The Minimum Spanning Tree Problem on networks with Neutrosophic numbers

The minimum spanning tree problem (MSTP) revolves around creating a spanning tree (ST) within a graph/network that incurs the least cost compared to all other potential STs. This represents a vital and fundamental issue in the realm of combinational optimization problems (COP). Supply chain management, communication, transportation, and routing are a few examples of real-world issues that have been represented using the MSTP. Uncertainties exist in almost every real life application of MSTP due to inconsistency, improperness, incompleteness, vagueness and indeterminacy of the information and It generates really challenging scenarios to determine the arc length precisely. The main motivation behind this research work is to design a method for MST which will be simple enough and effective in real world scenarios. Neutrosophic set (NS) is a well known renowned theory, which one can this type of uncertainty in the edge weights of the ST. In this article, we review trapezoid neutrosophic set/number to describe the arc weight of a neutrosophic network for MSTP. Here, we introduce an algorithm for solving MSTP in neutrosophic environment. In our proposed method, we describe the uncertainties in Prim’s algorithm for MSTP using trapezoid neutrosophic set as edge cost. Here examples of numerical sets are used to explain the proposed algorithm

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

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