Advertisement

Soft Computing

, Volume 22, Issue 15, pp 4941–4958 | Cite as

A novel interval-valued neutrosophic AHP with cosine similarity measure

Focus
  • 182 Downloads

Abstract

Neutrosophic Logic (Smarandache in Neutrosophy neutrosophic probability: set, and logic, American Research Press, Rehoboth, 1998) has been applied to many multicriteria decision-making methods such as Technique for Order Preference by Similarity to an Ideal Solution, Višekriterijumsko kompromisno rangiranje Resenje, and Evaluation based on Distance from Average Solution. Interval-valued neutrosophic sets are subclass of neutrosophic sets. Interval numbers can be used for their truth-membership, indeterminacy-membership, and falsity-membership degrees. The angle between the vector representations of two neutrosophic sets is defined cosine similarity measure. In this paper, we introduce a new Analytic Hierarchy Process (AHP) method with interval-valued neutrosophic sets. We also propose an interval-valued neutrosophic AHP (IVN-AHP) based on cosine similarity measures. The proposed method with cosine similarity provides an objective scoring procedure for pairwise comparison matrices under neutrosophic uncertainty. Finally, an application is given in energy alternative selection to illustrate the developed approaches.

Keywords

Neutrosophic sets AHP Multi criteria decision making Interval-valued neutrosophic sets Cosine similarity measures 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Abdel-Basset M, Mohamed, Mai, Sangaiah AK (2017) Neutrosophic Ahp-Delphi group decision making model based on trapezoidal neutrosophic numbers. J Ambient Intell Humanized Comput 1–17Google Scholar
  2. Abdullah L, Najib L (2016) Integration of interval Type-2 fuzzy sets and analytic hierarchy process: Implication to computational procedures. In: AIP Conference ProceedingsGoogle Scholar
  3. Atanassov KT (1983) Intuitionistic fuzzy sets. VII ITKR’s Session, SofiaMATHGoogle Scholar
  4. Baušys R, Juodagalvienė B (2017) Garage location selection for residential house by WASPAS-SVNS method. J Civil Eng Manag 23(3):421–429CrossRefGoogle Scholar
  5. Bausys R, Zavadskas E (2015) Multicriteria decision making approach by Vikor under interval neutrosophic set environment. Econ Comput Econ Cybern Stud Res 49(4):33–48Google Scholar
  6. Bausys R, Zavadskas EK, Kaklauskas A (2015) Application of neutrosophic set to multicriteria decision making by COPRAS. Econ Comput Econ Cybern Stud Res 49(2):1–15Google Scholar
  7. Bhowmik M, Pal M (2010) Intuitionistic neutrosophic set relations and some of its properties. J Inf Comput Sci 5(3):183–192Google Scholar
  8. Biswas P, Pramanik S, Giri BC (2014) A new methodology for neutrosophic multi-attribute decisionmaking with unknown weight information. Neutr Sets Syst 3:42–50Google Scholar
  9. Biswas P, Pramanik S, Giri BC (2016) TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Comput Appl 27(3):727–737CrossRefGoogle Scholar
  10. Broumi S, Smarandache F (2014) Cosine similarity measure of interval valued neutrosophic sets. Neutrosophic Sets Syst 5:15–20Google Scholar
  11. Broumi S, Talea M, Smarandache F, Bakali A (2017) Decision-making method based on the interval valued neutrosophic graph. In: FTC 2016-Proceedings of Future Technologies Conference, vol. 44Google Scholar
  12. Buyukozkan G, Feyzioglu O, Gocer F (2016) Evaluation of hospital web services using intuitionistic fuzzy AHP and intuitionistic fuzzy VIKOR. IEEE Int Conf Ind Eng Eng Manag 2016:607–611Google Scholar
  13. Candan SS, Sapino ML (2010) Data management for multimedia retrieval. Cambridge University Press, Cambridge.  https://doi.org/10.1017/CBO9780511781636 CrossRefMATHGoogle Scholar
  14. Cebi S, Kahraman C, Karasan A, Ilbahar E (2018) A novel approach to risk assessment for occupational health and safety using pythagorean fuzzy AHP & fuzzy inference system. Safety (Accepted)Google Scholar
