Abstract
The shortest path problem (SPP) is considerably important in several fields. After typhoons, the resulting damage leads to uncertainty regarding the path weight that can be expressed accurately. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership degrees of the elements. In an uncertain environment, neutrosophic numbers can express the edge distance more effectively. Based on the theories of interval valued neutrosophy and neutrosophic graphs, this paper proposes a shortest path solution method of interval valued neutrosophic graphs using the ant colony algorithm. Further, an analysis comparing the proposed algorithm with the Dijkstra algorithm was used to probe the potential shortcomings and advantages of the proposed method. In addition, this approach confirmed the effectiveness of the proposed algorithm. Furthermore, we investigated the convergence processes of the ant colony algorithm with different parameter settings, analyzed their results, and used different score functions to solve the SPP and analyze the results.
Highlights
In 1998, neutrosophy was introduced by Smarandache as a branch of philosophy that studies the nature, origin, and scope of neutrality and its interaction with various conceptual spectra [1]
This paper studies the neutrosophic graph with side weights represented by interval valued neutrosophic numbers (NN)
Thereafter, the ant colony algorithm is compared with the Bellman and Dijkstra algorithms
Summary
In 1998, neutrosophy was introduced by Smarandache as a branch of philosophy that studies the nature, origin, and scope of neutrality and its interaction with various conceptual spectra [1]. Ridvan et al [18] developed a method for solving multiple attribute decision-making problems with single valued neutrosophic information or interval neutrosophic information. Deli [34] proposed single valued trapezoidal neutrosophic operators and applied them to decision-making problems. Deli and Suba [35] put forward the weighted geometric operator with the single valued neutrosophic method and applied it to decision-making problems. Kumar et al [38] proposed an algorithm for solving SPP in a trapezoidal fuzzy neutrosophic environment. Broumi et al [39] proposed a neutrosophic network method for finding the shortest path length with single valued trapezoidal NN. This paper describes the shortest path solution method based on the ant colony algorithm with an interval valued neutrosophic graph. THEORETICAL BASIS A brief description of some basic concepts of NSs and some existing ranking functions for interval valued NN are given in the following subsections
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