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Cognitive Computation

, Volume 8, Issue 4, pp 649–669 | Cite as

A Neutrosophic Normal Cloud and Its Application in Decision-Making

  • Hong-yu Zhang
  • Pu Ji
  • Jian-qiang Wang
  • Xiao-hong Chen
Article

Abstract

In this study, a neutrosophic normal cloud (NNC) and several other related concepts, including a backward cloud generator, two aggregated operators, and an NNC distance measurement, are proposed. Using these concepts, we also construct a multi-criteria group decision-making approach to single-value neutrosophic environments. In the proposed approach, all evaluations provided by decision-makers are aggregated via the backward cloud generator. The resulting NNC reflects the distribution of customer evaluations. An empirical example and a comparative study are also provided in order to illustrate and validate the proposed approach. The results of an empirical case study using data from Tmall.com indicate that the proposed approach could be effectively applied to practical problems.

Keywords

Neutrosophic normal cloud (NNC) Backward cloud generator Aggregation operator Multi-criteria group decision-making 

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 71501192 and 71210003) and the Research Funds for the Scholars of Central South University (No. 2014JSJJ043). The authors also would like to express appreciation to the anonymous reviewers and editors for their helpful comments that improved the paper. Moreover, the authors thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.

Compliance with Ethical Standards

Conflict of Interest

Hong-yu Zhang, Pu Ji, Jian-qiang Wang and Xiao-hong Chen declares that they have no conflict of interest.

Informed Consent

All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2008 (5). Additional informed consent was obtained from all patients for which identifying information is included in this article.

