462 242
Full Length Article
Volume 3 , Issue 2, PP: 67-77 , 2020


Utilization of Jaccard Index Measures on Multiple Attribute Group Decision Making under Neutrosophic Environment

Authors Names :   N. Gayathri   1 *     Dr. M. Helen   2     P. Mounika   3  

1  Affiliation :  1Assistant Professor, Department of Mathematics, Sri Krishna Arts and Science College, CBE-08

    Email :  gayupadmagayu@gmail.com

2  Affiliation :  Associate Professor, Department of Mathematics, Nirmala College for Women, CBE-45

    Email :  N/A

3  Affiliation :  Research Scholar, Sri Krishna Arts and Science College, CBE-08

    Email :  N/A

Doi   :  10.5281/zenodo.3742151

Abstract :

In this paper, we introduce the concept of Jaccard  index measures under the neutrosophic environment to make the right decision in multiple attributes. Here, we insinuate two Jaccard  index measures based on distance and the included weighted Jaccard  of two vectors between the neutrosophic environment. Then, we determine the Multiple Attribute group decision-making method (in short MAGDM) based on the Jaccard  index measures under  the neutrosophic environment and also we compare the applications of the proposed MAGDM method in the neutrosophic environment. Finally, certain descriptive examples are on hand to verify the residential handle and to express its practicality and effectiveness.

Keywords :

Jaccard  index measure , Neutrosophic vague set , MAGDM

References :

[1]         Al-Quran A. and Hassan. N, “Neutrosophic Vague Soft Set and its Applications,” Malaysian Journal of Mathematical Sciences., vol 11(2), pp.141-163, 2017.  

[2]          Al-Quran. A and Hassan,N, “Neutrosophic vague soft expert set theory,” Artic. J. Intell. Fuzzy Syst.,vol 30(6), pp.3691–3702, 2016.

[3]          Al-Quran. A and Hassan. N, “Neutrosophic vague soft multiset for decision under uncertainty,” Songklanakarin J. Sci. Technolgy, vol 40(2), pp.290–305, 2018.

[4]         Atanassov. K and G. Gargov, “Interval valued intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol 31 , pp.343–349, 2014.

[5]         Atanassov. K, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, pp. 87-96, 1986.

[6]         Avishek Chakraborty, Said Broumi, Prem Kumar Singh, “Some properties of Pentagonal Neutrosophic Numbers and its Applications in Transportation Problem Environment,” Neutrosophic Sets and Systems; vol.28, pp.200-215, 2019.

[7]          Avishek Chakraborty, Sankar Prasad Mondal, Ali Ahmadian, Norazak Senu, Shariful Alam and Soheil Salahshour, “Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications,” Symmetry, Vol-10, 327;pp1-27, 2018.

[8]         Avishek Chakraborty, Sankar Prasad Mondal, Shariful Alam, Animesh MahataDifferent Linear and Non-linear Form of Trapezoidal Neutrosophic Numbers, De-Neutrosophication Techniques and its Application in Time-Cost Optimization Technique, Sequencing Problem;” Rairo Operations Research,pp. 1-30, 2019.

[9]         Broumi, S., Deli, I.,  Smarandache, F. “Distance and similarity measures of interval neutrosophic soft sets,” Critical Review, Center for Mathematics of Uncertainty, Creighton University, USA, vol 8, pp.14-31, 2014.  

[10]      Broumi. S and Deli. İ, “Correlation measure for neutrosophic Refined sets and its application ın medical Diagnosis,” Palestine journal of mathematics, vol 5(1) ,135–143, 2016.

[11]      Broumi. S and Smarandache F “Several similarity measures of  neutrosophic sets,” Neutrosophic Sets and Systems, vol 1(1) ,pp. 54–62, 2013. 

[12]      Broumi. S, Assia Bakali, MohamedTalea, Florentin Smarandache, Prem Kumar Singh, Vakkas Uluçay, Mohsin Khan ‘Bipolar Complex Neutrosophic Sets and its Application in Decision Making Problem ‘, In: Irem otay et al.,  Fuzzy Multi-criteria Decision Making Using Neutrosophic Sets, Studies in Fuzziness and Soft Computing ,Vol 369,  pp. 677-702, 2019.

[13]      Broumi. S, Deli . I, Smarandache. F. “N-valued Interval Neutrosophic Sets and Their Application in Medical Diagnosis,” Critical Review, Center for Mathematics of Uncertainty, Creighton University, USA, vol 10 ,pp.46-69, 2015.

[14]      Chakraborty.A, Mondal S. Broumi.S “De-Neutrosophication Technique of Pentagonal Neutrosophic Number and Application in Minimal Spanning Tree,” Neutrosophic Sets and Systems, vol.29, pp.1-18, 2019.

[15]      Chakraborty.A, Mondal. S.P , Alam . S, Ahmadian . A, Senu. N, De. D and Salahshour. S. “Disjunctive Representation of Triangular Bipolar Neutrosophic Numbers, De-Bipolarization Technique and Application in Multi-Criteria Decision-Making Problems,” Symmetry, Vol-11(7), 932-.pp.1-30, 2019.

