Design, Implementation and Evaluation of MTBDD based Fuzzy Sets and Binary Fuzzy Relations

Abstract

For fast and efficient analysis of large sets of fuzzy data, elimination of redundancies in the memory representation is needed. We used MTBDDs as the underlying data-structure to represent fuzzy sets and binary fuzzy relations. This leads to elimination of redundancies in the representation, less computations, and faster analyses. We have also extended a BDD package (BuDDy) to support MTBDDs in general and fuzzy sets and relations in particular. Different fuzzy operations such as max, min and max-min composition were implemented based on our representation. Effectiveness of our representation is shown by applying it on fuzzy connectedness and image segmentation problem. Compared to a base implementation, the running time of our MTBDD based implementation was faster (in our test cases) by a factor ranging from 2 to 27. Also, when the MTBDD based data-structure was employed, the memory needed to represent the final results was improved by a factor ranging from 37.9 to 265.5.