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

• Main Authors: Toussi, Hamid A, Bigham, Bahram Sadeghi
• Format: Journal Article
• Language: English
• Published: 05.03.2014
• Subjects: Computer Science - Data Structures and Algorithms; Computer Science - Symbolic Computation
• DOI: 10.48550/arxiv.1403.1279

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.