[16]      Chatterjee. P, Mondal. S.  and Boral S. “A novel hybrid method for non-traditional machining process selection using factor relationship and Multi-Attributive Border Approximation Method,” Facta Univ Ser Mech Eng 15 pp.439–456, 2017.

[17]      Chen S. M., “Similarity measures between vague sets and between elements,” IEEE    Transactions on Systems, Man and Cybernetics, Vol 27 (1) ,pp.153–158, 1997.

[18]      Chen S. M., “Analyzing fuzzy system reliability using vague set theory,” International   Journal of Applied Science and Engineering, Vol 1 (1) pp.82–88, 2003. 

[19]      Cross. V, “Relating fuzzy set similarity measures,”  Advances in Intelligent Systems  and Computing, vol. 648,  pp.9-21, 2018.  

[20]       Gau W.-L. and Buehrer D. J, “Vague sets,” IEEE Trans. Syst. Man. Cybern., vol 23(2) ,  pp.610–614, 1993.

[21]      Hazwani Hashim, Lazim Abdullah and Ashraf Al-Qura” Interval Neutrosophic Vague Sets,” Neutrosophic Sets and Systems, Vol. 25, pp.66-74, 2019.

[22]      Lu. Z. and Ye. J, “Cosine measures of neutrosophic cubic sets for multiple attribute decision-making,” Symmetry, vol 121, pp.1–10, 2017.

[23]      Mehmet Şahin , Irfan Deli and Vakkas Uluçay “Jaccard  Vector Similarity Measure of Bipolar Neutrosophic Set Based on Multi-Criteria Decision Making,” International Conference on Natural Science and Engineering (ICNASE’16) ,pp. 1972-1979, 2016.

[24]      Mohamed Abdel-Basset, Asmaa Atef “A Hybrid neutrosophic multiple  criteria group decision making approach for project selection,” Science direct:cognitive system research, vol 57,  pp.216-227, 2018.

[25]      Prem Kumar Singh, “Three-way bipolar neutrosophic concept lattice,” In: Irem otay et al. (Fuzzy Multi-criteria Decision Making Using Neutrosophic Sets, Studies in Fuzziness and Soft Computing”, Springer Vol 369, pp. 417-432 , 2019.

[26]      Mona Gamal Gafar, Mohamed Elhoseny, M. Gunasekaran, Modeling neutrosophic variables based on particle swarmoptimization and information theory measures for forestfires, The Journal of Supercomputing, First Online: 30 July 2018 (DOI: https://doi.org/10.1007/s11227-018-2512-5)

[27]      Shawkat Alkhazaleh “Neutrosophic Vague Set Theory,” Critical Review. Volume X, pp.29- 32, 2015.

[28]       Smarandache, F. “A unifying field in logics. Neutrosophy”: Neutrosophic probability, set and logic, American Research Press, Rehoboth, pp.287-297, 1999

[29]      Turksen . I “Interval valued fuzzy sets based on normal forms,” Fuzzy Sets and Systems, vol. 20, pp. 191-210, 1986.

[30]      Xu. W, Ma. J, Wang. S, and Hao. G, “Vague soft sets and their properties,” Comput. Math. with Appl., vol 59(2), pp787–794, 2010.  

[31]      Mohamed Abdel-Basset, Mai Mohamed, Mohamed Elhoseny, Le Hoang Son, Francisco Chiclana, Abd El-Nasser H.Zaied, Cosine Similarity Measures of Bipolar Neutrosophic Set for Diagnosis of Bipolar Disorder Diseases, Artificial Intelligence in Medicine, Available online 5 October 2019,  In Press (DOI:https://doi.org/10.1016/j.artmed.2019.101735)

[32]      Ye, J. “Vector similarity measures of simplified neutrosophic sets and their application in multi-criteria decision making,”  International Journal of Fuzzy Systems, vol 16(2),pp. 204-215, 2014. 

[33]       Ye. J, “Multi criteria decision-making method using the correlation coefficient under single-valued neutrosophic environment,” International Journal of General Systems, vol 42(4) , pp.386–394, 2013.  

[34]       Ye. J, “A multi criteria decision-making method using aggregation operators for simplified neutrosophic sets,” Journal of Intelligent and Fuzzy Systems, vol 26, pp.2459–2466, 2014.

[35]      Zadeh,L.A. “Fuzzy Sets,” Information and Control, vol 8,pp. 338–353, 1965.

[36]      Smarandache, F., “NeutroAlgebra is a Generalization of Partial Algebra,” International Journal of Neutrosophic Science,  Volume 2 , Issue 1, pp 08-17 , 2020.

[37]      Schweizer, P. “Uncertainty: two probabilities for the three states of neutrosophy,” International Journal of Neutrosophic Science,   Volume 2 , Issue 1, pp. 18-26 , 2020.

[38]      Edalatpanah, S. A. “A Direct Model for Triangular Neutrosophic Linear Programming,” International Journal of Neutrosophic Science, Volume 1 , Issue 1, pp. 19-28 , 2020.


[39]      Christianto, V., Smarandache, F., “Remark on Artificial Intelligence, humanoid and Terminator scenario: A Neutrosophic way to futurology,” International Journal of Neutrosophic Science,  Volume 1 , Issue 1, pp.8-13 , 2020