Soft Computing

, Volume 23, Issue 1, pp 211–225 | Cite as

Novel single-valued neutrosophic decision-making approaches based on prospect theory and their applications in physician selection

  • Ruixiao Sun
  • Junhua HuEmail author
  • Xiaohong Chen
Methodologies and Application


The selection of a proper physician in a network environment is an important event for most patients, and single-valued neutrosophic sets (SVNSs) can depict the uncertainty and fuzziness of online evaluation information for physicians. In addition, the psychological behavior of patients is a significant factor that influences physician selection. This paper proposes two multi-attribute decision-making methods based on prospect theory (PT) with single-valued neutrosophic information and utilizes them to solve physician selection problems. Firstly, a new distance measure for SVNSs is developed to overcome the drawbacks of existing distance measures. Secondly, we develop extended TODIM and extended ELECTRE III approaches based on PT and new distance. We utilize the two proposed approaches to handle a physician selection case that uses data from Parameter sensitivity and comparative analyses of the proposed methods are presented. Findings indicate that the two proposed methods can yield reasonable and credible solutions. With complementary advantages, the two methods are flexible for patients with various behavior preferences to select and use.


Single-valued neutrosophic sets Distance measure Prospect theory TODIM approach ELECTRE III approach Multi-attribute decision-making Physician selection 



The authors would like to thank the editors and the anonymous reviewers for their useful comments and valuable suggestions that helped us improve this paper. This work was supported by the National Natural Science Foundation of China (Nos. 71371196 and 71210003).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Human and animals rights

