Abstract
In this study we establish and investigate multiplicative co-derivative operators on BL-algebras. We also indicate that multiplicative co-derivative operators are more general operators than multiplicative interior operators and modal operators on BL-algebras. Furthermore, we describe relations between multiplicative co-derivative operators on BL-algebras and on the algebras of their regular elements. Moreover, 𝟋-filters (𝟋-derivative systems) will be introduced on BL-algebras depending on any multiplicative co-derivative operator 𝟋 on BL-algebras. We also show that some sets of BL-algebras are 𝟋-filters (𝟋-deductive systems) on BL-algebras. Next, we will define quotient BL-algebra by means of any multiplicative co-derivative operator 𝟋 on BL-algebra and any 𝟋-derivative systems on BL-algebra. Finally, we will define a new operator on the quotient BL-algebra with the aid of the operator 𝟋 and show that the new operator is a multiplicative co-derivative operator on the quotient BL-algebra.
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