De-Neutrosophication Technique of Pentagonal Neutrosophic Number and Application in Minimal Spanning Tree

In this current era, neutrosophic set theory is a crucial topic to demonstrate the ambiguous information due to existence of three disjunctive components appears in it and it provides a wide range of applications in distinct fields for the researchers. Generally, neutrosophic sets is the extended version of crisp set, fuzzy set and intuitionistic fuzzy sets to focus on the uncertain, hesitant and ambiguous datas of a real life mathematical problem. Demonstration of pentagonal neutrosophic number and its classification in different aspect is focused in this research article. Manifestation of de-neutrosophication technique of linear pentagonal neutrosophic number using removal area method has been developed here which has a remakable impact in crispfication of pentagonal neutrosophic number. Afterthat, utilizing this invented result, a minimal spanning tree problem has been solved in pentagonal neutrosophic environment. Comparision analysis is done with the other established method in this article and this noble design will be benificial for the researchers in neutrosophic domain in future.

[1]  Xiaofei Zhao,et al.  TOPSIS method for interval-valued intuitionistic fuzzy multiple attribute decision making and its application to teaching quality evaluation , 2014, J. Intell. Fuzzy Syst..

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

[3]  Mohamed Abdel-Basset,et al.  An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number , 2019, Appl. Soft Comput..

[4]  Florentin Smarandache,et al.  A Hybrid Plithogenic Decision-Making Approach with Quality Function Deployment for Selecting Supply Chain Sustainability Metrics , 2019, Symmetry.

[5]  Debashis De,et al.  The Pentagonal Fuzzy Number: Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problems , 2019, Symmetry.

[6]  Mohamed Abdel-Basset,et al.  Neutrosophic Multi-Criteria Decision Making Approach for IoT-Based Enterprises , 2019, IEEE Access.

[7]  Avishek Chakraborty,et al.  Different linear and non-linear form of trapezoidal neutrosophic numbers, de-neutrosophication techniques and its application in time-cost optimization technique, sequencing problem , 2019, RAIRO Oper. Res..

[8]  Mohamed Abdel-Basset,et al.  A novel group decision making model based on neutrosophic sets for heart disease diagnosis , 2019, Multimedia Tools and Applications.

[9]  S. Karthik,et al.  Application of Pentagonal Fuzzy Number in Neural Network , 2017 .

[10]  Florentin Smarandache,et al.  Energy and Spectrum Analysis of Interval Valued Neutrosophic Graph using MATLAB , 2019 .

[11]  Mohamed Abdel-Basset,et al.  A novel and powerful framework based on neutrosophic sets to aid patients with cancer , 2019, Future Gener. Comput. Syst..

[12]  Victor I. Chang,et al.  A Refined Approach for Forecasting Based on Neutrosophic Time Series , 2019, Symmetry.

[13]  Florentin Smarandache,et al.  Single-Valued Neutrosophic Techniques for Analysis of WIFI Connection , 2018, Advances in Intelligent Systems and Computing.

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

[15]  Victor I. Chang,et al.  Evaluation of the green supply chain management practices: A novel neutrosophic approach , 2019, Comput. Ind..

[16]  Saeid Abbasbandy,et al.  A new approach for ranking of trapezoidal fuzzy numbers , 2009, Comput. Math. Appl..

[17]  Prem Kumar Singh,et al.  Some properties of Pentagonal Neutrosophic Numbers and It’s Applications in Transportation Problem Environment Some properties of Pentagonal Neutrosophic Numbers and its Applications in Transportation Problem Environment , 2019 .

[18]  Jun Ye.  Fault diagnoses of steam turbine using the exponential similarity measure of neutrosophic numbers , 2016, J. Intell. Fuzzy Syst..

[19]  Mohamed Elhoseny,et al.  A novel model for evaluation Hospital medical care systems based on plithogenic sets , 2019, Artif. Intell. Medicine.

[20]  Surapati Pramanik,et al.  Neutrosophic Decision Making Model of School Choice , 2015 .

