Persistent Homology is a computational method of data mining in the field of Topological Data Analysis. Large-scale data analysis with persistent homology is computationally expensive and memory intensive. The performance of persistent homology has been rigorously studied to optimize data encoding and intermediate data structures for high-performance computation. This paper provides an application-centric survey of the High-Performance Computation of Persistent Homology. Computational topology concepts are reviewed and detailed for a broad data science and engineering audience.

In crisp rule-based systems with rules such as "If u is A, then v is B" an exact match between the given rule antecedent value A and the observed input must occur in order to output the rule consequent value B. Fuzzy inferencing extends crisp rule- based systems to allow uncertainty in both the rule antecedent A and the rule consequent B in the form of fuzzy sets for their values. Here the observed input value A' does not have to exactly match the antecedent value A in order to produce the output B' which does not have to exactly match B. This paper examines the traditional fuzzy inferencing method for fuzzy control that is similarity-based and uses Zadeh's consistency or partial matching index and distance-based methods, one referred to as geometric compatibility modification (GCM) and the other transformation constraint-based generalized modus ponens (T-CGMP). These fuzzy inferencing methods are compared based on the results from test cases and different methods of aggregation when multiple fuzzy sets occur in the rule antecedent.