Association rule mining is an important machine learning tool for unveiling critical biological relations between genes from omics data. Previous approaches typically are designed for one single genomic dataset, and most of them use a single minimum support threshold globally. To overcome the above two general limitations, in this work, we present a novel Transcriptomic and Proteomic Rule Mining (TrapRM) method using Weighted Shortest Distance based Multiple Minimum Supports for Multi-Omics Dataset that integrates gene expression, methylation and protein-protein interaction data. To do so, we initially introduce three new thresholds: Weighted Shortest Distance based Multiple Minimum Supports (WSDMS), Weighted Shortest Distance based Multiple Minimum Confidences (WSDMC), and Weighted Shortest Distance based Multiple Minimum Lifts (WSDML). Our algorithm is superior to the related existing algorithms since it generates substantially fewer number of rules and smaller average weighted shortest distance value than the existing methods. Finally, our TrapRM algorithm is useful for extracting the rules that are critical for translational and clinical applications when being applied to drug or disease related multi-omics data.