  15. Deepika M, Kannan ASK (2016) Global supplier selection using intuitionistic fuzzy analytic hierarchy process. Int Conf Electr, Electron, Optim Tech, ICEEOT 2016:2390Google Scholar
  16. Deli I, Subas Y (2017) Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision making problems. J Intell Fuzzy Syst 32(1):291–301CrossRefMATHGoogle Scholar
  17. Deli I, Ali M, Smarandache F (2015) Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In: International Conference on Advanced Mechatronic Systems, ICAMechS: 249Google Scholar
  18. Deli I, Subas Y, Smarandache F, Ali M (2016) Interval valued bipolar fuzzy weighted neutrosophic sets and their application. In: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2016:2460Google Scholar
  19. Elhassouny A, Smarandache F (2016) Neutrosophic-simplified-TOPSIS multi-criteria decision-making using combined simplified-TOPSIS method and neutrosophics. In: IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2016:2468Google Scholar
  20. Erdogan M, Kaya I (2016) Evaluating alternative-fuel busses for public transportation in Istanbul using interval type-2 fuzzy AHP and TOPSIS. J Multi Valued Log Soft Comput 26(6):625–642Google Scholar
  21. Garg H, Nancy (2017) Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment. Appl Intell 1–15Google Scholar
  22. Hu J, Pan L, Chen X (2017) An interval neutrosophic projection-based VIKOR method for selecting doctors. Cognit Comput 1–16Google Scholar
  23. Huang H (2016) New distance measure of single-valued neutrosophic sets and its application. Int J Intell Syst 31(10):1021–1032CrossRefGoogle Scholar
  24. Ji P, Zhang H (2016) A subsethood measure with the hausdorff distance for interval neutrosophic sets and its relations with similarity and entropy measures. In: Proceedings of the 28th Chinese Control and Decision Conference, CCDC 2016:4152-4157Google Scholar
  25. Ji P, Zhang H, Wang J (2016) A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection. Neural Comput Appl : 1–14Google Scholar
  26. Ji P, Zhang H, Wang J (2017) Fuzzy decision-making framework for treatment selection based on the combined QUALIFLEX-TODIM method. Int J Syst Sci 48(14):3072–3086CrossRefMATHGoogle Scholar
  27. Kahraman C, Bolturk E, Onar SC, Oztaysi B, Goztepe K (2016) Multi-attribute warehouse location selection in humanitarian logistics using hesitant fuzzy AHP. Int J Anal Hierarchy Process 8(2):271–298Google Scholar
  28. Kahraman C, Öztayşi B, Uçal Sari I, Turanoğlu E (2014) Fuzzy analytic hierarchy process with interval type-2 fuzzy sets. Knowl-Based Syst 59:48–57CrossRefGoogle Scholar
  29. Karaaslan F (2017) Multicriteria decision-making method based on similarity measures under single-valued neutrosophic refined and interval neutrosophic refined environments. Int J Intell Syst.  https://doi.org/10.1002/int.21906 Google Scholar
  30. Karasan A, Kahraman C (2018) Interval-valued neutrosophic extension of EDAS method. Adv Intell Syst Comput 642:343–357Google Scholar
  31. Kharal A (2014) A neutrosophic multi-criteria decision making method. N Math Nat Comput 10(2):143–162MathSciNetCrossRefMATHGoogle Scholar
  32. Li Y, Wang Y, Liu P (2016) Multiple attribute group decision-making methods based on trapezoidal fuzzy two-dimension linguistic power generalized aggregation operators. Soft Comput 20(7):2689–2704CrossRefMATHGoogle Scholar
  33. Liang R, Wang J, Zhang H (2017) Evaluation of e-commerce websites: An integrated approach under a single-valued trapezoidal neutrosophic environment. Knowl-Based Syst 135:44–59CrossRefGoogle Scholar
  34. Liang R, Wang J, Li L (2016) Multi-criteria group decision-making method based on interdependent inputs of single-valued trapezoidal neutrosophic information. Neural Comput Appl 1–20Google Scholar
