Regular Partial Residuated Lattices and Their Filters

To express wider uncertainty, B?hounek and Da?ková studied fuzzy partial logic function. At the same time, Borzooei generalized t-norms put forward concept of when studying lattice valued quantum effect algebras. Based on t-norms, Zhang et al. residuated implications (PRIs) proposed lattices (PRLs). In this paper, we mainly study related algebraic structure logic. First, provide definitions regular implication (rPRI) through general forms implication. Second, define (rPRLs) their corresponding properties. Third, relations among commutative quasi-residuated lattices, Q-residuated lattices. Last, in order to obtain filter theory restrict certain conditions then propose special (srPRLs) finally construct quotient