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A Multi Objective Programming Approach to Solve Integer Valued Neutrosophic Shortest Path Problems

Ranjan Kumar; S A Edalatpanah; Sripati Jha; S. Broumi; Ramayan Singh; Arindam Dey

Neutrosophic (NS) set hypothesis gives another way to deal with the vulnerabilities of the shortest path problems
(SPP). Several researchers have worked on fuzzy shortest path problem (FSPP) in a fuzzy graph with vulnerability data and completely different applications in real world eventualities. However, the uncertainty related to the inconsistent information and indeterminate information isn't properly expressed by fuzzy set. The neutrosophic set deals these forms of uncertainty. This paper presents a model for shortest path problem with various arrangements of integer-valued trapezoidal neutrosophic (INVTpNS) and integer-valued triangular neutrosophic (INVTrNS). We characterized this issue as Neutrosophic Shortest way problem (NSSPP). The established linear programming (LP) model solves the classical SPP that consists of crisp parameters. To the simplest of our data, there's no multi objective applied mathematics approach in literature for finding the Neutrosophic shortest path problem (NSSPP). During this paper, we tend to introduce a multi objective applied mathematics approach to unravel the NSPP. The subsequent integer valued neutrosophic shortest path (IVNSSP) issue is changed over into a multi objective linear programming (MOLP) issue. At that point, a lexicographic methodology is utilized to acquire the productive arrangement of the subsequent MOLP issue. The optimization process affirms that the optimum integer valued neutrosophic shortest path weight conserves the arrangement of an integer valued neutrosophic number. Finally, some numerical investigations are given to demonstrate the adequacy and strength of the new model.

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