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Projection models for multiple attribute decision making with picture fuzzy information

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Abstract

In this paper, we investigate the picture fuzzy multiple attribute decision making problems where the attribute values are expressed in picture fuzzy numbers. We introduce some notions, such as picture fuzzy ideal point, the modules of picture fuzzy numbers. We also introduce the cosine of the included angle between the attribute value vectors of each alternative and the picture fuzzy ideal point. Then we establish the projection model to measure the similarity degrees between each alternative and the picture fuzzy ideal point. Based on the projection models, we can rank the given alternatives and then select the most desirable one. Finally, we illustrate the developed projection models with a numerical example for potential evaluation of emerging technology commercialization.

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References

  1. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MATH  Google Scholar 

  2. Atanassov K (1989) More on intuitionistic fuzzy sets. Fuzzy Sets Syst 33:37–46

    Article  MathSciNet  MATH  Google Scholar 

  3. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–356

    Article  MATH  Google Scholar 

  4. Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349

    Article  MathSciNet  MATH  Google Scholar 

  5. Atanassov K (1994) Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 64(2):159–174

    Article  MathSciNet  MATH  Google Scholar 

  6. Bustince H, Burillo P (1995) Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 74(2):237–244

    Article  MathSciNet  MATH  Google Scholar 

  7. Atanassov K, Pasi G, Yager R (2005) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36(14):859–868

    Article  MathSciNet  MATH  Google Scholar 

  8. Ronald R, Yager A (2015) Note on measuring fuzziness for intuitionistic and interval-valued fuzzy sets. Int J Gen Syst 44(7–8):889–901

    MathSciNet  MATH  Google Scholar 

  9. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187

    Article  Google Scholar 

  10. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433

    Article  MathSciNet  MATH  Google Scholar 

  11. Wei Guiwu, Merigó José M (2012) Methods for strategic decision making problems with immediate probabilities in intuitionistic fuzzy setting. Sci Iran E 19(6):1936–1946

    Article  Google Scholar 

  12. Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl-Based Syst 24:749–760

    Article  Google Scholar 

  13. Zhang Xiaolu, Zeshui Xu (2015) Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making. Appl Soft Comput 26:42–56

    Article  Google Scholar 

  14. Jian Wu, Chiclana Francisco (2014) A risk attitudinal ranking method for interval-valued intuitionistic fuzzy numbers based on novel attitudinal expected score and accuracy functions. Appl Soft Comput 22:272–286

    Article  Google Scholar 

  15. Liu HW, Wang GJ (2007) Multi-criteria decision-making methods based on intuitionistic fuzzy sets. Eur J Oper Res 179:220–233

    Article  MATH  Google Scholar 

  16. Chen TY (2011) Bivariate models of optimism and pessimism in multi-criteria decision-making based on intuitionistic fuzzy sets. Inf Sci 181:2139–2165

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen TY, Li CH (2010) Determining objective weights with intuitionistic fuzzy entropy measures: a comparative analysis. Inf Sci 180:4207–4222

    Article  Google Scholar 

  18. Chen Ting-Yu (2014) Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis. Inf Sci 261:149–169

    Article  MathSciNet  MATH  Google Scholar 

  19. Chen Ting-Yu (2016) An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis. Appl Soft Comput 42:390–409

    Article  Google Scholar 

  20. Chen Shyi-Ming, Chiou Chu-Han (2015) Multiattribute decision making based on interval-valued intuitionistic fuzzy sets, PSO techniques, and evidential reasoning methodology. IEEE Trans Fuzzy Syst 23(6):1905–1916

    Article  Google Scholar 

  21. Wang Jian-qiang, Wang Pei, Wang Jing, Zhang Hong-yu, Chen Xiao-hong (2015) Atanassov’s interval-valued intuitionistic linguistic multicriteria group decision-making method based on the trapezium cloud model. IEEE Trans Fuzzy Syst 23(3):542–554

    Article  Google Scholar 

  22. Garg Harish (2016) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999

    Article  Google Scholar 

  23. Li DF (2011) Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information. Appl Soft Comput 11:3402–3418

    Article  Google Scholar 

  24. Li Deng-Feng, Ren Hai-Ping (2015) Multi-attribute decision making method considering the amount and reliability of intuitionistic fuzzy information. J Intell Fuzzy Syst 28(4):1877–1883

