International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 19 , Issue 4 , PP: 58-76, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

Implementation of Neutrosophic Bipolar Pentagonal Fuzzy Set on Multi-Criteria Decision-Making Scenario

P. Hemavathi 1 * , M. Muthumeenakshi 2 , P. Chanthini 3 , P. Muralikrishna 4 , R. Vinodkumar 5

  • 1 Department of Mathematics, Saveetha School of Engineering, SIMATS, Thandalam-602 105, INDIA - (hemavathip.sse@saveetha.com)
  • 2 Department of Commerce, Vellore Institute of Technology (VIT), Vellore- 632 014, INDIA - (muthumeenakshi.m@vit.ac.in)
  • 3 Department of Computer Applications College of Science & Humanities, SRMIST, Potheri Campus. INDIA - (chanthini19@gmail.com)
  • 4 Department of Mathematics, Muthurangam Government Arts College (A), Vellore-632 002, INDIA - (pmkrishna@rocketmail.com)
  • 5 Department of Mathematics, Prathyusha Engineering College, Aranvoyal kuppam-602 025, INDIA - (vinodmaths85@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.190405

    Received: May 26, 2022 Accepted: October 18, 2022
    Abstract

    Several others have already discussed various types of new techniques in multi-criteria decision-making problems. De-fuzzification, De-eutrophication, and De-Bipolarisation all of these are new approaches that have been established. But this work depicts the concept and features of the Neutrosophic Bipolar Pentagonal Fuzzy number. The relationships and products of the picture fuzzy set, as well as their associated results, are investigated. The different kinds of neutrosophic single-typed bipolar pentagonal numbers (nbpnum) were also discussed. A multi-criteria choice is also done in a triangular Bipolar Neutrosophic Fuzzy Set to identify the ideal output depending on several attributes. A multi-criteria choice is also done in a triangular Bipolar Neutrosophic Fuzzy Set to identify the ideal output depending on several attributes.

    Keywords :

    Neutrosohic set , Bipolar Fuzzy Set , Pentagonal Fuzzy Set , Decision Making

    References

    [1] Abdullah, S., Aslam, M., & Ullah, K., Bipolar fuzzy soft sets and its applications in decision making

    problem. J Intell Fuzzy Syst 27(2), 729–74, 2014.

    [2] Abbasbandy, S., & Hajjari, T., A new approach for ranking of trapezoidal fuzzy numbers.Computers and

    Mathematics with Applications, 57(3), 413-419 , 2009.

    [3] Ali, M., Son, 1., Deli, I., & Geng, Y., Multi-criteria decision-making method based on single -valued

    neutrosophic Schweizer-sklar muirhead mean aggregation operators. Symmetry,11,152 , 2019.

    [4] Aslam, M., Abdullah, S., & Ullah, K., Bipolar fuzzy soft sets and its applications in decision making

    problem. arXiv, arXiv:1303.6932 , 2013.

    [5] Attanassov, K., Intuitionistic fuzzy sets. Fuzzy sets Syst.20, 87-96 , 1986.

    [6] Broumi, S., Smarandache, F., Talea, M., & Bakali, A., An introduction to bipolar single valued

    neutrosophic graph theory. Applied Mechanics and Materials, 841,184-191 , 2016.

    [7] Chakraborty, A., Mondal, S. P., Ahmadian, A., Senu, N., Dey, D., Alam, S., & Salahshour, S., The

    pentagonal fuzzy number: Its different representations, properties, ranking, defuzzification and application

    in game problem. Symmetry,11,248 , 2019.

    [8] Chakraborty, A., Mondal, S. P., Ahmadian, A., Senu, N., Alam, S., & Salahshour, S., Different Forms of

    Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications, Symmetry,

    Vol-10, 327.

    [9] Chakraborty, A., Mondal, S. P., Mahata, A., & Alam, S., Different linear and non-linear form of

    Trapezoidal Neutrosophic Numbers, De-Neutrosophication Techniques and its Application in time cost

    optimization technique, sequencing problem; RAIRO Operation Research, doi:10.1051/ro/2019090.

    [10] Chakraborty, A., Mondal, S. P., Alam, S., Ahmadian, A., Senu, N., De, D., & Salahshour, S., Disjunctive

    Representation of Triangular Bipolar Neutrosophic Numbers, De-Bipolarization Technique and Application

    in Multi-Criteria Decision-Making Problems,Symmetry,11(7), 2019.

