A new similarity method based on weighted-linear temporal logic tree and weighted directed acyclic graph for graph-based business process models

A business process is a set of activities that needs to be considered in organizations or companies. Linear temporal logic (LTL) can models relationships of activities; however, the existing LTL does not consider occurrences probability of relationships of activities based on the event log. Weighted Linear Temporal Logic (W-LTL) extends the existing LTL by giving weights based on the occurrences probabilities. This paper proposes a new similarity method that combines Weighted-Linear Temporal Logic (W-LTL) Tree and Weighted Directed Acyclic Graph (wDAG) that modifies the original wDAG similarity, so it can distinguish the similarity value of two wDAGs that have two branches with opposite weight values. The proposed method (W-LTLDAG) will be verified by comparing with the original wDAG similarity, TPED, Cosine-TDP, and WGED. Based on the comparison, wDAG and WGED gives similarity value of 1 for all experiments, shows that both cannot distinguish weight between 2 graphs. TPED only concerns on relation without giving regards to the number of traces, Cosine-TDP and proposed method are able to distinguish parallel relations that have different occurrence probability of activity relations, but proposed method is proven to give a better calculation by giving a high similarity value, 0.976 for graphs with a small difference value of weights between branches, and low similarity value, 0.327 for graphs with a large difference value of weights between branches.