A Preliminary Analysis of the Time Complexity of Dijkstra's Algorithm in a Z-Number Environment
Dijkstra's algorithm is an efficient method widely used in solving shortest-path problems. However, the classical Dijkstra's algorithm is usually designed to work in certain and specific data environments. In the literature, there are also studies in which the shortest path is found using Dijkstra's algorithm for graphs where uncertainties are handled with fuzzy numbers. In this paper, the time complexity of Dijkstra's algorithm on graphs weighted by Z-numbers is studied. Z-numbers provide a more comprehensive modeling of uncertainty by representing both a fuzzy value and a degree of confidence. With these features, Z-numbers provide a more realistic solution for uncertain systems. In graphs weighted by Z-numbers, in addition to this basic time complexity, additional costs associated with the processing of Z-numbers must also be considered. The graphs weighted by classical and fuzzy numbers shows similar time complexity measurements of O(n(2)), while the z-numbered based is O(n(4)). The computational costs of the classical and fuzzy Dijkstra algorithms are 0.1023 and 0.1322 s, respectively, while the computational cost of the z-numbered Dijkstra algorithm is 125.6246 s. In this study, the applicability of Dijkstra's algorithm in the Z-number environment and comparatively analyze its impact on the time complexity of the algorithm is evaluated. This study aims to contribute to the literature by providing a new perspective on shortest path problems in uncertain systems.
- Journal
- INTELLIGENT AND FUZZY SYSTEMS, INFUS 2025, VOL 4
- Year
- 2025
- Volume
- 1531
- Pages
- 85-94
- ISSN
- 2367-3370
- eISSN
- 2367-3389
- DOI
- 10.1007/978-3-031-98304-7_10
- WoS UID
- WOS:001587127900010