A Framework Design of Dataset Relation Discovery for Solving Inconsistencies by Connection of Heterogeneity in the Big Data Era

We highlight the inconsistencies of past research on the connections among such heterogeneous fields as Linked Data, Semantic Web, Bridge Ontology, and Schema Mapping, as well as our own past researches. Graph structures are commonly represented as links in relationships. For the same domain, relationships agree with each other in the domain because the transitive and order relations are defined. However, in most heterogeneous domains, we have to define the new order relation to link heterogeneous sets. This limitation exists when we consider the relation among heterogeneous fields in set theory. There are three inconsistencies of linking heterogeneous resources: 1) where the relation does not guarantee the future; 2) where no transitive relation is true when anyone connects links for heterogeneous fields; and 3) where no relation in heterogeneous fields can be discovered in set theory. Closed assumption systems have already reached their limits. We call this problem the “Three Opened Assumption’s Inconsistencies,” which is the limit through which we consider the relation between heterogeneous fields in set theory. In the big data era, we must consider a new framework for the Three Opened Assumption’s Inconsistencies. As a solution, we propose a map transformation method from set theory to the Cartesian coordinate system to interconnect these heterogeneous sets and the Three Opened Assumption’s Inconsistencies using two easy mathematical proofs of transitive and order relations to interconnect the heterogeneous resources. In addition, we define a new functional predicate as an example of map transformation from set theory to a Cartesian coordinate system to interconnect the heterogeneous resources for our solution. We also define a correlate function as an example of this framework.