  35. Liang R, Wang J, Zhang H (2017) A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information. Neural Comput Appl 1–16Google Scholar
  36. Liu P, Wang Y (2014) Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean. Neural Comput Appl 25(7–8):2001–2010CrossRefGoogle Scholar
  37. Liu P, Zhang L (2017) Multiple criteria decision making method based on neutrosophic hesitant fuzzy heronian mean aggregation operators. J Intell Fuzzy Syst 32(1):303–319CrossRefMATHGoogle Scholar
  38. Liu P, Zhang L, Liu X, Wang P (2016) Multi-valued neutrosophic number bonferroni mean operators with their applications in multiple attribute group decision making. Int J Inf Technol Decis Making 15(5):1181–1210CrossRefGoogle Scholar
  39. Liu PD (2016) The aggregation operators based on archimedean t-Conorm and t-Norm for single-valued neutrosophic numbers and their application to decision making. Int J Fuzzy SystGoogle Scholar
  40. Liu C (2016) Interval neutrosophic fuzzy stochastic multi-criteria decision-making methods based on MYCIN certainty factor and prospect theory. Revista Tecnica de la Facultad de Ingenieria Universidad del Zulia 39(10):52–58Google Scholar
  41. Liu P, Tang G (2016) Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and choquet integral. Cognit Comput 8(6):1036–1056CrossRefGoogle Scholar
  42. Ma H, Hu Z, Li K, Zhang H (2016) Toward trustworthy cloud service selection: a time-aware approach using interval neutrosophic set. J Parallel Distrib Comput 96:75–94CrossRefGoogle Scholar
  43. Ma H, Zhu H, Hu Z, Li K, Tang W (2017) Time-aware trustworthiness ranking prediction for cloud services using interval neutrosophic set and ELECTRE. Knowl-Based Syst 138:27–45CrossRefGoogle Scholar
  44. Ma Y, Wang J, Wang J, Wu X (2017) An interval neutrosophic linguistic multi-criteria group decision-making method and its application in selecting medical treatment options. Neural Comput Appl 28(9):2745–2765CrossRefGoogle Scholar
  45. Nǎdǎban S, Dzitac S (2016) Neutrosophic TOPSIS: a general view. In: 6th International Conference on Computers Communications and Control, ICCCC 2016: 250Google Scholar
  46. Otay I, Kahraman C (2018) Six sigma project selection using interval neutrosophic TOPSIS. Adv Intell Syst Comput 643:83–93Google Scholar
  47. Oztaysi B, Cevik Onar S, Kahraman C (2018) Prioritization of business analytics projects using interval type-2 fuzzy AHP. Adv Intell Syst Comput 643:106–117Google Scholar
  48. Oztaysi B, Onar SC, Bolturk E, Kahraman C (2015) Hesitant fuzzy analytic hierarchy process. In: IEEE International Conference on Fuzzy Systems: pp 1–7Google Scholar
  49. Peng X, Dai J (2016) Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function. Neural Comput Appl 1–16Google Scholar
  50. Peng H, Zhang H, Wang J (2016) Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems. Neural Comput Appl 1–21Google Scholar
  51. Peng J, Wang J, Wu X (2016) An extension of the ELECTRE approach with multi-valued neutrosophic information. Neural Comput Appl 1–12Google Scholar
  52. Peng J, Wang J, Yang W (2017) A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems. Int J Syst Sci 48(2):425–435MathSciNetCrossRefMATHGoogle Scholar
  53. Peng J, Wang J, Wang J, Zhang H, Chen X (2016) Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci 47(10):2342–2358CrossRefMATHGoogle Scholar
  54. Peng J, Wang Yang L, Qian J (2017) A novel multi-criteria group decision-making approach using simplified neutrosophic information. Int J Uncertain Quantif 7(4):355–376CrossRefGoogle Scholar
  55. Peng J, Wang J, Zhang H, Chen X (2014) An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput J 25:336–346CrossRefGoogle Scholar