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


  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Set Syst 20(1):87–96zbMATHGoogle Scholar
  2. Benayoun R, Roy B, Sussman N (1966) Manual de reference du programme electre. Note De Synthese et Formaton, 25th edn. Direction Scientifique SEMA, ParisGoogle Scholar
  3. Bornstein BH, Marcus D, Cassidy W (2000) Choosing a doctor: an exploratory study of factors influencing patients’ choice of a primary care doctor. J Eval Clin Pract 6(3):255–262Google Scholar
  4. Broumi S, Deli I (2015) Correlation measure for neutrosophic refined sets and its application in medical diagnosis. J Macromol Sci Part B 54(10):1248–1258zbMATHGoogle Scholar
  5. Broumi S, Smarandache F (2014) New distance and similarity measures of interval neutrosophic sets. In: International conference on information fusion, pp 1–7Google Scholar
  6. Cheng SH, Chen SM, Lan TC (2016) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343:15–40MathSciNetzbMATHGoogle Scholar
  7. Deli I (2016) Refined neutrosophic sets and refined neutrosophic soft sets: theory and applications. In. IGI Global, pp 321–343Google Scholar
  8. Deli I, Şubaş Y (2016) A ranking method of single valued neutrosophic numbers and its applications to multi-attribute decision making problems. Int J Mach Learn Cybern 8(4):1309–1322Google Scholar
  9. Deli I, Şubaş Y (2017) Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision making problems. J Intell Fuzzy Syst 32(1):291–301zbMATHGoogle Scholar
  10. 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, pp 249–254Google Scholar
  11. Dias L, Clímaco J (2000) ELECTRE TRI for groups with imprecise information on parameter values. Group Decis Negot 9(5):355–377Google Scholar
  12. Emmert M, Meier F (2013) An analysis of online evaluations on a physician rating website: evidence from a german public reporting instrument. J Med Internet Res 15(8):324–327Google Scholar
  13. Emmert M, Meier F, Heider AK, Dürr C, Sander U (2014) What do patients say about their physicians? an analysis of 3000 narrative comments posted on a German physician rating website. Health Policy 118(1):66–73Google Scholar
  14. Fhkam YTWM, Lam KF (2010) How do patients choose their doctors for primary care in a free market? J Eval Clin Pract 16(6):1215–1220Google Scholar
  15. Figueira JR, Greco S, Ehrgott M (2005) Multiple criteria decision analysis: state of the art surveys. Kluwer, BostonzbMATHGoogle Scholar
  16. Gomes LFAM (1992) From modelling individual preferences to multicriteria ranking of discrete alternatives: a look at prospect theory and the additive difference model. Found Comput Decis Sci 17(3):171–184zbMATHGoogle Scholar
  17. Gomes LFAM, Lima MMPP (1992) TODIM: basic and application to multicriteria ranking of projects with environmental impacts. Found Comput Decis Sci 16(4):113–127zbMATHGoogle Scholar
  18. Gomes LFAM, Rangel LAD (2009) An application of the TODIM method to the multicriteria rental evaluation of residential properties. Eur J Oper Res 193(1):204–211zbMATHGoogle Scholar
  19. Harris KM (2003) How do patients choose physicians? Evidence from a national survey of enrollees in employment-related health plans. Health Serv Res 38(2):711–732Google Scholar
  20. Hu JH, Pan L, Chen XH (2017a) An interval neutrosophic projection-based VIKOR method for selecting doctors. Cogn Comput. Google Scholar
  21. Hu JH, Yang Y, Chen XH (2017b) A novel TODIM method-based three-way decision model for medical treatment selection. Int J Fuzzy Syst. Google Scholar
  22. Hu JH, Yang Y, Chen XH (2017c) Three-way linguistic group decisions model based on cloud for medical care product investment. J Intell Fuzzy Syst. Google Scholar
  23. Hu JH, Yang Y, Zhang XL, Chen XH (2017d) Similarity and entropy measures for hesitant fuzzy sets. Int Trans Oper Res. zbMATHGoogle Scholar
  24. Jiang YP, Liang X, Liang HM (2017) An I-TODIM method for multi-attribute decision making with interval numbers. Soft Comput 21(18):5489–5506zbMATHGoogle Scholar
  25. Kadry B, Chu LF, Kadry B, Gammas D, Macario A (2011) Analysis of 4999 online physician ratings indicates that most patients give physicians a favorable rating. J Med Internet Res 13(4):2854–2866Google Scholar
  26. Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision risk. Econom J Econom Soc 47(2):263–292zbMATHGoogle Scholar
  27. Kaya T, Kahraman C (2011) An integrated fuzzy AHP–ELECTRE methodology for environmental impact assessment. Expert Syst Appl 38(7):8553–8562Google Scholar
  28. Krohling RA, de Souza TTM (2012) Combining prospect theory and fuzzy numbers to multi-criteria decision making. Expert Syst Appl 39(13):11487–11493Google Scholar
  29. Lahdelma R, Salminen P (2009) Prospect theory and stochastic multicriteria acceptability analysis (SMAA). Omega Int J Manag Sci 37(5):961–971Google Scholar
  30. Liang RX, Wang JQ, Zhang HY (2017) A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information. Neural Comput Appl. Google Scholar
  31. 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):2001–2010Google Scholar