    [11] Chakraborty.A ., Broumi. S., & Singh, P. K., Some properties of Pentagonal Neutrosophic Numbers and its

    Applications in Transportation Problem Environment, Neutrosophic Sets and Systems, vol.28,200-215,

    2019.

    [12] Chakraborty, A., Shreyashree Mondal., & Said Broumi., De-Neutrosophication Technique of Pentagonal

    Neutrosophic Number and Application in Minimal Spanning Tree , Neutrosophic Sets and Systems,1-18,

    29, 2019.

    [13] Chakraborty, A., Mondal, S.P., Alam, S., Dey, A., Classification of trapezoidal bipolar neutrosophic

    number, de-bipolarization technique and its execution in cloud service-based MCGDM problem. Complex

    Intell. Syst. 7, 145–162 , 2021.

    [14] Chakraborty, A., Banik, B., Mondal, S., & Alam, S., Arithmetic and Geometric Operators of Pentagonal

    Neutrosophic Number and its Application in Mobile Communication Based MCGDM Problem,

    Neutrosophic Sets and System, Vol 32, 61-79.

    [15] Chakraborty, A., Mondal, S. P., Alam, S., & Mahata, A., Cylindrical neutrosophic single-valued number

    and its application in networking problem, multi-criterion group decision-making problem and graph

    theory. CAAI Transactions on Intelligence Technology, 5(2), 68-77, 2020.

    [16] Deli, I., Ali, M., & Smarandache, F., Bipolar neutrosophic sets and their application based on multi-criteria

    decision making problems. In proceedings of the 2015 International conference on Advanced Mechatronic

    Systems, Beijing, China,22-24 , 2015.

    [17] Deli, I., Broumi, S., & Smarandache, S.F., On neutrosophic refined sets and their applications in medical

    diagnosis. J. New Theory, 6,88-98 , 2015.

    [18] Florentin Smarandache., n-Valued Refined Neutrosophic Logic and Its Applications to Physics. Progress in

    physics, 4,143-146 , 2013.

    [19] Haque, T. S., Chakraborty, A., Mondal, S., & Alam, S., A New Approach to Solve Multi-Criteria Group

    Decision Making Problems by Exponential Operational Law in Generalised Spherical Fuzzy Environment,

    CAAI Transactions on Intelligence Technology, Vol-5(2), pp: 106-114,

    [20] Helen R., & Uma, G., A new operation and ranking on pentagon fuzzy numbers, Int Jr. of Mathematical

    Sciences & Applications, Vol. 5, No. 2, 341-346 , 2015.

    [21] Lee, K., J., Bipolar fuzzy sub algebras and bipolar fuzzy ideals of BCK/BCI-algebras. Bull. Malays Math.

    Sci. Soc.,32,361-373 , 2009.

    [22] Maissam, Jdid., Basel Shahin., & Fatima A1 Suleiman., Important Neutrosophic rules for Decision-

    Making in the Case of uncertain Data. International Journal of Neutrosophic Science, 18(3), 166-176,2022.

    [23] Mani Parimala., Muthusamy, K., Sivaraman Murali., Florentin Smarandache., Muhammad Riaz., & Saeid

    Jafari., Multi Criteria Decision Making Algorithm Via Complex Neutrosophic Nano Topological Spaces.

    International Journal of Neutrosophic Science, 17(2), 127-143, 2021.

    [24] Necmiya Merve Sahin., & Azize Dayan., Multicriteria Decision- Making Applications Based on

    Generalised Hamming Measure for Law. International Journal of Neutrosophic Science, 17(1),8-29, 2021.

    [25] Pathinathan, P., & Ponnivalavan, K., Reverse order Triangular, Trapezoidal and Pentagonal Fuzzy

    Numbers, Annals of Pure and Applied Mathematics, Vol. 9, No. 1, 107-117, 2015.

    [26] Soman Debnath., Introduction to Restricted Netrosophic Sets and Its Application. International Journal of

    Neutrosophic Science, 18(2), 227-242, 2022.

    [27] Radhika, K., & Arun Prakash, K., Ranking of Pentagonal Neutrosophic Numbers and its Applications to

    solve Assignment Problem, Neutrosophic Sets and Systems, Vol. 35, 463-477 , 2020.