  56. Peng J, Wang J, Wu X, Wang J, Chen X (2015) Multi-valued neutrosophic sets and power aggregation operators with their applications in multi-criteria group decision-making problems. Int J Comput Intell Syst 8(2):345–363CrossRefGoogle Scholar
  57. Radwan NM, Senousy MB, Riad AEDM (2016) Neutrosophic AHP multi criteria decision making method applied on the selection of learning management system. Int J Adv Comput Technol (IJACT) 8(5):95–105Google Scholar
  58. Ren S (2017) Multicriteria decision-making method under a single valued neutrosophic environment. Int J Intell Inf Technol 13(4):23–37CrossRefGoogle Scholar
  59. Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15:234–281MathSciNetCrossRefMATHGoogle Scholar
  60. Sahin R, Yigider M (2016) A multi-criteria neutrosophic group decision making method based TOPSIS for supplier selection. Appl Math Inf Sci 10(5):1843–1852CrossRefGoogle Scholar
  61. Sahin R, Kucuk A (2015) Subsethood measure for single valued neutrosophic sets. J Intell Fuzzy Syst 29(2):525–530CrossRefMATHGoogle Scholar
  62. Sahin R, Liu P (2017) Possibility-induced simplified neutrosophic aggregation operators and their application to multi-criteria group decision-making. J Exp Theor Artif Intell 29(4):769–785CrossRefGoogle Scholar
  63. Sahin R, Liu P (2017) Some approaches to multi criteria decision making based on exponential operations of simplified neutrosophic numbers. J Intell Fuzzy Syst 32(3):2083–2099CrossRefMATHGoogle Scholar
  64. Sahin R. (2017) An approach to neutrosophic graph theory with applications. Soft Comput 1–13Google Scholar
  65. Sahin R (2017) Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural Comput Appl 28(5):1177–1187CrossRefGoogle Scholar
  66. Senvar OA (2018) Systematic customer oriented approach based on hesitant fuzzy AHP for performance assessments of service departments. Adv Intell Syst Comput 643:289–300Google Scholar
  67. Smarandache F (1998) Neutrosophy neutrosophic probability: set, and logic, American Research Press, Rehoboth, pp 12–20Google Scholar
  68. Stanujkic D, Zavadskas EK, Smarandache F, Brauers WKM, Karabasevic D (2017) A neutrosophic extension of the MULTIMOORA method. Informatica (Netherlands) 28(1):181–192CrossRefGoogle Scholar
  69. Sun H, Sun M (2016) Simplified neutrosophic weighted average operators and their application to e-commerce. ICIC Express Lett 10(1):27–33Google Scholar
  70. Sun H, Yang H, Wu J, Ouyang Y (2015) Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making. J Intell Fuzzy Syst 28(6):2443–2455MathSciNetCrossRefMATHGoogle Scholar
  71. Tan J, Low KY, Sulaiman NMN, Tan RR, Promentilla MAB (2015) Fuzzy analytical hierarchy process (AHP) for multi-criteria selection in drying and harvesting process of microalgae system. Chem Eng Trans 45:829–834Google Scholar
  72. Tian Z, Wang J, Wang J, Zhang H (2017) Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development. Group Decis Negot 26(3):597–627CrossRefGoogle Scholar
  73. Tian Z, Wang J, Zhang H, Chen X, Wang J (2016) Simplified neutrosophic linguistic normalized weighted bonferroni mean operator and its application to multi-criteria decision-making problems. Filomat 30(12):3339–3360CrossRefMATHGoogle Scholar
  74. Tian Z, Zhang H, Wang J, Wang J, Chen X (2016) Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. Int J Syst Sci 47(15):3598–3608CrossRefMATHGoogle Scholar
  75. Tooranloo HS, Iranpour A (2017) Supplier selection and evaluation using interval-valued intuitionistic fuzzy AHP method. Int J Procure Manag 10(105):539–554CrossRefGoogle Scholar
  76. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539MATHGoogle Scholar
  77. Ulucay V, Deli I, Sahin M (2016) Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making. Neural Comput Appl 1–10Google Scholar
  78. Wang J, Li X (2015) TODIM method with multi-valued neutrosophic sets. Kongzhi yu Juece/Control and Decision 30(6):1139–1142MathSciNetGoogle Scholar
