Arithmetic and Geometric Operators of Pentagonal Neutrosophic Number and its Application in Mobile Communication Service Based MCGDM Problem

In this paper, the theory of pentagonal neutrosophic number has been studied in a disjunctive frame of reference. Moreover, the dependency and independency of the membership functions for the pentagonal neutrosophic number are also classified here. Additionally, the development of a new score function and its computation have been formulated in distinct rational perspectives. Further, weighted arithmetic averaging operator and weighted geometric averaging operator in the pentagonal neutrosophic environment are introduced here using an influx of different logical & innovative thought. Also, a multi-criteria group decision-making problem (MCGDM) in a mobile communication system is formulated in this paper as an application in the pentagonal neutrosophic arena. Lastly, the sensitivity analysis portion reflects the variation of this noble work.

[1]  Florentin Smarandache,et al.  A Scientific Decision Framework for Supplier Selection under Neutrosophic Moora Environment , 2018 .

[2]  Mee-Kwang Kang,et al.  BIPOLAR FUZZY SET THEORY APPLIED TO SUB-SEMIGROUPS WITH OPERATORS IN SEMIGROUPS , 2012 .

[3]  Mohamed Elhoseny,et al.  Modeling neutrosophic variables based on particle swarm optimization and information theory measures for forest fires , 2018, The Journal of Supercomputing.

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

[5]  Faruk Karaaslan.  Gaussian single-valued neutrosophic numbers and its application in multi-attribute decision making , 2018 .

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

[7]  Avishek Chakraborty,et al.  Cylindrical neutrosophic single-valued number and its application in networking problem, multi-criterion group decision-making problem and graph theory , 2020, CAAI Trans. Intell. Technol..

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

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

[10]  Lazim Abdullah,et al.  Multi-Valued Interval Neutrosophic Soft Set: Formulation and Theory , 2019 .

[11]  Florentin Smarandache,et al.  Shortest Path Problem under Bipolar Neutrosphic Setting , 2016 .

[12]  Faruk Karaaslan,et al.  Correlation Coefficient between Possibility Neutrosophic Soft Sets , 2016 .

[13]  F. Smarandache,et al.  The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment , 2019, Complex & Intelligent Systems.

[14]  Saleem Abdullah,et al.  Bipolar fuzzy soft sets and its applications in decision making problem , 2013, J. Intell. Fuzzy Syst..

[15]  Madhumangal Pal,et al.  Trapezoidal neutrosophic aggregation operators and its application in multiple attribute decision making process , 2018, Scientia Iranica.

[16]  Le Hoang Son,et al.  Bipolar neutrosophic soft sets and applications in decision making , 2017, J. Intell. Fuzzy Syst..

[17]  Mehmet Sahin,et al.  Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making , 2018, Neural Computing and Applications.

[18]  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..

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

[20]  Faruk Karaaslan,et al.  Some new operations on single-valued neutrosophic matrices and their applications in multi-criteria group decision making , 2018, Applied Intelligence.

[21]  Patrick Bosc,et al.  On a fuzzy bipolar relational algebra , 2013, Inf. Sci..

[22]  Kaviya.  Transportation Problem with Nanogonal Intuitionistic Fuzzy Numbers Solved Using Ranking Technique and Russell’s Method , 2018 .

[23]  Faruk Karaaslan,et al.  Multicriteria Decision‐Making Method Based on Similarity Measures under Single‐Valued Neutrosophic Refined and Interval Neutrosophic Refined Environments , 2015, Int. J. Intell. Syst..

[24]  Avishek Chakraborty,et al.  Approach to solve multi-criteria group decision-making problems by exponential operational law in generalised spherical fuzzy environment , 2020, CAAI Trans. Intell. Technol..

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

[26]  Florentin Smarandache,et al.  Bipolar neutrosophic sets and their application based on multi-criteria decision making problems , 2015, 2015 International Conference on Advanced Mechatronic Systems (ICAMechS).

[27]  Said Broumi,et al.  De-Neutrosophication Technique of Pentagonal Neutrosophic Number and Application in Minimal Spanning Tree , 2019 .

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

[29]  Avishek Chakraborty,et al.  A New Score Function of Pentagonal Neutrosophic Number and its Application in Networking Problem , 2020, International Journal of Neutrosophic Science.

[30]  Florentin Smarandache,et al.  Complex neutrosophic set , 2016, Neural Computing and Applications.

[31]  Florentin Smarandache,et al.  Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview , 2019, Complex & Intelligent Systems.

[32]  Harish Garg,et al.  A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem , 2016, J. Intell. Fuzzy Syst..

[33]  Hong-yu Zhang,et al.  Frank Choquet Bonferroni Mean Operators of Bipolar Neutrosophic Sets and Their Application to Multi-criteria Decision-Making Problems , 2018, Int. J. Fuzzy Syst..

[34]  Faruk Karaaslan,et al.  Correlation coefficients of single-valued neutrosophic refined soft sets and their applications in clustering analysis , 2015, Neural Computing and Applications.

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

[36]  Faruk Karaaslan,et al.  SIMILARITY MEASURE BETWEEN POSSIBILITY NEUTROSOPHIC SOFT SETS AND ITS APPLICATIONS , 2015 .

[37]  Amarpreet Kaur,et al.  A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers , 2012, Appl. Soft Comput..

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

[39]  Arindam Dey,et al.  Shortest path problem using Bellman algorithm under neutrosophic environment , 2019, Complex & Intelligent Systems.

[40]  Avishek Chakraborty,et al.  Hexagonal fuzzy number and its distinctive representation, ranking, defuzzification technique and application in production inventory management problem , 2020, Granular Computing.

[41]  F. Smarandache,et al.  Shortest Path Problem Under Interval Valued Neutrosophic Setting , 2018 .

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

[43]  Faruk Karaaslan,et al.  Possibility neutrosophic soft sets and PNS-decision making method , 2014, Appl. Soft Comput..

[44]  Rajshekhar Sunderraman,et al.  Single Valued Neutrosophic Sets , 2010 .

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

[46]  Victor I. Chang,et al.  An integrated neutrosophic ANP and VIKOR method for achieving sustainable supplier selection: A case study in importing field , 2019, Comput. Ind..

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

[48]  Seifedine Kadry,et al.  Neutrosophic cubic Heronian mean operators with applications in multiple attribute group decision-making using cosine similarity functions , 2019, Int. J. Distributed Sens. Networks.

[49]  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..

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

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

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

[53]  Mohamed Abdel-Basset,et al.  Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases , 2019, Artif. Intell. Medicine.

[54]  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 .

[55]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .