Research on the Shortest Path Solution Method of Interval Valued Neutrosophic Graphs Based on the Ant Colony Algorithm

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. INDEX TERMS Ant colony algorithm, interval valued neutrosophic numbers, neutrosophic graph, shortest path problem.

An Improved Discrete Jaya Algorithm for Shortest Path Problems in Transportation-Related Processes

“…IDJaya is compared with typical Dijkstra [16] and very recent methods based on ant colony optimization (ACO) [31,66,67]. This work selects an improved ACO in [31] for comparison.…”

“…[30] designed an efficient shortest-path algorithm that compresses an original network into a small one that preserves the graph properties used to calculate a path. Yang, et al (2020) [31] present an ant colony algorithm to solve the shortest path problem. Krauss, et al (2020) [32] propose three different approaches for solving SPP using a quadratic unconstrained binary optimization formulation suitable for development on a quantum annealing machine.…”

CPT-Todim Method for Interval Neutrosophic Magdm and Its Application to Third-Party Logistics Service Providers Selection

“…Wang et al (2005) designed the interval neutrosophic set (INS). Many scholars used SVNS or INS to study the problem of MADM or MAGDM (Biswas et al, 2016;Kahraman, et al, 2020;Meng et al, 2019;Nafei et al, 2019;Wu et al, 2018;Yang et al, 2020). Wang et al (2019) researched the choice about strategic supplier by utilizing interval neutrosophic information.…”

Decision-making method based on game theory and grey theory in a single-value neutrosophic environment and its application to typhoon disaster assessment

“…For example, Wang et al (2018) introduced single-valued NSs (SVNSs) as a practical application of NSs. Wang et al (2005) proposed interval NSs, while Ye (2014) defined simplified NSs, Biswas et al (2014b) studied trapezoidal fuzzy NSs (Biswas et al , 2014b), Tian et al (2015) defined simplified neutrosophic linguistic sets, Wang et al (2015) proposed multi-valued NSs (Wang et al , 2015), Deli et al (2015) bipolar NSs, Deli and Broumi (2015) neutrosophic soft sets, Broumi et al (2014) rough NSs, Mondal and Pramanik (2015a,b) tri-complex rough NSs, Mondal et al (2016) rough neutrosophic hyper-complex sets, Ali et al (2016) neutrosophic cubic sets, Pramanik et al (2017) neutrosophic cubic soft sets, Liu and You (2019) linguistic NSs (Liu and You, 2019), Ye (2017) linguistic neutrosophic cubic numbers, Ye and Smarandache (2016) refined single-valued NSs, Deli and Şubaş (2016) bipolar neutrosophic refined sets, Abdel-Basset et al (2019) type-2 NN sets, Chatterjee et al (2016) quadripartitioned single-valued NSs and Broumi et al (2016) and Yang et al (2020) neutrosophic graphs. Based on the different forms of neutrosophic numbers, scholars have proposed numerous decision-making models, which are widely used in practical problems, such as medical diagnosis, investment selection, image processing, supply chain selection, circuit design, personality grouping and fault diagnosis.…”