Null-norm On A Bounded Lattice

In this paper,we mainly study the construction methods of the nullnorms on bounded lattices and idempotent nullnorms on bounded polygonal chain lattices.Then we propose five conditions equivalent to the definition of ordered isomorphism and proceed with prove.The first chapter is the introduction.We briefly describe the research background,research status and main research results and innovations of this thesis.In the second chapter,we introduce some related definitions and theorems that need to be used in this paper.In the third chapter,we start with the discussion of the different intervals of the nullnorm,and prove that there are only three construction methods for the nullnorm on the bounded lattice.In the second section,the predecessors' propositions are negated and we give a counterexample.Then a new proposition is proposed to indicate the relationship(ie,the order relationship)between the three nullnorms.In the third section,we first define a type of bounded polygon chain lattice,and give the two construction methods of the idempotent nullnorm on the bounded polygon chain lattice.In the fourth chapter,we start with the definition of order isomorphism,and put forward five equivalent conditions and prove it.