Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure
Single-valued neutrosophic set (SVNS) is an important contrivance for directing the decision-making queries with unknown and indeterminant data by employing a degree of “acceptance”, “indeterminacy”, and “non-acceptance” in quantitative terms. Under this set, the objective of this paper is to propos...
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| Published in | AIMS mathematics Vol. 5; no. 3; pp. 2671 - 2693 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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01.01.2020
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| Abstract | Single-valued neutrosophic set (SVNS) is an important contrivance for directing the decision-making queries with unknown and indeterminant data by employing a degree of “acceptance”, “indeterminacy”, and “non-acceptance” in quantitative terms. Under this set, the objective of this paper is to propose some new distance measures to find discrimination between the SVNSs. The basic axioms of the measures have been highlighted and examined their properties. Furthermore, to examine the relevance of proposed measures, an extended TOPSIS (“technique for order preference by similarity to ideal solution”) method is introduced to solve the group decision-making problems. Additionally, a new clustering technique is proposed based on the stated measures to classify the objects. The advantages, comparative analysis as well as superiority analysis is given to shows its influence over existing approaches. |
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| AbstractList | Single-valued neutrosophic set (SVNS) is an important contrivance for directing the decision-making queries with unknown and indeterminant data by employing a degree of “acceptance”, “indeterminacy”, and “non-acceptance” in quantitative terms. Under this set, the objective of this paper is to propose some new distance measures to find discrimination between the SVNSs. The basic axioms of the measures have been highlighted and examined their properties. Furthermore, to examine the relevance of proposed measures, an extended TOPSIS (“technique for order preference by similarity to ideal solution”) method is introduced to solve the group decision-making problems. Additionally, a new clustering technique is proposed based on the stated measures to classify the objects. The advantages, comparative analysis as well as superiority analysis is given to shows its influence over existing approaches. |
| Author | Garg, Harish Nancy |
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| Cites_doi | 10.3233/JIFS-18040 10.17654/AS050040261 10.31181/dmame180151b 10.1016/j.omega.2005.12.003 10.1080/0952813X.2019.1592236 10.1007/s00521-016-2607-y 10.1016/j.ins.2008.06.008 10.1007/s12559-017-9462-8 10.1007/s40815-016-0180-2 10.1016/j.measurement.2019.02.031 10.31181/dmame1901066n 10.1016/S0165-0114(86)80034-3 10.1007/s00521-015-1891-2 10.1615/Int.J.UncertaintyQuantification.2016018603 10.1016/j.asoc.2014.08.066 10.1007/s10489-017-1070-5 10.1002/int.21815 10.1080/00207721.2014.994050 10.1615/Int.J.UncertaintyQuantification.2016018441 10.1016/j.cogsys.2018.09.001 10.1007/s00521-016-2660-6 10.1016/S0019-9958(69)90591-9 10.31181/dmame1801121r 10.1016/j.asoc.2018.05.003 10.1007/s12652-018-0738-y 10.1016/S0019-9958(65)90241-X 10.3233/IFS-130916 |
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| References | J. J. Peng, J. Q. Wang, J. Wang (6) 44 X. H. Wu, J. Q. Wang, J. J. Peng (22) 23 45 24 25 J. Ye (5) Nancy, H. Garg (10) H. L. Huang (19) K. T. Atanassov (2) Z. S. Xu, J. Chen, J. J. Wu (42) M. Noureddine, M. Ristic (43) H. Garg, Nancy (46) Nancy, H. Garg (7) H. Pouresmaeil, E. Shivanian, E. Khorram (30) L. A. Zadeh (1) 31 Y. Guo, A. Şengür (37) P. Ji, J. Q. Wang, H. Y. Zhang (15) 13 35 14 36 38 F. Liu, G. Aiwu, V. Lukovac (26) N. D. Thanh, M. Ali, L. H. Son (39) Nancy, H. Garg (27) D. Rani, H. Garg (8) H. Garg, Nancy (47) X. D. Peng, J. G. Dai (32) I. Mukhametzyanov, D. Pamucar (33) 4 E. H. Ruspini (34) H. Garg, Nancy (11) G. Wei, Z. Zhang (12) 9 X. Wang, E. Triantaphyllou (41) A. S. Ashour, Y. Guo, E. Kucukkulahli (40) 20 P. Biswas, S. Pramanik, B. C. Giri (29) |
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