  32. Madupu DOCV (2009) How did you find your physician? An exploratory investigation into the types of information sources used to select physicians. Int J Pharm Healthc Mark 3(1):46–58Google Scholar
  33. Marzouk MM (2011) ELECTRE III model for value engineering applications. Autom Constr 20(5):596–600Google Scholar
  34. Peng JJ, Wang JQ, Zhang HY, Chen XH (2014) An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput 25:336–346Google Scholar
  35. Peng HG, Zhang HY, Wang JQ (2016a) Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems. Neural Comput Appl. Google Scholar
  36. Peng JJ, Wang JQ, Wu XH (2016b) Novel multi-criteria decision-making approaches based on hesitant fuzzy sets and prospect theory. Int J Inf Tech Decis 15(3):621–643Google Scholar
  37. Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH (2016c) Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci 47(10):2342–2358zbMATHGoogle Scholar
  38. Qin JD, Liu XW, Pedrycz W (2015) An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2 fuzzy environment. Knowl Based Syst 86(C):116–130Google Scholar
  39. Roy B (1977) Partial preference analysis and decision aid: the fuzzy outranking relation concept. In: Bell D, Keeney RL, Raiffa H (eds) Conflicting objectives in decisions. Wiley, New York, pp 40–75Google Scholar
  40. Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theory Decis 31(31):49–73MathSciNetGoogle Scholar
  41. Smarandache F (1999) A unifying field in logics. Neutrosophic: neturosophic probability, set, and logic. American Research Press, RehobothGoogle Scholar
  42. Stewart TJ (1996) Robustness of additive value function methods in MCDM. J Multi-Cri Decis Anal 5(4):301–309zbMATHGoogle Scholar
  43. Sun RX, Hu JH, Zhou JD, Chen XH (2017) A hesitant fuzzy linguistic projection-based MABAC method for patients’ prioritization. Int J Fuzzy Syst. Google Scholar
  44. Tian ZP, Wang J, Wang JQ, Zhang HY (2017a) Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development. Group Decis Negot 26(3):597–627Google Scholar
  45. Tian ZP, Wang JQ, Zhang HY (2017b) single-valued neutrosophic MCGDM with QFD for market segment evaluation and selection. J Intell Fuzzy Syst. Google Scholar
  46. Vahdani B, Hadipour H (2011) Extension of the ELECTRE method based on interval-valued fuzzy sets. Soft Comput 15(3):569–579Google Scholar
  47. Verhoef LM, Belt THVD, Engelen LJ, Schoonhoven L, Kool RB (2014) Social media and rating sites as tools to understanding quality of care: a scoping review. J Med Internet Res 16(2):e56Google Scholar
  48. Wang H, Smarandache F, Zhang Y, Sunderraman R (2010) Single valued neutrosophic set. Mulispace Multistruct 4:410–413zbMATHGoogle Scholar
  49. Wang JQ, Yang Y, Li L (2016) Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators. Neural Comput Appl. Google Scholar
  50. Wang J, Wang JQ, Tian ZP, Zhao DY (2017a) A multihesitant fuzzy linguistic multicriteria decision-making approach for logistics outsourcing with incomplete weight information. Int Trans Oper Res. zbMATHGoogle Scholar
  51. Wang JQ, Peng JJ, Zhang HY, Chen XH (2017b) Outranking approach for multi-criteria decision-making problems with hesitant interval-valued fuzzy sets. Soft Comput. Google Scholar
  52. Wang L, Zhang HY, Wang JQ (2017c) Frank choquet Bonferroni mean operators of bipolar neutrosophic sets and their application to multi-criteria decision-making problems. Int J Fuzzy Syst. Google Scholar
  53. Yang Y, Hu JH, An QX, Chen XH (2017a) Group decision making with multiplicative triangular hesitant fuzzy preference relations and cooperative games method. Int J Uncertain Quantif 7(3):271–284MathSciNetGoogle Scholar
  54. Yang Y, Hu JH, Sun RX, Chen XH (2017b) Medical tourism destinations prioritization using group decision making method with neutrosophic fuzzy preference relations. Sci Iran.
  55. Ye J (2013) Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst 42(4):386–394MathSciNetzbMATHGoogle Scholar
  56. Ye J (2014a) Clustering methods using distance-based similarity measures of single-valued neutrosophic sets. J Intell Syst 23(4):379–389Google Scholar
  57. Ye J (2014b) A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. J Intell Fuzzy Syst 26(5):2459–2466MathSciNetzbMATHGoogle Scholar
  58. Ye J (2014c) Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl Math Model 38(3):1170–1175MathSciNetzbMATHGoogle Scholar
  59. Yu SM, Wang J, Wang JQ (2016) An extended TODIM approach with intuitionistic linguistic numbers. Int Trans Oper Res. zbMATHGoogle Scholar
  60. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353zbMATHGoogle Scholar
  61. Zhang HY, Ji P, Wang JQ, Chen XH (2016) A neutrosophic normal cloud and its application in decision-making. Cogn Comput 8(4):649–669Google Scholar
  62. Zhang HY, Ji P, Wang JQ, Chen XH (2017) A novel decision support model for satisfactory restaurants utilizing social information: a case study of Tour Manag 59:281–297Google Scholar
  63. Zhou H, Wang JQ, Zhang HY (2017) Stochastic multicriteria decision-making approach based on SMAA-ELECTRE with extended gray numbers. Int Trans Oper Res. Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of BusinessCentral South UniversityChangshaChina

Personalised recommendations