On Implicative Derivations of MTL-Algebras

Abstract

This paper introduces the implicative derivations and gives some of their characterizations on MTL-algebras. Furthermore, we provide some representation of MTL-algebras by implicative derivations and obtain some representation of Boolean algebra via the algebra of all implicative derivations. Finally, we explore the relationship between implicative derivation and other operators on MTL-algebras and show that there exists a bijection between the sets of multiplier and implicative derivations on IMTL-algebras. The results of this paper can provide the common properties of implicative derivations in the t-norm-based fuzzy logical algebras.

Keywords

• MTL-algebra
• implicative derivation
• k-modal operator
• Galois connection