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

Abstract

Neutrosophic (NS) set hypothesis gives another way to deal with the vulnerabilities of the shortest path problems (SPP). Several researchers have worked on the 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 the fuzzy set. The neutrosophic set deals with these forms of uncertainty. This paper presents a model for the shortest path problem with various arrangements of integer-valued trapezoidal neutrosophic (INVTpNS) and integer-valued triangular neutrosophic (INVTrNS). We characterized this issue as the 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.