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

TL;DR

This paper presents a novel MTBDD-based data structure for representing fuzzy sets and relations, significantly reducing memory usage and computation time in fuzzy data analysis tasks.

Contribution

The paper extends a BDD package to support MTBDDs for fuzzy data, enabling more efficient analysis and demonstrating substantial improvements in speed and memory usage.

Findings

Speedup factor of 2 to 27 in test cases

Memory reduction factor of 37.9 to 265.5

Effective application to fuzzy connectedness and image segmentation

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.