Open Access

ARTICLE

Floyd-Warshall Algorithm Based on Picture Fuzzy Information

Shaista Habib¹, Aqsa Majeed¹, Muhammad Akram^2,*, Mohammed M. Ali Al-Shamiri^3,4

1 School of Systems and Technology, University of Management and Technology, Lahore, Pakistan
2 Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
3 Department of Mathematics, Faculty of Science and Arts, Mahayl Assir, King Khalid University, Abha, Saudi Arabia
4 Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen

* Corresponding Author: Muhammad Akram. Email:

(This article belongs to the Special Issue: Decision making Modeling, Methods and Applications of Advanced Fuzzy Theory in Engineering and Science)

Computer Modeling in Engineering & Sciences 2023, 136(3), 2873-2894. https://doi.org/10.32604/cmes.2023.026294

Received 28 August 2022; Accepted 30 November 2022; Issue published 09 March 2023

Abstract

The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes. It works well for crisp weights, but the problem arises when weights are vague and uncertain. Let us take an example of computer networks, where the chosen path might no longer be appropriate due to rapid changes in network conditions. The optimal path from among all possible courses is chosen in computer networks based on a variety of parameters. In this paper, we design a new variant of the Floyd-Warshall algorithm that identifies an All-Pair Shortest Path (APSP) in an uncertain situation of a network. In the proposed methodology, multiple criteria and their mutual association may involve the selection of any suitable path between any two node points, and the values of these criteria may change due to an uncertain environment. We use trapezoidal picture fuzzy addition, score, and accuracy functions to find APSP. We compute the time complexity of this algorithm and contrast it with the traditional Floyd-Warshall algorithm and fuzzy Floyd-Warshall algorithm.

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Graphic Abstract

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