Human and Animals Rights

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

References

  1. 1.
    Akusok A, Miche Y, Hegedus J, Nian R, Lendasse A. A two-stage methodology using K-NN and false-positive minimizing ELM for nominal data classification. Cogn Comput. 2014;6:432–45.CrossRefGoogle Scholar
  2. 2.
    Czubenko M, Kowalczuk Z, Ordys A. Autonomous driver based on an intelligent system of decision-making. Cogn Comput. 2015;7:569–81.CrossRefGoogle Scholar
  3. 3.
    Yang J, Gong L, Tang Y, Yan J, He H, Zhang L, Li G. An improved SVM-based cognitive diagnosis algorithm for operation states of distribution grid. Cogn Comput. 2015;7:582–93.CrossRefGoogle Scholar
  4. 4.
    Ye J. Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses. Artif Intell Med. 2015;63:171–9.CrossRefPubMedGoogle Scholar
  5. 5.
    Mak DK. A fuzzy probabilistic method for medical diagnosis. J Med Syst. 2015. doi: 10.1007/s10916-10015-10203-10919.PubMedGoogle Scholar
  6. 6.
    Meng F, Wang C, Chen X. Linguistic interval hesitant fuzzy sets and their application in decision making. Cogn Comput. 2015. doi: 10.1007/s12559-12015-19340-12551.Google Scholar
  7. 7.
    Meng F, Chen X. Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput. 2015;7:445–63.CrossRefGoogle Scholar
  8. 8.
    Gómez D, Yáñez J, Guada C, Rodríguez JT, Montero J, Zarrazola E. Fuzzy image segmentation based upon hierarchical clustering. Knowl-Based Syst. 2015;87:26–37.CrossRefGoogle Scholar
  9. 9.
    Zarinbal M, Zarandi MHF, Turksen IB, Izadi M. A type-2 fuzzy image processing expert system for diagnosing brain tumors. J Med Syst. 2015. doi: 10.1007/s10916-10015-10311-10916.PubMedGoogle Scholar
  10. 10.
    Zenebe A, Zhou L, Norcio AF. User preferences discovery using fuzzy models. Fuzzy Sets Syst. 2010;161:3044–63.CrossRefGoogle Scholar
  11. 11.
    Le HS, Thong NT. Intuitionistic fuzzy recommender systems: an effective tool for medical diagnosis. Knowl-Based Syst. 2014;74:133–50.Google Scholar
  12. 12.
    Vahidov R, Ji F. A diversity-based method for infrequent purchase decision support in e-commerce. Electron Commer Res Appl. 2005;4:143–58.CrossRefGoogle Scholar
  13. 13.
    Zadeh LA. Fuzzy sets. Inf Control. 1965;8:338–56.CrossRefGoogle Scholar
  14. 14.
    Zadeh LA. Probability measures of fuzzy events. J Math Anal Appl. 1968;23:421–7.CrossRefGoogle Scholar
  15. 15.
    Turksen IB. Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst. 1986;20:191–210.CrossRefGoogle Scholar
  16. 16.
    Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986;20:87–96.CrossRefGoogle Scholar
  17. 17.
    Atanassov K, Gargov G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 1989;31:343–9.CrossRefGoogle Scholar
  18. 18.
    Torra V. Hesitant fuzzy sets. Int J Intell Syst. 2010;25:529–39.Google Scholar
  19. 19.
    Peng JJ, Wang JQ, Wu XH. Novel multi-criteria decision-making approaches based on hesitant fuzzy sets and prospect theory. Int J Inf Tech Decis. 2016. doi: 10.1142/S0219622016500152.
  20. 20.
    Chaira T. Intuitionistic fuzzy set approach for color region extraction. J Sci Ind Res. 2010;69:426–32.Google Scholar
  21. 21.
    Joshi BP, Kumar S. Fuzzy time series model based on intuitionistic fuzzy sets for empirical research in stock market. Int J Appl Evol Comput. 2012;3:71–84.CrossRefGoogle Scholar
  22. 22.
    Qi X, Liang C, Zhang J. Generalized cross-entropy based group decision making with unknown expert and attribute weights under interval-valued intuitionistic fuzzy environment. Comput Ind Eng. 2015;79:52–64.CrossRefGoogle Scholar
  23. 23.
    Dragoni M, Tettamanzi AG, Costa da Pereira C. Propagating and aggregating fuzzy polarities for concept-level sentiment analysis. Cogn Comput. 2015;7:186–97.CrossRefGoogle Scholar
  24. 24.
    Hu J, Zhang X, Chen X, Liu Y. Hesitant fuzzy information measures and their applications in multi-criteria decision making. Int J Syst Sci. 2016;47:62–76.CrossRefGoogle Scholar
  25. 25.
    Tian Z-P, Wang J, Wang J-Q, Chen X-H. Multi-criteria decision-making approach based on gray linguistic weighted Bonferroni mean operator. Int Trans Oper Res. 2015. doi: 10.1111/itor.12220.Google Scholar
  26. 26.
    Ye J. Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. Int J Gen Syst. 2013;42:386–94.CrossRefGoogle Scholar
  27. 27.
    Smarandache F. A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, probability. Rehoboth: American Research Press; 1999. p. 1–141.Google Scholar
  28. 28.