    MathSciNet  Google Scholar 

  25. Wan Shu-Ping, Li Deng-Feng (2014) Atanassov’s intuitionistic fuzzy programming method for heterogeneous multiattribute group decision making with Atanassov’s intuitionistic fuzzy truth degrees. IEEE Trans Fuzzy Syst 22(2):300–312

    Article  MathSciNet  Google Scholar 

  26. Wan Shu-Ping, Li Deng-Feng (2015) Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees. Inf Sci 325:484–503

    Article  MathSciNet  Google Scholar 

  27. Wei GW (2008) Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting. Knowl-Based Syst 21:833–836

    Article  Google Scholar 

  28. Wei GW (2009) Some geometric aggregation functions and their application to dynamic multiple attribute decision making in intuitionistic fuzzy setting. Int J Uncertain Fuzziness Knowl-Based Syst 17:179–196

    Article  MathSciNet  MATH  Google Scholar 

  29. Wei GW (2010) GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting. Knowl-Based Syst 23:243–247

    Article  Google Scholar 

  30. Wei GW (2010) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10:423–431

    Article  Google Scholar 

  31. Wei GW, Wang HJ, Lin R (2011) Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowl Inf Syst 26:337–349

    Article  Google Scholar 

  32. Ye J (2009) Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Syst Appl 36(2):899–6902

    Article  Google Scholar 

  33. Ye J (2010) Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets. Appl Math Model 34:3864–3870

    Article  MathSciNet  MATH  Google Scholar 

  34. Wei GW, Zhao XF (2012) Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making. Expert Syst Appl 39(2):2026–2034

    Article  Google Scholar 

  35. Wei GW (2011) Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making. Expert Syst Appl 38:11671–11677

    Article  Google Scholar 

  36. Park JH, Park Y, Young CK, Xue T (2009) Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems. Math Comput Model 50:1279–1293

    Article  MathSciNet  MATH  Google Scholar 

  37. Cuong BC (2013) Picture fuzzy sets—first results (Part 1). In: Seminar on neuro-fuzzy systems with applications. Institute of Mathematics, Hanoi (preprint)

  38. Singh P (2014) Correlation coefficients for picture fuzzy sets. J Intell Fuzzy Syst 27:2857–2868

    Google Scholar 

  39. Son L (2015) DPFCM: a novel distributed picture fuzzy clustering method on picture fuzzy sets. Expert Syst Appl 2:51–66

    Article  Google Scholar 

  40. Thong PH, Son LH (2015) A new approach to multi-variables fuzzy forecasting using picture fuzzy clustering and picture fuzzy rules interpolation method. In: 6th International Conference on Knowledge and Systems Engineering, Hanoi, Vietnam, pp 679–690

  41. Thong NT (2015) HIFCF: an effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis. Expert Syst Appl 42(7):3682–3701

    Article  Google Scholar 

  42. Zeshui Xu, Hui Hu (2010) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak 9(2):267–280

    Article  MATH  Google Scholar 

  43. Zeshui Xu, Cai Xiaoqiang (2008) Intuitionistic fuzzy information aggregation: theory and applications. Science Press, Copenhagen

    MATH  Google Scholar 

Download references

Acknowledgments

The work was supported by the National Natural Science Foundation of China under Grant No. 61174149 and 71571128 and the Humanities and Social Sciences Foundation of Ministry of Education of the People’s Republic of China (No. 15XJA630006, 15YJCZH138) and the construction plan of scientific research innovation team for colleges and universities in Sichuan Province (15TD0004).

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Authors and Affiliations

  1. School of Business, Sichuan Normal University, Chengdu, 610101, People’s Republic of China

    Guiwu Wei

  2. Communications Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Guiwu Wei & Fuad E. Alsaadi

  3. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    Tasawar Hayat

  4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Tasawar Hayat & Ahmed Alsaedi

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  1. Guiwu Wei
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  2. Fuad E. Alsaadi
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  3. Tasawar Hayat
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  4. Ahmed Alsaedi
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Correspondence to Guiwu Wei.

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Wei, G., Alsaadi, F.E., Hayat, T. et al. Projection models for multiple attribute decision making with picture fuzzy information. Int. J. Mach. Learn. & Cyber. 9, 713–719 (2018). https://doi.org/10.1007/s13042-016-0604-1

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  • DOI: https://doi.org/10.1007/s13042-016-0604-1

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