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Year 2020, Volume: 10 Issue: 1, 128 - 137, 01.01.2020

Abstract

References

  • Atanassov K.T., (1999). Intuitionistic fuzzy sets, Pysica-Verlag A Springer-Verlag Company, New York.
  • Basset M.A., Mohamed M., Hussien A.N., Sangaiah A.K., (2018). A novel group decision-making model based on triangular neutrosophic numbers, Soft Compututing, 22, 6629-6643.
  • Basset A.B., Mohamed M., Sangaiah A.K., (2018). Neutrosophic AHP-Delphi group decision making model based on trapezoidal neutrosophic numbers, J. Ambient Intell. Human Comput., 9, 1427-1443. [4] Basset M.A., Mohamed M., Smarandache F., (2018). A hybrid neutrosophic group ANP-TOPSIS framework for supplier selection problems, Symmetry, 10(226) 1-21.
  • Biswas P., Pramanik S., Giri B.C., (2016). TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment, Neural Comput. Appl. 27(3) 727–737.
  • Biswas P., Pramanik S., Giri B.C., (2016). Aggregation of triangular fuzzy neutrosophic set infor- mation and its application to multi-attribute decision making, Neutrosophic Sets and Systems, 12, 20–40.
  • Biswas P., Pramanik S., Giri B.C., (2018). TOPSIS strategy for MADM with trapezoidal neutrosophic numbers, Neutrosophic Sets and Systems, 19, 29–39.
  • Biswas P., Pramanik S., Giri B.C., (2018). T-Distance measure MADM strategy with interval trape- zoidal neutrosophic numbers, Neutrosophic Sets and Systems, 19, 40–46.
  • Biswas P., Pramanik S., Giri B.C., (2018). Neutrosophic TOPSIS with group decision making, Stud. Fuzz. Soft Comput., Springer, Cham, 543–585.
  • Broumi S., Talea M., Bakali A., Smarandache F., Patro S.K., (2019). Minimum Spanning Tree Problem with single-valued trapezoidal neutrosophic numbers, Studies in Fuzziness and Soft Computing, Soft Comput., 22, Springer Nature Switzerland AG.
  • Broumi S., Dey A., Bakali A., Talea M., Smarandache F., Son L.H., Koley D., (2017). Uniform single valued neutrosophic graphs, Neutrosophic Sets and Systems, 17, 42–49.
  • Deli I., (2017). Interval-valued neutrosophic soft sets and its decision making, Int. J. Mach. Learn. Cybern., 8(2) 665–676.
  • Deli I., Subas Y., (2017). A ranking method of single valued neutrosophic numbers and its applica- tions to multi-attribute decision making problems, International Journal of Machine Learning and Cybernatics, 8(4) 1309–1322.
  • Li D.F., (2014). Decision and game theory in management with intuitionistic fuzzy sets, Studies in Fuzziness and Soft Computing, Volume 308, Springer, Springer Heidelberg New York Dordrecht London.
  • Giri B.C., Molla M.U., Biswas P., (2018). TOPSIS method for MADM based on interval trapezoidal neutrosophic number,Neutrosophic Sets and Systems, 22, 151–167.
  • Georgiev K., (2005). A simplification of the neutrosophic sets. Neutrosophic logic and intuitionistic fuzzy sets, in: Proceedings of the 9th International Conference on IFSs, Sofia, Bulgaria. [17] Jha S., Kumar R., Neutrosophic soft Khari M., stock (2018).
  • http://dx.doi.org/10.1007/s12530-018-9247-7. set decision making for trending analysis, Evolv.
  • Syst., [18] Jha S., Son L.H., Kumar R., Priyadarshini I., Smarandache F., Long H.V., (2019). Neutrosophic image segmentation with dice coefficients, Measurement, 134, 762–772.
  • Ju D., Ju Y., Wang A., (2018). Multiple attribute group decision making based on Maclaurin symmet- ric mean operator under single-valued neutrosophic interval 2-tuple linguistic environment, J. Intell. Fuzzy Syst., 34(4) 2579–2595.