  79. Wang J, Yang Y, Li L (2016) Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators. Neural Comput Appl 1–19Google Scholar
  80. Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistruct 4:410–413MATHGoogle Scholar
  81. Wang N, Zhang H (2017) Probability multivalued linguistic neutrosophic sets for multi-criteria group decision-making. Int J Uncertain Quantif 7(3):207–228CrossRefGoogle Scholar
  82. Wang Z (2016) Optimized GCA based on interval neutrosophic sets for urban flood control and disaster reduction program evaluation. Revista Tecnica de la Facultad de Ingenieria Universidad del Zulia 39(11):151–158Google Scholar
  83. Wu J, H-b Huang, Q-w Cao (2013) Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems. Appl Math Model 37:9898–9906MathSciNetCrossRefGoogle Scholar
  84. Wu X, Wang J, Peng J, Chen X (2016) Cross-entropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision-making problems. Int J Fuzzy Syst 18(6):1104–1116CrossRefGoogle Scholar
  85. Ye J (2015) Trapezoidal neutrosophic set and its application to multiple attribute decision-making. Neural Comput Appl 26(5):1157–1166CrossRefGoogle Scholar
  86. Ye J (2017) Multiple attribute decision-making method using correlation coefficients of normal neutrosophic sets. Symmetry 9:80CrossRefGoogle Scholar
  87. Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst 42(4):386–394MathSciNetCrossRefMATHGoogle Scholar
  88. Ye J (2014) A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26(5):2459–2466MathSciNetMATHGoogle Scholar
  89. Ye J (2014) Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. J Intell Fuzzy Syst 26(1):165–172MATHGoogle Scholar
  90. Ye J (2014) Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int J Fuzzy Syst 16(2):204–211Google Scholar
  91. Ye J (2015) Improved cross entropy measures of single valued neutrosophic sets and interval neutrosophic sets and their multicriteria decision making methods. Cybern Inf Technol 15(4):13–26MathSciNetGoogle Scholar
  92. Zavadskas EK, Bausys R, Kaklauskas A, Ubarte I, Kuzminske A, Gudiene N (2017) Sustainable market valuation of buildings by the single-valued neutrosophic MAMVA method. Appl Soft Comput J 57:74–87CrossRefGoogle Scholar
  93. Zavadskas EK, Baušys R, Lazauskas M (2015) Sustainable assessment of alternative sites for the construction of a waste incineration plant by applying WASPAS method with single-valued neutrosophic set. Sustainability (Switzerland) 7(12):15923–15936CrossRefGoogle Scholar
  94. Zavadskas EK, Baušys R, Stanujkic D, Magdalinovic-Kalinovic M (2016) Selection of lead-zinc flotation circuit design by applying WASPAS method with single-valued neutrosophic set. Acta Montanistica Slovaca 21(2):85–92Google Scholar
  95. Zhang H, Wang J, Chen X (2016) An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets. Neural Comput Appl 27(3):615–627CrossRefGoogle Scholar
  96. Zhang H, Ji P, Wang J, Chen X (2015) An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making problems. Int J Computat Intell Syst 8(6):1027–1043CrossRefGoogle Scholar
  97. Zhang H, Ji P, Wang J, Chen X (2016) A neutrosophic normal cloud and its application in decision-making. Cognit Comput 8(4):649–669CrossRefGoogle Scholar
  98. Zhang HY, Wang JQ, Chen XH (2014) Interval neutrosophic sets and their application in multicriteria decision-making problems. Sci World J 2014:15Google Scholar
  99. Zhang M, Liu P, Shi L (2016) An extended multiple attribute group decision-making TODIM method based on the neutrosophic numbers. J Intell Fuzzy Syst 30(3):1773–1781CrossRefMATHGoogle Scholar
  100. Zhu B, Xu Z, Zhang R, Hong M (2016) Hesitant analytic hierarchy process. Eur J Oper Res 250(2):602–614MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Industrial Engineering DepartmentIstanbul Technical UniversityMaçkaTurkey

Personalised recommendations