    [28] Tourad, M.C., & Abdal, A., An Intelligent Similarity model between Generalized Trapezoidal Fuzzy

    Numbers in Large Scale. Int. J. Fuzzy LogicIntell. Syst. 18, 3.3-315 (2018)

    [29] Ulucay, V., Deli, I., & Sahin, M., Similaity measures of bipolar neutrosophic sets and their application to

    multiple criteria decision making. Neural Comput. Appl. 29,739-748, 2018.

    [30] Vigin Raj, A., & Karthik, S., Application of Pentagonal Fuzzy Number in Neural Network, International

    Journal of Mathematics And its Applications, Volume 4, Issue 4 149-154, 2016.

    [31] Wang, H., Smarandache, F., Zhang,Q., & Sunderraman,R., Single valued neutrosophic sets. Multispace and

    Multistructure, 4, 410-413, 2010.

    [32] Wang,L., Zhang, H., Wang, J., & Frank choguet ., Bonferroni mean operators of bipolar neutrosophic sets

    and their applicaton to multi-criteria decision-making problems. Int. J. Fuzzy Syst. 20,13-28, 2018.

    [33] Wang, J.Q., & Li, X.E., The TODIM method with multi- valued neutrosophic sets. Control Decis. 30,

    1139-1142, 2015.

    [34] Ye, J., prioritized aggregation operators of trapezoidal intuitionistic fuzzy sets and their application to

    multi criteria decision making, Neural Computing and Applications, 25(6), 1447-1454, 2014.

    [35] Yun, Ye., Trapezoidal neutrosophic set and its application to multiple characteristics decision-making,

    Neural Comput& Applic 26,1157–1166 DOI 10.1007/s00521-014-1787-6, 2015.

    [36] Zadeh, L.A., Fuzzy sets. Inf. Control 8,338-353, 1965.

    [37] Zhang, W.R., Bipolar fuzzy sets. In proceedings of the 1998 IEEE International Conference on Fuzzy

    Systems, Anchorage, AK, USA,4-9 May 835-840.28, 1998.

    Cite This Article As :
    Hemavathi, P.. , Muthumeenakshi, M.. , Chanthini, P.. , Muralikrishna, P.. , Vinodkumar, R.. Implementation of Neutrosophic Bipolar Pentagonal Fuzzy Set on Multi-Criteria Decision-Making Scenario. International Journal of Neutrosophic Science, vol. , no. , 2022, pp. 58-76. DOI: https://doi.org/10.54216/IJNS.190405
    Hemavathi, P. Muthumeenakshi, M. Chanthini, P. Muralikrishna, P. Vinodkumar, R. (2022). Implementation of Neutrosophic Bipolar Pentagonal Fuzzy Set on Multi-Criteria Decision-Making Scenario. International Journal of Neutrosophic Science, (), 58-76. DOI: https://doi.org/10.54216/IJNS.190405
    Hemavathi, P.. Muthumeenakshi, M.. Chanthini, P.. Muralikrishna, P.. Vinodkumar, R.. Implementation of Neutrosophic Bipolar Pentagonal Fuzzy Set on Multi-Criteria Decision-Making Scenario. International Journal of Neutrosophic Science , no. (2022): 58-76. DOI: https://doi.org/10.54216/IJNS.190405
    Hemavathi, P. , Muthumeenakshi, M. , Chanthini, P. , Muralikrishna, P. , Vinodkumar, R. (2022) . Implementation of Neutrosophic Bipolar Pentagonal Fuzzy Set on Multi-Criteria Decision-Making Scenario. International Journal of Neutrosophic Science , () , 58-76 . DOI: https://doi.org/10.54216/IJNS.190405
    Hemavathi P. , Muthumeenakshi M. , Chanthini P. , Muralikrishna P. , Vinodkumar R. [2022]. Implementation of Neutrosophic Bipolar Pentagonal Fuzzy Set on Multi-Criteria Decision-Making Scenario. International Journal of Neutrosophic Science. (): 58-76. DOI: https://doi.org/10.54216/IJNS.190405
    Hemavathi, P. Muthumeenakshi, M. Chanthini, P. Muralikrishna, P. Vinodkumar, R. "Implementation of Neutrosophic Bipolar Pentagonal Fuzzy Set on Multi-Criteria Decision-Making Scenario," International Journal of Neutrosophic Science, vol. , no. , pp. 58-76, 2022. DOI: https://doi.org/10.54216/IJNS.190405