1
Department of Basic Science, Academy of Technology, Adisaptagram, Hooghly, 712502, India
(tirtha.avishek93@gmail.com)
2
Department of Mathematics, IIESTS, Howrah, W.B- 71103, India
(baisakhibanik14@gmail.com)
3
Laboratory of Information Processing, Faculty of Science Ben MSik, University Hassan II, B.P 7955, Sidi Othman, Casablanca, Morocco
(broumisaid78@gmail.com)
4
Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
(soheil.salahshour@eng.bau.edu.tr)
Abstract :
This article exceedingly induces a completely new impression of graded mean integral representation in trapezoidal neutrosophic number domain corresponding to each membership function. Furthermore employing these integral representations, a new fangled graded mean integral distance measure is produced between two trapezoidal neutrosophic numbers. Notably, a numerical business economy based Multi Criteria Decision Making (MCDM) problem is fabricated along with the explication of neutrosophic theory to authenticate our suggested course of action in the decision making policy with the prominent solution scheme of VlseKriterijumska Optimizcija I Kaompromisno Resenje (VIKOR) technique for recognising the best alternative from a finite set. Lastly, the comparison work acts as an additional encouragement of our proposed scheme.
Keywords :
Trapezoidal neutrosophic number; VIKOR; graded mean integral representation; MCDM.
References :
[1] L.A Zadeh; (1965); Fuzzy sets. Information and Control, 8(5): 338- 353.
[2] Atanassov K; (1986); Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20: 87-96.
[3] Jiang T, Li Y; (1996); Generalized defuzzification strategies and their parameter learning Procedures. IEEE Transactions on fuzzy systems, 4(1): 64-71.
[4] Smarandache F; (1998); A unifying field in logics neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth.
[5] Opricovic S; (1998); Multicriteria Optimization of Civil Engineering Systems. Faculty of Civil Engineering, Belgrade, Serbia.
[6] Opricovic S, Tzeng GH; (2004); Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European journal of operational research, 156 : 445–455.
[7] Liu F, Yuan XH; (2007); Fuzzy number intuitionistic fuzzy set. Fuzzy Systems and Mathematics, 21(1): 88- 91.
[8] Opricovic S, Tzeng GH; (2007); Extended VIKOR method in comparison with outranking methods. European journal of operational research, 178 (2): 514-529.
[9] Xu ZS, (2008); Group decision making based on multiple types of linguistic preference relations. Information Sciences, 178: 452–467.
[10] Wang H, Smarandache F, Zhang Q, Sunderraman R; (2010); Single valued neutrosophic sets. Multispace and Multistructure, 4: 410–413.
[11] Abdel-Basset, M., Atef, A., & Smarandache, F. (2019), A hybrid Neutrosophic multiple criteria group decision making approach for project selection. Cognitive Systems Research, 57, 216-227.
[12] Ye J; (2014); Prioritized aggregation operators of trapezoidal intuitionistic fuzzy sets and their application to multi criteria decision making. Neural Computing and Applications, 25(6): 1447-1454.
[13] Guo Y, Sengur A, Ye J; (2014); A novel image thresholding algorithm based on neutrosophic similarity score. Measurement, 58: 175–186.
[14] Liu P, Zhang L; (2014); The extended VIKOR method for multiple criteria decision making problem based on neutrosophic hesitant fuzzy set, DOI- 10.5281/zenodo.34907.
[15] Ye J; (2014); Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making. J Intelligent Fuzzy Systems, 27(5): 2231–2241.
[16] Peng JJ, Wang JQ, Wu XH, Wang J, Chen XH; (2015); Multi-valued neutrosophic sets and power aggregation operators with their applications in multi-criteria group decision-making problems. International Journal of Computational Intelligent Systems, 8(2): 345–363.
[17] Broumi S, Ye J, Smarandache F; (2015); An extended TOPSIS method for multiple attribute decision making based on interval neutrosophic uncertain linguistic variables. Neutrosophic Sets Systems, 8: 22–31.
[18] Deli I, Broumi S; (2015); Neutrosophic soft matrices and NSM- decision making. Journal of Intelligent and Fuzzy Systems, 28(5): 2233–2241.
[19] Liu PD, Teng F; (2015); Multiple attribute decision making method based on normal neutrosophic generalized weighted power averaging operator. International Journal of Machine Learning and Cybernetics, 9: 281-293.
[20] Peng X, Dai J; (2018); A bibliometric analysis of neutrosophic set: two decades review from 1998 to 2017, Artificial Intelligence Review, DOI - 10.1007/s10462-018-9652-0
[21] Zhang HY, Ji P, Wang J, Chen XH; (2015); An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making problems. International Journal of Computational Intelligence Systems, 8(6): 1027–1043.