[21]  Jun Ye,et al.  Dice Similarity Measure between Single Valued Neutrosophic Multisets and Its Application in Medical Diagnosis , 2015 .

[22]  F. Smarandache,et al.  Linear fractional programming based on triangular neutrosophic numbers , 2019, International Journal of Applied Management Science.

[23]  Hong-yu Zhang,et al.  Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems , 2016, Int. J. Syst. Sci..

[24]  F. Smarandache,et al.  An Introduction to Bipolar Single Valued Neutrosophic Graph Theory , 2016 .

[25]  Florentin Smarandache,et al.  On Bipolar Single Valued Neutrosophic Graphs , 2016 .

[26]  Ilanthenral Kandasamy,et al.  Double-Valued Neutrosophic Sets, their Minimum Spanning Trees, and Clustering Algorithm , 2018, J. Intell. Syst..

[27]  Jun Ye,et al.  Trapezoidal neutrosophic set and its application to multiple attribute decision-making , 2015, Neural Computing and Applications.

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

[29]  Florentin Smarandache,et al.  A hybrid neutrosophic multiple criteria group decision making approach for project selection , 2019, Cognitive Systems Research.

[30]  H. Wee,et al.  Economic ordering policy of deteriorated item for vendor and buyer: An integrated approach , 2000 .

[31]  Surapati Pramanik,et al.  An Extended Topsis for Multi-Attribute Decision Making Problems with Neutrosophic Cubic Information , 2017 .

[32]  Florentin Smarandache,et al.  Decision-making method based on the interval valued neutrosophic graph , 2016, 2016 Future Technologies Conference (FTC).

[33]  Avishek Chakraborty,et al.  A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment , 2020, RAIRO Oper. Res..

[34]  Yuan Xue-hai,et al.  Fuzzy Number Intuitionistic Fuzzy Set , 2007 .

[35]  Norazak Senu,et al.  Disjunctive Representation of Triangular Bipolar Neutrosophic Numbers, De-Bipolarization Technique and Application in Multi-Criteria Decision-Making Problems , 2019, Symmetry.

[36]  M. Mullai,et al.  Shortest Path Problem by Minimal Spanning Tree Algorithm using Bipolar Neutrosophic Numbers , 2017 .

[37]  Surapati Pramanik,et al.  Multi-criteria Group Decision Making Approach for Teacher Recruitment in Higher Education under Simplified Neutrosophic Environment , 2014 .

[38]  Florentin Smarandache,et al.  Shortest path problem on single valued neutrosophic graphs , 2017, 2017 International Symposium on Networks, Computers and Communications (ISNCC).

[39]  Mohamed Abdel-Basset,et al.  A Novel Intelligent Medical Decision Support Model Based on Soft Computing and IoT , 2020, IEEE Internet of Things Journal.

[40]  Ahmed Aboelfetouh,et al.  Utilising neutrosophic theory to solve transition difficulties of IoT-based enterprises , 2020, Enterp. Inf. Syst..

[41]  Jun Ye,et al.  Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making , 2014, J. Intell. Fuzzy Syst..

[42]  Florentin Smarandache,et al.  A Group Decision Making Framework Based on Neutrosophic TOPSIS Approach for Smart Medical Device Selection , 2019, Journal of Medical Systems.

[43]  Florentin Smarandache,et al.  Single valued neutrosophic graphs: Degree, order and size , 2016, 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[44]  Jun Ye.  Prioritized aggregation operators of trapezoidal intuitionistic fuzzy sets and their application to multicriteria decision-making , 2014, Neural Computing and Applications.

[45]  Luige Vladareanu,et al.  Applying Dijkstra algorithm for solving neutrosophic shortest path problem , 2016, 2016 International Conference on Advanced Mechatronic Systems (ICAMechS).

[46]  T. Pathinathan,et al.  Reverse order Triangular , Trapezoidal and Pentagonal Fuzzy Numbers , 2015 .