure called BCI-algebra, where we present the concepts of bipolar fuzzy (closed) BCI-positive implicative ideals and bipolar fuzzy (closed) BCI-commutative ideals of BCI-algebras. The relationship between bipolar fuzzy (closed) BCI-positive implicative ideals and bipolar fuzzy ideals is investigated, and various conditions are provided for a bipolar fuzzy ideal to be a bipolar fuzzy BCI-positive implicative ideal. Furthermore, conditions are presented for a bipolar fuzzy (closed) ideal to be a bipolar fuzzy BCI-commutative ideal.
Title: Bipolar Fuzzy Set Theory Applied to the Certain Ideals in BCI-Algebras
Description:
The study of symmetry is one of the most important and beautiful themes uniting various areas of contemporary arithmetic.
Algebraic structures are useful structures in pure mathematics for learning a geometrical object’s symmetries.
In this paper, we introduce new concepts in an algebraic structure called BCI-algebra, where we present the concepts of bipolar fuzzy (closed) BCI-positive implicative ideals and bipolar fuzzy (closed) BCI-commutative ideals of BCI-algebras.
The relationship between bipolar fuzzy (closed) BCI-positive implicative ideals and bipolar fuzzy ideals is investigated, and various conditions are provided for a bipolar fuzzy ideal to be a bipolar fuzzy BCI-positive implicative ideal.
Furthermore, conditions are presented for a bipolar fuzzy (closed) ideal to be a bipolar fuzzy BCI-commutative ideal.
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