A CMFFP-tree algorithm to mine complete multiple fuzzy frequent itemsets

In the past, many algorithms were proposed to adopt fuzzy-set theory for discovering fuzzy association rules from quantitative databases. The fuzzy frequent pattern (FFP)-tree and the compressed fuzzy frequent pattern (CFFP)-tree algorithms were respectively proposed to mine the incomplete fuzzy frequent itemsets from the tree-based structures. In the past, multiple fuzzy frequent pattern (MFFP)-tree algorithm was proposed to keep more linguistic terms for mining fuzzy frequent itemsets. Since the MFFP-tree algorithm inherits the property of the FFP-tree algorithm, numerous tree nodes are thus required to build the MFFP-tree structure for mining the desired multiple fuzzy frequent itemsets. In this paper, the compressed multiple fuzzy frequent pattern (CMFFP)-tree algorithm is designed to keep not only the linguistic term with maximum membership value but also the other frequent linguistic terms for mining the completely fuzzy frequent itemsets. In the designed CMFFP-tree algorithm, the multiple frequent linguistic terms are sorted in descending order of their occurrence frequencies to build the CMFFP-tree structure. The construction process is the same as the CFFP-tree algorithm except more information are kept for later mining process to discover the completely fuzzy frequent itemsets. Each node in the CMFFP-tree uses the additional array to keep the membership values of its prefix path by intersection operation. A CMFFP-mine algorithm is also designed to efficiently mine the multiple fuzzy frequent itemsets from the developed CMFFP-tree structure. Experiments are then conducted to show the performance of the proposed CMFFP-tree algorithm in terms of execution time and the number of tree nodes, compared to those of the MFFP-tree and CFFP-tree algorithms.