Tense Operators "Until" and "Since" on Residuated Lattices

In this paper, two binary tense operators on residuated lattices are introduced. These operators are inspired by the logical connectives Until and Since. Using them an algebra called advanced tense residuated lattice is defined. It is shown that if the underlying residuated lattice is involutive, then the induced algebra is converted into the fuzzy tense algebra introduced by Chajda and Paseka via defined appropriate related operators. Given a time frame a new advanced tense residuated lattice is constructed by defining related tense operators (U) over cap and (S) over cap on the residuated lattice of direct power. In the sequel some algebraic notions such as tense filter, quotient algebra and homomorphism in this algebra are introduced and some properties are investigated.