Partial Residuated Implications Induced by Partial Triangular Norms and Partial Residuated Lattices

This paper reveals some relations between fuzzy logic and quantum on partial residuated implications (PRIs) induced by t-norms as well proposes monoids (PRMs) lattices (PRLs) defining adjoint pairs. First of all, we introduce the connection lattice effect algebra according to concept given Borzooei, together with proof that operation in any commutative quasiresiduated is t-norm. Then, offer general form PRI definition implication (PFI), give condition a implication, prove each PFI. Next, propose PRLs, study their basic characteristics, discuss correspondence PRLs algebras (LEAs), point out relationship LEAs algebras. In addition, like t-norms, provide notions triangular conorms (partial t-conorms) corresponding co-residuated (PcRLs). Lastly, based lattices, define (wPRLs), filter then construct quotient structure PRMs.