  • Kahraman C., Otay I., (eds.), (2019). Fuzzy multi criteria decision making using neutrosophic sets, Studies in Fuzziness and Soft Computing, 369, Springer Nature Switzerland AG.
  • Karaaslan F., (2018). Gaussian single-valued neutrosophic numbers and its application in multi- attribute decision making, Neutrosophic Sets and Systems, 22, 101–117.
  • Liang R.X., Wang J.Q., Li L., (2018). Multi-criteria group decision-making method based on interde- pendent inputs of single-valued trapezoidal neutrosophic information, Neural Comput. and Applic., 30, 241-260.
  • Liu P., Zhang X.H., (2018). Some maclaurin symmetric mean operators for single-valued trapezoidal neutrosophic numbers and their applications to group decision making, Int. J. Fuzzy Syst., 20(1) 45-61.
  • Mohamed M., Zhou Y.Q., Baset M.A., Smarandache F., (2017). A critical path problem using trian- gular neutrosophic number, Neutrosophic Operational Research I, section X, Pons Brussels.
  • Liu P., Chu Y., Li Y., Chen Y., (2014). Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making, International Journal of Fuzzy Systems, 16(2) 242–255.
  • Liu P., Liu X., (2018). The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group decision making, Int. J. Mach. Learn. Cybern., 9(2) 347–358. [27] Nguyen G.N., Ashour A.S., Dey N., (2017). A survey of the state-of-the-arts on neutrosophic sets in biomedical diagnoses, Int. J. Mach. Learn. Cybern., 10(1) 1–13.
  • Porchelvi R.S., Umamaheswari M., (2018). A Study on intuitionistic fuzzy multi objective LPP into LCP with neutrosophic triangular numbers approach, Journal of Applied Science and Computations, 5(9) 570–576.
  • Pramanik S., Mallick R., (2018). VIKOR based MAGDM strategy with trapezoidal neutrosophic numbers, Neutrosophic Sets and Systems, 22, 118–129.
  • Peng J.J., Wang J.Q., Zhang H.Y., Chen X.H., (2014). An outranking approach for multi-criteria decision-making problemswith simplified neutrosophic sets, Applied Soft Computing, 25, 336-346.
  • Smarandache F., (1998). Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth, USA 105p.
  • S¸ahin R., Yiˇgider M., (2014). A Multi-criteria neutrosophic group decision making metod based TOP- SIS for supplier selection, http://arxiv.org/abs/1412.5077.
  • Tuan T.M., Chuan P.M., Ali M., Ngan T.T., Mittal M., Son L.H., (2018). Fuzzy and neutrosophic modeling for link prediction in social networks, Evolv. Syst., http://dx.doi.org/10.1007/s12530-018- 9251-y.
  • Wang H., Smarandache F., Zhang Y.Q., Sunderraman R., (2010). Single valued neutrosophic sets, Multisp. Multistruct, 4, 410–413.
  • Wang J.Q., Yang Y., Li L., (2018). Multi-criteria decision-making method based on single valued neutrosophic linguistic Maclaurin symmetric mean operators, Neural Comput. Appl., 30(5) 1529– 1547.
  • Wu X., Qian J., Peng J.J., Xue C.C., (2018). A multi-criteria group decision making method with possibility degree and power aggregation operators of single trapezoidal neutrosophic numbers, Sym- metry, 10(590) 1–21.
  • Ye J., (2017). Some weighted aggregation operators of trapezoidal neutrosophic numbers and their multiple attribute decision making method, Informatica, 28(2) 387–402.
  • Ye J., (2014). A multicriteria decision-making method using aggregation operators for simplified neu- trosophic sets, Journal of Intelligent and Fuzzy Systems, 26, 2459–2466.
  • Zadeh L.A., (1965). Fuzzy Sets, Information and Control, 8, 338–353.

