Novel Neutrosophic Cubic Graphs Structures With Application in Decision Making Problems

Graphs allow us to study the different patterns of inside the data by making a mental image. The aim of this paper is to develop a neutrosophic cubic graph structure, which is the extension of neutrosophic cubic graphs. As neutrosophic cubic graphs are defined for one set of edges between vertices, while neutrosophic cubic graphs structures are defined for more than one set of edges. Further, we defined some basic operations, such as Cartesian product, composition, union, join, cross product, strong product, and lexicographic product of two neutrosophic cubic graph structures. Several types of other interesting properties of neutrosophic cubic graph structures are discussed in this paper. Finally, a decision-making algorithm based on the idea of neutrosophic cubic graph structures is constructed. The proposed decision-making algorithm is applied in a decision-making problem to check the validity.

[1]  Muhammad Shabir,et al.  Neutrosophic cubic (α, β)-ideals in semigroups with application , 2018, J. Intell. Fuzzy Syst..

[2]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[3]  Bijan Davvaz,et al.  Properties of single-valued neutrosophic graphs , 2018, Journal of Intelligent & Fuzzy Systems.

[4]  Young Bae Jun,et al.  Neutrosophic Cubic Sets , 2016, New Math. Nat. Comput..

[5]  Madhumangal Pal,et al.  Interval-valued fuzzy threshold graph , 2016 .

[6]  Ismat Beg,et al.  A new approach in decision making problems under the environment of neutrosophic cubic soft matrices , 2019, J. Intell. Fuzzy Syst..

[7]  Sankar Sahoo,et al.  Product of intuitionistic fuzzy graphs and degree , 2017, J. Intell. Fuzzy Syst..

[8]  Fred Buckley.  Self‐Centered Graphs , 1989 .

[9]  Florentin Smarandache,et al.  Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor , 2018, Symmetry.

[10]  Muhammad Gulistan,et al.  Cubic Graphs with Application , 2018 .

[11]  Heng-Da Cheng,et al.  A NEW NEUTROSOPHIC APPROACH TO IMAGE THRESHOLDING , 2008 .

[12]  Florentin Smarandache,et al.  Applications of Neutrosophic Bipolar Fuzzy Sets in HOPE Foundation for Planning to Build a Children Hospital with Different Types of Similarity Measures , 2018, Symmetry.

[13]  Prabir Bhattacharya,et al.  Some remarks on fuzzy graphs , 1987, Pattern Recognit. Lett..

[14]  Madhumangal Pal,et al.  Some Results on Interval-Valued Fuzzy Graphs , 2015 .

[15]  Muhammad Gulistan,et al.  A Generalized Approach towards Soft Expert Sets via Neutrosophic Cubic Sets with Applications in Games , 2019, Symmetry.

[16]  Jeong Gi Kang,et al.  MAPPINGS OF CUBIC SETS , 2016 .

[17]  Majid Khan,et al.  Neutrosophic Cubic Einstein Hybrid Geometric Aggregation Operators with Application in Prioritization Using Multiple Attribute Decision-Making Method , 2019, Mathematics.

[18]  F. Smarandache,et al.  P-union and P-intersection of neutrosophic cubic sets , 2017 .

[19]  Krassimir T. Atanassov,et al.  Operations on intuitionistic fuzzy graphs , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[20]  Young Bae Jun,et al.  P-union and P-intersection of neutrosophic cubic sets , 2015 .

[21]  Seifedine Kadry,et al.  Complex Intuitionistic Fuzzy Graphs with Application in Cellular Network Provider Companies , 2019, Mathematics.

[22]  Pinaki Majumdar,et al.  On similarity and entropy of neutrosophic sets , 2013, J. Intell. Fuzzy Syst..

[23]  Muhammad Gulistan,et al.  Neutrosophic Triplet Non-Associative Semihypergroups with Application , 2018, Symmetry.

[24]  Muhammad Akram,et al.  Bipolar fuzzy graphs with applications , 2013, Knowl. Based Syst..

[25]  Muhammad Akram,et al.  Bipolar fuzzy graphs , 2011, Inf. Sci..

[26]  Madhumangal Pal,et al.  Interval-valued fuzzy planar graphs , 2016, Int. J. Mach. Learn. Cybern..

[27]  Faruk Karaaslan,et al.  ENERGY OF A BIPOLAR FUZZY GRAPH AND ITS APPLICATION IN DECISION MAKING , 2018 .

[28]  Young Bae Jun,et al.  The generalized version of Jun's cubic sets in semigroups , 2015, J. Intell. Fuzzy Syst..

[29]  Anita Pal,et al.  Coherent Category of Interval-valued Intuitionistic Fuzzy Graphs , 2017, J. Multiple Valued Log. Soft Comput..

[30]  Muhammad Akram,et al.  Interval-valued fuzzy graphs , 2012, Comput. Math. Appl..

[31]  Young Bae Jun,et al.  Cubic structures applied to ideals of BCI-algebras , 2011, Comput. Math. Appl..

[32]  Florentin Smarandache,et al.  A Study on Neutrosophic Cubic Graphs with Real Life Applications in Industries , 2018, Symmetry.

[33]  Florentin Smarandache,et al.  Neutrosophic Cubic Einstein Geometric Aggregation Operators with Application to Multi-Criteria Decision Making Method , 2019, Symmetry.

[34]  B. Davvaz,et al.  Strong Intuitionistic Fuzzy Graphs , 2012 .