Application of neutrosophic minimum spanning tree in electrical power distribution network

The problem of finding the minimum spanning tree (MST) is one of the most studied and important combinatorial optimisation problems in graph theory. Several types of uncertainties exist in real-life problems, which make it very hard to find the exact length of the arc. The neutrosophic set is an efficient tool to model and deal with the uncertainties in information due to inconsistent and indeterminate. In this study, the authors use triangular neutrosophic numbers to represent the edge weights of a neutrosophic graph for the MST problem in the neutrosophic environment. They call this problem a neutrosophic MST (NMST) problem. They formulate the NMST problem in terms of the linear programming model. Here, they introduce an algorithmic method based on a genetic algorithm for solving the NMST problem. They present the utility of triangular neutrosophic numbers as edge weights and their application in the electrical distribution network.

[1]  Harish Garg,et al.  A Novel Improved Accuracy Function for Interval Valued Pythagorean Fuzzy Sets and Its Applications in the Decision‐Making Process , 2017, Int. J. Intell. Syst..

[2]  Arindam Dey,et al.  Fuzzy minimum spanning tree with interval type 2 fuzzy arc length: formulation and a new genetic algorithm , 2020, Soft Comput..

[3]  Le Hoang Son,et al.  A new algorithm for finding minimum spanning trees with undirected neutrosophic graphs , 2018 .

[4]  Harish Garg,et al.  AN IMPROVED SCORE FUNCTION FOR RANKING NEUTROSOPHIC SETS AND ITS APPLICATION TO DECISION-MAKING PROCESS , 2017 .

[5]  Hiroaki Ishii,et al.  An Approach Based on Necessity Measure to the Fuzzy Spanning Tree Problems , 1996 .

[6]  Adam Janiak,et al.  The minimum spanning tree problem with fuzzy costs , 2008, Fuzzy Optim. Decis. Mak..

[7]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[8]  Yusuf Subas,et al.  A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems , 2016, International Journal of Machine Learning and Cybernetics.

[9]  Jinwu Gao,et al.  Fuzzy quadratic minimum spanning tree problem , 2005, Appl. Math. Comput..

[10]  Harish Garg,et al.  Some New Biparametric Distance Measures on Single-Valued Neutrosophic Sets with Applications to Pattern Recognition and Medical Diagnosis , 2017, Inf..

[11]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[12]  Harish Garg,et al.  Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment , 2017, Applied Intelligence.

[13]  Tandra Pal,et al.  Interval Type 2 Fuzzy Set in Fuzzy Shortest Path Problem , 2016 .

[14]  P. K. Kishore Kumar,et al.  A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications , 2019, Mathematics.

[15]  Kanika Mandal,et al.  Improved similarity measure in neutrosophic environment and its application in finding minimum spanning tree , 2017, J. Intell. Fuzzy Syst..

[16]  Harish Garg,et al.  Some hybrid weighted aggregation operators under neutrosophic set environment and their applications to multicriteria decision-making , 2018, Applied Intelligence.

[17]  Jun Ye,et al.  Single-Valued Neutrosophic Minimum Spanning Tree and Its Clustering Method , 2014, J. Intell. Syst..

[18]  Harish Garg,et al.  Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment , 2018, Symmetry.

[19]  Fan Yang,et al.  Fuzzy α-minimum spanning tree problem: definition and solutions , 2016, Int. J. Gen. Syst..

[20]  Robert E. Tarjan,et al.  Fast Algorithms for Finding Nearest Common Ancestors , 1984, SIAM J. Comput..

[21]  Ronald L. Graham,et al.  On the History of the Minimum Spanning Tree Problem , 1985, Annals of the History of Computing.

[22]  R. Prim.  Shortest connection networks and some generalizations , 1957 .

[23]  Arindam Dey,et al.  A GENETIC ALGORITHM FOR SOLVING FUZZY SHORTEST PATH PROBLEMS WITH INTERVAL TYPE-2 FUZZY ARC LENGTHS , 2018, Malaysian Journal of Computer Science.

[24]  Harish Garg,et al.  New logarithmic operational laws and their applications to multiattribute decision making for single-valued neutrosophic numbers , 2018, Cognitive Systems Research.