[22] Bausys R, Zavadskas EK; (2015); Multicriteria decision making approach by VIKOR under interval neutrosophic set environment. Economic Computation and Economic Cybernetics Studies and Research, 4: 33-48.
[23] Ali M, Smarandache F; (2016); Complex neutrosophic set. Neural Computing and Applications, 25: 1–18.
[24] Biswas P, Pramanik S, Giri BC; (2016); TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural computing and Applications, 27(3): 727-737.
[25] Wu XH, Wang J, Peng JJ, Chen XH; (2016); Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision-making problems. International Journal of Fuzzy Systems, 18: 1104-1116.
[26] Deli I, Subas Y; (2016); A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems. International Journal of Machine Learning and Cybernetics, 8: 1309-1322.
[27] Deli I, Subas Y; (2016); A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems. International Journal of Machine Learning and Cybernetics, 8: 1309-1322.
[28] Stanujkic D, Zavadskas EK, Smarandache F, Brauer WK, Karabasevic D; (2017); A neutrosophic extension of the MULTIMOORA method. Informatica, 28(1): 181-192.
[29] Pouresmaeil H, Shivanian E, Khorram E, Fathabadi HS; (2017); An extended method using TOPSIS and VIKOR for multiple attribute decision making with multiple decision makers and single valued neutrosophic numbers. Advances and Applications in Statistics, 50(4): 261.
[30] Pouresmaeil H, Shivanian E, Khorram E, Fathabadi HS; (2017); An extended method using TOPSIS and VIKOR for multiple attribute decision making with multiple decision makers and single valued neutrosophic numbers. Advances and Applications in Statistics, 50(4): 261.
[31] Selvakumari K, Priyadharshini MA; (2017); VIKOR method for decision making problem using octagonal neutrosophic soft matrix. International Journal of Latest Engineering Research and Applications, 2(7): 41-45.
[32] Pramanik S, Dalapati S, Alam S, Roy TK; (2018); VIKOR based MAGDM strategy under bipolar neutrosophic set environment. Neutrosophic Sets and Systems, 19: 57-69.
[33] Chakraborty A, Mondal SP, Ahmadian A, Senu N, Alam S, Salahshour S; (2018); Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications. Symmetry, 10: 327.
[34] Wang L, Zhang HY, Wang JQ; (2018) ; Frank Choquet Bonferroni Mean Operators of Bipolar Neutrosophic Sets and Their Application to Multi-criteria Decision-Making Problems, International journal of Fuzzy Systems, 20: 13–28.
[35] Wang J, Wei G, Lu M; (2018); An Extended VIKOR Method for Multiple Criteria Group Decision Making with Triangular Fuzzy Neutrosophic Numbers. Symmetry, 10(497): 2-15.
[36] Nabeeh NA, Basset AM, El-Ghareeb HA, Aboelfetouh A; (2019); Neutrosophic multi-criteria decision making approach for IoT-based enterprises. IEEE Access, 7, 59559-59574.
[37] Chakraborty A, Mondal SP, Alam S, Mahata A; (2019); Different 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, doi: 10.1051/ro/2019090.
[38] A. Chakraborty, T. S Haque, S. P Mondal and S. Alam, A Novel Logarithmic Operational Law and Aggregation Operators for Trapezoidal Neutrosophic Number And MCGDM Skill to Determine Most Harmful Virus, Applied Intelligence, (SCI), (2021), I.F- 5.08, DOI: 10.1007/s10489-021-02583-0.
[40] Chakraborty A, Mondal SP, Ahmadian A, Senu N, Dey D, Alam S, Salahshour S; (2019); The Pentagonal Fuzzy Number: Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problem. Symmetry, 11(2): 248. doi: 10.3390/sym11020248.
[41] Basset A M, Saleh M, Gamal A, Smarandache F; (2019); An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number. Applied Soft Computing, 77: 438-452.
[42] Sumathi, I.R., Antony Crispin Sweety, C., New approach on differential equation via trapezoidal neutrosophic number, Complex Intell. Syst. 5, 417–424 (2019) https://doi.org/10.1007/s40747-019-00117-3
[43] Chakraborty A, Mondal SP, Alam S, Ahmadian A, Senu N, De D, Salahshour S; (2019); Disjunctive Representation of Triangular Bipolar Neutrosophic Numbers, De-Bipolarization Technique and Application in Multi-Criteria Decision-Making Problems. Symmetry, 11(7): 932.
[44] Maity S, Chakraborty A, De SK, Mondal SP, Alam S; (2019); A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment. Rairo Operations Research, 54(1): 267-286.
[45] Mahata A, Mondal SP, Alam S, Chakraborty A, Goswami A, Dey S; (2019); Mathematical model for diabetes in fuzzy environment and stability analysis- Journal of of intelligent and Fuzzy System, Vol- 36(3):2923-2932.