LINEAR OPTIMIZATION METHOD ON SINGLE VALUED NEUTROSOPHIC SET AND ITS SENSITIVITY ANALYSIS

Year 2020, Volume: 10 Issue: 1, 128 - 137, 01.01.2020

Abstract

Recently, decision making problems has prompted extensive awareness, es- pecially multi-attribute decision-making problem in single valued neutrosophic sets. Given the inherent characteristics of this case, a multi-attribute decision-making problem with a single valued neutrosophic sets SVN-sets is explored with both weights and attribute ratings expressed by single valued neutrosophic information. Firstly, some basic concepts concerning SVN-sets are reviewed for the subsequent analysis. Secondly, a linear optimization method of SVN-sets are developed to describe the sensitivity analysis of attribute weights which give changing intervals of attribute weights in which the ranking order of the alternatives is required to remain unchanging. Finally, we presented an illustrative example to show its applicability and e ectiveness.

References

  • Atanassov K.T., (1999). Intuitionistic fuzzy sets, Pysica-Verlag A Springer-Verlag Company, New York.
  • Basset M.A., Mohamed M., Hussien A.N., Sangaiah A.K., (2018). A novel group decision-making model based on triangular neutrosophic numbers, Soft Compututing, 22, 6629-6643.
  • Basset A.B., Mohamed M., Sangaiah A.K., (2018). Neutrosophic AHP-Delphi group decision making model based on trapezoidal neutrosophic numbers, J. Ambient Intell. Human Comput., 9, 1427-1443. [4] Basset M.A., Mohamed M., Smarandache F., (2018). A hybrid neutrosophic group ANP-TOPSIS framework for supplier selection problems, Symmetry, 10(226) 1-21.
  • Biswas P., Pramanik S., Giri B.C., (2016). TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment, Neural Comput. Appl. 27(3) 727–737.
  • Biswas P., Pramanik S., Giri B.C., (2016). Aggregation of triangular fuzzy neutrosophic set infor- mation and its application to multi-attribute decision making, Neutrosophic Sets and Systems, 12, 20–40.
  • Biswas P., Pramanik S., Giri B.C., (2018). TOPSIS strategy for MADM with trapezoidal neutrosophic numbers, Neutrosophic Sets and Systems, 19, 29–39.
  • Biswas P., Pramanik S., Giri B.C., (2018). T-Distance measure MADM strategy with interval trape- zoidal neutrosophic numbers, Neutrosophic Sets and Systems, 19, 40–46.
  • Biswas P., Pramanik S., Giri B.C., (2018). Neutrosophic TOPSIS with group decision making, Stud. Fuzz. Soft Comput., Springer, Cham, 543–585.
  • Broumi S., Talea M., Bakali A., Smarandache F., Patro S.K., (2019). Minimum Spanning Tree Problem with single-valued trapezoidal neutrosophic numbers, Studies in Fuzziness and Soft Computing, Soft Comput., 22, Springer Nature Switzerland AG.
  • Broumi S., Dey A., Bakali A., Talea M., Smarandache F., Son L.H., Koley D., (2017). Uniform single valued neutrosophic graphs, Neutrosophic Sets and Systems, 17, 42–49.
  • Deli I., (2017). Interval-valued neutrosophic soft sets and its decision making, Int. J. Mach. Learn. Cybern., 8(2) 665–676.
  • Deli I., Subas Y., (2017). A ranking method of single valued neutrosophic numbers and its applica- tions to multi-attribute decision making problems, International Journal of Machine Learning and Cybernatics, 8(4) 1309–1322.
  • Li D.F., (2014). Decision and game theory in management with intuitionistic fuzzy sets, Studies in Fuzziness and Soft Computing, Volume 308, Springer, Springer Heidelberg New York Dordrecht London.
  • Giri B.C., Molla M.U., Biswas P., (2018). TOPSIS method for MADM based on interval trapezoidal neutrosophic number,Neutrosophic Sets and Systems, 22, 151–167.
  • Georgiev K., (2005). A simplification of the neutrosophic sets. Neutrosophic logic and intuitionistic fuzzy sets, in: Proceedings of the 9th International Conference on IFSs, Sofia, Bulgaria. [17] Jha S., Kumar R., Neutrosophic soft Khari M., stock (2018).
  • http://dx.doi.org/10.1007/s12530-018-9247-7. set decision making for trending analysis, Evolv.
