Speeding up the Hungarian algorithm
Computers and Operations Research
Fuzzy Sets and Systems: Theory and Applications
Fuzzy Sets and Systems: Theory and Applications
Applied Fuzzy Arithmetic: An Introduction with Engineering Applications
Applied Fuzzy Arithmetic: An Introduction with Engineering Applications
| Hi-index | 0.00 |
The article presents an extension of the Hungarian algorithm (also known as Kuhn-Munkres algorithm) which is used for solving the assignment problems in polynomial time. The fact that the original version of the algorithm is only able to solve the assignment problems with precisely defined inputs (i.e. demands and resources) presents a major problem in many real-life scenarios while the nature of these problems is such that inputs are commonly defined only vaguely (i.e. fuzzily). In order to solve them, their precise formalization is needed which is normally far from being a straightforward procedure and can present large costs in the meaning of time and money. Fuzzy logic on the other hand successfully copes with the processing of imprecise data. The Hungarian algorithm was extended with the introduction of fuzzy logic methods in order to be able to efficiently solve vaguely defined assignment problems. The extended version of the algorithm (i.e. fuzzy Hungarian algorithm) is thus able to cope with vaguely defined assignment problems, can be used more efficiently (i.e. with no further formalization of vaguely defined terms) and in a wider scope of assignment problems than the basic approach. Here we describe the basic version of the Hungarian algorithm which was firstly presented by Harold Kuhn. Its extension with the introduction of fuzzy methods is also described. Its usage is justified by the comparison of the results between its crisp (i.e. basic) and fuzzy (i.e. extended) version on the same problem.