Said Broumi

Arindam Dey

Ranjan Kumar

Sripati Jha

S A Edaltpanah

Neutrosophic set theory provides a new tool to handle the uncertainties in shortest path problem (SPP). This paper introduces the SPP from a source node to a destination node on a neutrosophic graph in which a positive neutrosophic number is assigned to each edge as its edge cost. We define this problem as neutrosophic shortest path problem (NSSPP). A simple algorithm is also introduced to solve the NSSPP. The proposed algorithm finds the neutrosophic shortest path (NSSP) and its corresponding neutrosophic shortest path length (NSSPL) between source node and destination node.

Neutrosophic Shortest Path Problem

Ranber Singh

Thermoelectricity and Advanced Thermoelectric Materials reviews emerging thermoelectric materials, including skutterudites, clathrates, and half-Heusler alloys. In addition, the book discusses a number of oxides and silicides that have promising thermoelectric properties. Because 2D materials with high figures of merit have emerged as promising candidates for thermoelectric applications, this book presents an updated introduction to the field of thermoelectric materials, including recent advances in materials synthesis, device modeling, and design. Finally, the book addresses the theoretical difficulties and methodologies of computing the thermoelectric properties of materials that can be used to understand and predict highly efficient thermoelectric materials. This book is a key reference for materials scientists, physicists, and engineers in energy. Reviews the most relevant, emerging thermoelectric materials, including 2D materials, skutterudites, clathrates and half-Heusler alloys Focuses on how electronic structure engineering can lead to improved materials performance for thermoelectric energy conversion applications Includes the latest advances in the synthesis, modeling and design of advanced thermoelectric materials

Thermoelectricity and Advanced Thermoelectric Materials

S. Broumi

S A Edalatpanah

Ramayan Singh

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).

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

Ranjan Kumar

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