    Smarandache F. Neutrosophy: neutrosophic probability, set, and logic. Rehoboth: American Research Press; 1998. Google Scholar
  29. 29.
    Rivieccio U. Neutrosophic logics: prospects and problems. Fuzzy Sets Syst. 2008;159:1860–8.CrossRefGoogle Scholar
  30. 30.
    Majumdar P, Samanta SK. On similarity and entropy of neutrosophic sets. J Intell Fuzzy Syst. 2014;26:1245–52.Google Scholar
  31. 31.
    Wang HB, Smarandache F, Zhang YQ, Sunderraman R. Single valued neutrosophic sets. Rev Air Force Acad. 2010;17:10–4.Google Scholar
  32. 32.
    Ye J. Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. J Intell Fuzzy Syst. 2014;26:165–72.Google Scholar
  33. 33.
    Guo YH, Cheng HD. New neutrosophic approach to image segmentation. Pattern Recogn. 2009;42:587–95.CrossRefGoogle Scholar
  34. 34.
    Zhang M, Zhang L, Cheng HD. A neutrosophic approach to image segmentation based on watershed method. Sig Process. 2010;90:1510–7.CrossRefGoogle Scholar
  35. 35.
    Guo Y, Şengür A. A novel image segmentation algorithm based on neutrosophic similarity clustering. Appl Soft Comput. 2014;25:391–8.CrossRefGoogle Scholar
  36. 36.
    Ansari A, Biswas R, Aggarwal S. Proposal for applicability of neutrosophic set theory in medical AI. Int J Comput Appl. 2011;27:5–11.Google Scholar
  37. 37.
    Guo Y, Sengur A. NCM: neutrosophic c-means clustering algorithm. Pattern Recogn. 2015;48:2710–24.CrossRefGoogle Scholar
  38. 38.
    Şahin R, Yiğider M, A multi-criteria neutrosophic group decision making method based TOPSIS for supplier selection. arXiv preprint arXiv:1412.5077 (2014).
  39. 39.
    Tian ZP, Wang J, Zhang HY, Chen XH, Wang JQ. Simplified neutrosophic linguistic normalized weighted Bonferroni mean operator and its application to multi-criteria decision-making problems. FILOMAT. 2015. doi: 10.2298/FIL1508576F.Google Scholar
  40. 40.
    Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH. Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci. 2015. doi: 10.1080/00207721.00202014.00994050.Google Scholar
  41. 41.
    Peng JJ, Wang JQ, Zhang HY, Chen XH. An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput. 2014;25:336–46.CrossRefGoogle Scholar
  42. 42.
    Ye J. Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl Math Model. 2014;38:1170–5.CrossRefGoogle Scholar
  43. 43.
    Sahin M, Alkhazaleh S, Ulucay V. Neutrosophic soft expert sets. Appl Math. 2015;06:116–27.CrossRefGoogle Scholar
  44. 44.
    Şahin R, Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment. arXiv preprint arXiv:1412.5202 (2014).
  45. 45.
    Liu P, Chu Y, Li Y, Chen Y. Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making. Int J Fuzzy Syst. 2014;16:242–55.Google Scholar
  46. 46.
    Zhang HY, Wang JQ, Chen XH. An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets. Neural Comput Appl. 2015. doi: 10.1007/s00521-00015-01882-00523.Google Scholar
  47. 47.
    Zhang H-Y, Ji P, Wang J-Q, Chen X-H. An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making problems. Int J Comput Intell Syst. 2015;8:1027–43.CrossRefGoogle Scholar
  48. 48.
    Yang XJ, Yan LL, Peng H, Gao XD. Encoding words into cloud models from interval-valued data via fuzzy statistics and membership function fitting. Knowl-Based Syst. 2014;55:114–24.CrossRefGoogle Scholar
  49. 49.
    Li DY, Meng HJ, Shi XM. Membership clouds and membership cloud generators. J Comput Res Dev. 1995;32:15–20.Google Scholar
  50. 50.
    Li DY, Liu CY, Du Y, Han X. Artificial intelligence with uncertainty. J Softw. 2004;15:1583–94.Google Scholar
  51. 51.
    Wang GY, Xu CL, Li DY. Generic normal cloud model. Inf Sci. 2014;280:1–15.CrossRefGoogle Scholar
  52. 52.
    Li DY, Han JW, Shi XM, Chan MC. Knowledge representation and discovery based on linguistic atoms. Knowl-Based Syst. 1998;10:431–40.CrossRefGoogle Scholar
  53. 53.
    Yang CH, Li DY. Planar model and its application in prediction. Chin J Comput. 1998;21:961–9.Google Scholar
  54. 54.
    Jiang JB, Liang JR, Jiang W, Gu ZP. Application of trapezium-cloud model in conception division and conception exaltation. Comput Eng Des. 2008;29:1235–40.Google Scholar
  55. 55.
    Wang JQ, Yang WE. Multiple criteria group decision making method based on intuitionistic normal cloud by Monte Carlo simulation. Syst Eng Theory Pract. 2013;33:2859–65.Google Scholar
  56. 56.
    Zhang FZ, Fan Y, Li D. Intelligent control based on membership cloud generators. Acta Aeronaut Astronaut Sin-ser. 1999;20:89–92.Google Scholar
  57. 57.