[46] Chakraborty A, Maity S, Jain S, Mondal SP, Alam S; (2020); Hexagonal Fuzzy Number and its Distinctive Representation, Ranking, Defuzzification Technique and Application in Production Inventory Management Problem, Granular Computing, Springer, DOI: 10.1007/s41066-020-00212-8.
[47] Chakraborty A, Banik B, Mondal SP, Alam S; (2020); Arithmetic and Geometric Operators of Pentagonal Neutrosophic Number and its Application in Mobile Communication Service Based MCGDM Problem. Neutrosophic Sets and Systems, 32: P.P-61-79.
[48] Chakraborty A; (2020); A New Score Function of Pentagonal Neutrosophic Number and its Application in Networking Problem, International Journal of Neutrosophic Science (IJNS), 1(1).
[49] Chakraborty A; (2020); Application of Pentagonal Neutrosophic Number in Shortest Path Problem. International Journal of Neutrosophic Science (IJNS), Vol-3(1), 21-28.
[50] A. Chakraborty, S.P Mondal, S. Alam, A. Dey, Classification of Trapezoidal Bipolar Neutrosophic Numbers, De-Bipolarization and Implementation in Cloud Service Based MCGDM Problem, , Complex and Intelligence System, Springer, Vol-7(1), pp: 145-161, (2021) DOI: 10.1007/s40747-020-00170-3, I.F – 3.79.
[51] Pal S, Chakraborty A; (2020); Triangular Neutrosophic-based EOQ model for non Instantaneous Deteriorating Item under Shortages, American Journal of Business and Operations Research, Vol- 1(1); pp- 28-35.
[52] T. S Haque, A. Chakraborty, S.P Mondal and S. Alam, A New Exponential Operational Law for Trapezoidal Neutrosophic Number and Pollution in Megacities related MCGDM Problem, Journal of Ambient Intelligence and Humanized Computing, Springer, (2021), I.F–7.104, DOI: 10.1007/s12652-021-03223-8.
[53] Kundogdu F K, Kahraman C, Karasan A; (2020); Spherical Fuzzy VIKOR Method and Its Application to Waste Management. In: INFUS 2019, AISC 1029, Springer Nature, 997-1005.
| Style | # |
|---|---|
| MLA | Avishek Chakraborty, Baisakhi Banik, Said Broumi, Soheil Salahshour. "Graded Mean Integral Distance Measure and VIKOR Strategy Based MCDM Skill in Trapezoidal Neutrosophic Number." International Journal of Neutrosophic Science, Vol. 18, No. 2, 2022 ,PP. 210-226 (Doi : https://doi.org/10.54216/IJNS.180205) |
| APA | Avishek Chakraborty, Baisakhi Banik, Said Broumi, Soheil Salahshour. (2022). Graded Mean Integral Distance Measure and VIKOR Strategy Based MCDM Skill in Trapezoidal Neutrosophic Number. Journal of International Journal of Neutrosophic Science, 18 ( 2 ), 210-226 (Doi : https://doi.org/10.54216/IJNS.180205) |
| Chicago | Avishek Chakraborty, Baisakhi Banik, Said Broumi, Soheil Salahshour. "Graded Mean Integral Distance Measure and VIKOR Strategy Based MCDM Skill in Trapezoidal Neutrosophic Number." Journal of International Journal of Neutrosophic Science, 18 no. 2 (2022): 210-226 (Doi : https://doi.org/10.54216/IJNS.180205) |
| Harvard | Avishek Chakraborty, Baisakhi Banik, Said Broumi, Soheil Salahshour. (2022). Graded Mean Integral Distance Measure and VIKOR Strategy Based MCDM Skill in Trapezoidal Neutrosophic Number. Journal of International Journal of Neutrosophic Science, 18 ( 2 ), 210-226 (Doi : https://doi.org/10.54216/IJNS.180205) |
| Vancouver | Avishek Chakraborty, Baisakhi Banik, Said Broumi, Soheil Salahshour. Graded Mean Integral Distance Measure and VIKOR Strategy Based MCDM Skill in Trapezoidal Neutrosophic Number. Journal of International Journal of Neutrosophic Science, (2022); 18 ( 2 ): 210-226 (Doi : https://doi.org/10.54216/IJNS.180205) |
| IEEE | Avishek Chakraborty, Baisakhi Banik, Said Broumi, Soheil Salahshour, Graded Mean Integral Distance Measure and VIKOR Strategy Based MCDM Skill in Trapezoidal Neutrosophic Number, Journal of International Journal of Neutrosophic Science, Vol. 18 , No. 2 , (2022) : 210-226 (Doi : https://doi.org/10.54216/IJNS.180205) |