The Encyclopedia of Neutrosophic Researchers - vol. 3

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

Shortest path problem using Bellman algorithm under neutrosophic environment

An elongation of the single-valued neutrosophic set is an interval-valued neutrosophic set. It has been demonstrated to deal indeterminacy in a decision-making problem. Real-world problems have some kind of uncertainty in nature and among them; one of the influential problems is solving the shortest path problem (SPP) in interconnections

A New Concept of Matrix Algorithm for MST in Undirected Interval Valued Neutrosophic Graph

In this chapter, we introduce a new algorithm for finding a minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph whose edge weights are represented by an interval valued neutrosophic number

Spanning Tree Problem with Neutrosophic Edge Weights

Neutrosophic set and neutrosophic logic theory are renowned theories to deal with complex, not clearly explained and uncertain real life problems, in which classical fuzzy sets/models may fail to model properly. This paper introduces an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (abbr. UNWCG) where the arc/edge lengths are represented by a single valued neutrosophic numbers. To build the MST of UNWCG, a new algorithm based on matrix approach has been introduced. The proposed algorithm is compared to other existing methods and finally a numerical example is provided

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