    Li DY. The cloud control method and balancing patterns of triple link inverted pendulum systems. Chin Eng Sci. 1999;1:41–6.Google Scholar
  58. 58.
    Zhang X, Zhao L, Zang J, Fan H, Cheng L. Flatness intelligent control based on TS cloud inference neural network. Trans Iron Steel Inst Japan. 2014;54:2608–17.CrossRefGoogle Scholar
  59. 59.
    Li DY, Cheung D, Shi XM, Ng V. Uncertainty reasoning based on cloud models in controllers. Comput Math Appl. 1998;35:99–123.CrossRefGoogle Scholar
  60. 60.
    Chen H, Li B, Qualitative rules mining and reasoning based on cloud model. In: 2nd international conference on software engineering and data mining (SEDM), 2010, IEEE; 2010, p. 523–526.Google Scholar
  61. 61.
    Qin K, Xu K, Liu FL, Li DY. Image segmentation based on histogram analysis utilizing the cloud model. Comput Math Appl. 2011;62:2824–33.CrossRefGoogle Scholar
  62. 62.
    Wu T, Xiao J, Qin K, Chen Y. Cloud model-based method for range-constrained thresholding. Comput Electr Eng. 2015;42:33–48.CrossRefGoogle Scholar
  63. 63.
    Yang WE, Qiang WJ, Ma CQ, Wang XF. Hesitant linguistic multiple criteria decision making method based on cloud generating algorithm. Control Decis. 2015;30:371–4.Google Scholar
  64. 64.
    Wang JQ, Liu T. Uncertain linguistic multi-criteria group decision-making approach based on integrated cloud. Control Decis. 2012;27:1185–90.Google Scholar
  65. 65.
    Wang JQ, Peng JJ, Zhang HY, Liu T, Chen XH. An uncertain linguistic multi-criteria group decision-making method based on a cloud model. Group Decis Negot. 2015;24:171–92.CrossRefGoogle Scholar
  66. 66.
    Wang JQ, Peng L, Zhang HY, Chen XH. Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information. Inf Sci. 2014;274:177–91.CrossRefGoogle Scholar
  67. 67.
    Wang JQ, Wang P, Wang J, Zhang HY, Chen XH. Atanassov’s interval-valued intuitionistic linguistic multi-criteria group decision-making method based on trapezium cloud model. IEEE Trans Fuzzy Syst. 2014;23:542–54.CrossRefGoogle Scholar
  68. 68.
    Lu HJ, Wang Y, Li DY, Liu CY. The application of backward cloud in qualitative evaluation. Chin J Comput. 2003;26:1009–14.Google Scholar
  69. 69.
    Liu CY, Feng M, Dai XJ, Li DY. A new algorithm of backward cloud. Acta Simulata Syst Sin. 2004;16:2417–20.Google Scholar
  70. 70.
    Luo ZQ, Zhang GW. A new algorithm of backward normal one-variate cloud. J Front Comput Sci Technol. 2007;1:234–40.Google Scholar
  71. 71.
    Yu SW, Shi ZK. New algorithm of backward cloud based on normal interval number. Syst Eng-Theory Pract. 2011;31:2021–6.Google Scholar
  72. 72.
    Biswas P, Pramanik S, Giri BC. TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Comput Appl. 2015. doi: 10.1007/s00521-00015-01891-00522.Google Scholar
  73. 73.
    Ye J. Multiple attribute group decision-making method with completely unknown weights based on similarity measures under single valued neutrosophic environment. J Intell Fuzzy Syst. 2014;27:2927–35.Google Scholar
  74. 74.
    Sun M. How does the variance of product ratings matter? Manag Sci. 2012;58:696–707.CrossRefGoogle Scholar
  75. 75.
    Liu PD, Wang YM. Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean. Neural Comput Appl. 2014;25:2001–10.CrossRefGoogle Scholar
  76. 76.
    Li DY, Liu CY. Study on the universality of the normal cloud model. Eng Sci. 2004;6:28–34.Google Scholar
  77. 77.
    Zhang GW, Li DY, Li P, Kang JC, Chen GS. A collaborative filtering recommendation algorithm based on cloud model. J Softw. 2007;18:2403–11.CrossRefGoogle Scholar
  78. 78.
    Hdioud F, Frikh B, Ouhbi B, Multi-criteria recommender systems based on multi-attribute decision making. In: Proceedings of international conference on information integration and web-based applications & services, ACM; 2013, p. 203–211.Google Scholar
  79. 79.
    Xia Y, Cambria E, Hussain A, Zhao H. Word polarity disambiguation using Bayesian model and opinion-level features. Cogn Comput. 2015;7:369–80.CrossRefGoogle Scholar
  80. 80.
    Agarwal B, Poria S, Mittal N, Gelbukh A, Hussain A. Concept-level sentiment analysis with dependency-based semantic parsing: a novel approach. Cogn Comput. 2015. doi: 10.1007/s12559-12014-19316-12556.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Hong-yu Zhang
    • 1
  • Pu Ji
    • 1
  • Jian-qiang Wang
    • 1
  • Xiao-hong Chen
    • 1
  1. 1.School of BusinessCentral South UniversityChangshaChina

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