  • Syst., [18] Jha S., Son L.H., Kumar R., Priyadarshini I., Smarandache F., Long H.V., (2019). Neutrosophic image segmentation with dice coefficients, Measurement, 134, 762–772.
  • Ju D., Ju Y., Wang A., (2018). Multiple attribute group decision making based on Maclaurin symmet- ric mean operator under single-valued neutrosophic interval 2-tuple linguistic environment, J. Intell. Fuzzy Syst., 34(4) 2579–2595.
  • Kahraman C., Otay I., (eds.), (2019). Fuzzy multi criteria decision making using neutrosophic sets, Studies in Fuzziness and Soft Computing, 369, Springer Nature Switzerland AG.
  • Karaaslan F., (2018). Gaussian single-valued neutrosophic numbers and its application in multi- attribute decision making, Neutrosophic Sets and Systems, 22, 101–117.
  • Liang R.X., Wang J.Q., Li L., (2018). Multi-criteria group decision-making method based on interde- pendent inputs of single-valued trapezoidal neutrosophic information, Neural Comput. and Applic., 30, 241-260.
  • Liu P., Zhang X.H., (2018). Some maclaurin symmetric mean operators for single-valued trapezoidal neutrosophic numbers and their applications to group decision making, Int. J. Fuzzy Syst., 20(1) 45-61.
  • Mohamed M., Zhou Y.Q., Baset M.A., Smarandache F., (2017). A critical path problem using trian- gular neutrosophic number, Neutrosophic Operational Research I, section X, Pons Brussels.
  • Liu P., Chu Y., Li Y., Chen Y., (2014). Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making, International Journal of Fuzzy Systems, 16(2) 242–255.
  • Liu P., Liu X., (2018). The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group decision making, Int. J. Mach. Learn. Cybern., 9(2) 347–358. [27] Nguyen G.N., Ashour A.S., Dey N., (2017). A survey of the state-of-the-arts on neutrosophic sets in biomedical diagnoses, Int. J. Mach. Learn. Cybern., 10(1) 1–13.
  • Porchelvi R.S., Umamaheswari M., (2018). A Study on intuitionistic fuzzy multi objective LPP into LCP with neutrosophic triangular numbers approach, Journal of Applied Science and Computations, 5(9) 570–576.
  • Pramanik S., Mallick R., (2018). VIKOR based MAGDM strategy with trapezoidal neutrosophic numbers, Neutrosophic Sets and Systems, 22, 118–129.
  • Peng J.J., Wang J.Q., Zhang H.Y., Chen X.H., (2014). An outranking approach for multi-criteria decision-making problemswith simplified neutrosophic sets, Applied Soft Computing, 25, 336-346.
  • Smarandache F., (1998). Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth, USA 105p.
  • S¸ahin R., Yiˇgider M., (2014). A Multi-criteria neutrosophic group decision making metod based TOP- SIS for supplier selection, http://arxiv.org/abs/1412.5077.
  • Tuan T.M., Chuan P.M., Ali M., Ngan T.T., Mittal M., Son L.H., (2018). Fuzzy and neutrosophic modeling for link prediction in social networks, Evolv. Syst., http://dx.doi.org/10.1007/s12530-018- 9251-y.
  • Wang H., Smarandache F., Zhang Y.Q., Sunderraman R., (2010). Single valued neutrosophic sets, Multisp. Multistruct, 4, 410–413.
  • Wang J.Q., Yang Y., Li L., (2018). Multi-criteria decision-making method based on single valued neutrosophic linguistic Maclaurin symmetric mean operators, Neural Comput. Appl., 30(5) 1529– 1547.
  • Wu X., Qian J., Peng J.J., Xue C.C., (2018). A multi-criteria group decision making method with possibility degree and power aggregation operators of single trapezoidal neutrosophic numbers, Sym- metry, 10(590) 1–21.
  • Ye J., (2017). Some weighted aggregation operators of trapezoidal neutrosophic numbers and their multiple attribute decision making method, Informatica, 28(2) 387–402.
  • Ye J., (2014). A multicriteria decision-making method using aggregation operators for simplified neu- trosophic sets, Journal of Intelligent and Fuzzy Systems, 26, 2459–2466.
  • Zadeh L.A., (1965). Fuzzy Sets, Information and Control, 8, 338–353.
There are 37 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

I. Deli This is me

Publication Date January 1, 2020
Published in Issue Year 2020 Volume: 10 Issue: 1

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