Article Code : 13950426161622864(DOI : 10.7508/jist.2016.02.007)

Article Title : Design, Implementation and Evaluation of Multi-terminal Binary Decision Diagram based Binary Fuzzy Relations

Journal Number : 14 Spring 2016

Visited : 1498

Files : 421 KB

List of Authors

  Full Name Email Grade Degree Corresponding Author
1 Hamid Alavi Toussi Faculty Member M.Sc
2 Bahram Sadeghi Bigham Associate Professor PhD


Elimination of redundancies in the memory representation is necessary for fast and efficient analysis of large sets of fuzzy data. In this work, we use 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 also extended a BDD package (BuDDy) to support MTBDDs in general and fuzzy sets and relations in particular. Representation and manipulation of MTBDD based fuzzy sets and binary fuzzy relations are described in this paper. These include design and implementation of different fuzzy operations such as max, min and max-min composition. In particular, an efficient algorithm for computing max-min composition is presented.Effectiveness of our MTBDD based implementation is shown by applying it on fuzzy connectedness and image segmentation problem. Compared to a base implementation, the running time of the 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. We also describe our base implementation which is based on matrices.