Soft Computing

, Volume 22, Issue 3, pp 797–810 | Cite as

Multiple attribute decision-making method based on 2-dimension uncertain linguistic density generalized hybrid weighted averaging operator

Methodologies and Application

Abstract

Two-dimension uncertain linguistic variables (2DULVs) are very effective tools in describing the uncertain and fuzzy information, which are composed of I class linguistic information and II class linguistic information. Density aggregation operators not only consider the importance of all attributes but also take the importance of the density and the order positions of attributes into account, so they can more accurately deal with the fuzzy decision-making problems. In this paper, firstly, some basic theories, such as the definition, the expectation value and the operational laws of the 2DULVs, are briefly introduced. Then, some density aggregation operators based on 2DULVs are proposed, such as 2-dimension uncertain linguistic density arithmetic aggregation operators, 2-dimension uncertain linguistic density geometric aggregation operators and 2-dimension uncertain linguistic density generalized aggregation operators. Furthermore, we propose a multiple attribute decision-making method based on the 2-dimension uncertain linguistic density generalized hybrid weighted averaging operators. Finally, we use an illustrative example to demonstrate the practicality and effectiveness of the proposed method.

Keywords

2-dimension uncertain linguistic variables Density aggregation operator Multiple attribute decision making Generalized hybrid weighted averaging operator 

Notes

Acknowledgments

This paper is supported by the National Natural Science Foundation of China (Nos. 71471172 and 71271124), the Special Funds of Taishan Scholars Project of Shandong Province, National Soft Science Project of China (2014GXQ4D192), Shandong Provincial Social Science Planning Project (No. 15BGLJ06), the teaching reform research project of undergraduate colleges and Universities in Shandong province (2015Z057) and the science and technology project of colleges and universities in Shandong Province (J13LN19). The authors also would like to express appreciation to the anonymous reviewers and Editors for their very helpful comments that improved the paper.

Compliance with ethical standards

Conflicts of interest

Disclosure of potential conflicts of interest. We declare that we do have no commercial or associative interests that represent a conflict of interests in connection with this manuscript. There are no professional or other personal interests that can inappropriately influence our submitted work.

Human participants

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

References

  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRefMATHGoogle Scholar
  2. Atanassov KT, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 3:343–349MathSciNetCrossRefMATHGoogle Scholar
  3. Chu TC (2002) A fuzzy number interval arithmetic based fuzzy MCDM algorithm. Int J Fuzzy Syst 4:867–872MathSciNetGoogle Scholar
  4. Churchman CW, Ackoff RL, Arnoff EL (1957) Introduction to operations research. wiley, New YorkMATHGoogle Scholar
  5. Delgado M, Verdegay JL, Vila MA (1993) On aggregation operations of linguistic labels. Int J Intell Syst 8:351–370CrossRefMATHGoogle Scholar
  6. Herrera F, Verdegay JL (1993) Linguistic assessments in group decision. In: Proceedings of 1st European congress on fuzzy and intelligent technologies, Aachen, pp 941–948Google Scholar
  7. Hou F, Guo YJ (2008) Interval number density middle operator in uncertain multiple attribute decision making. J Northeast Univ Nat Sci 29(10):1509–1516MATHGoogle Scholar
  8. Li WW, Yi PT, Guo YJ (2012) Interval number density operator and its application. J Northeast Univ Nat Sci 33(7):1043–1046MathSciNetMATHGoogle Scholar
  9. Liu PD (2012) An approach to group decision making based on 2-dimension uncertain linguistic assessment information. Technol Econ Dev Econ 18(3):424–437CrossRefGoogle Scholar
  10. Liu PD, Liu ZM, Zhang X (2014) Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making. Appl Math Comput 230:570–586MathSciNetGoogle Scholar
  11. Liu PD, Teng F (2016) An extended TODIM method for multiple attribute group decision \(\backslash \) making based on 2-dimension uncertain linguistic variable. Complexity 21(5):20–30MathSciNetCrossRefGoogle Scholar
  12. Liu PD, Wang YM (2014) Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators. Appl Soft Comput 17:90–104CrossRefGoogle Scholar
  13. Liu PD, Yu XC (2013) Density aggregation operators based on the intuitionistic trapezoidal fuzzy numbers for multiple attribute decision making. Technol Econ Dev Econ 19:S454–S470CrossRefGoogle Scholar
  14. Liu PD, Yu XC (2014) 2-dimension uncertain linguistic power generalized weighted aggregation operator and its application for multiple attribute group decision making. Knowl Based Syst 57(1):69–80CrossRefGoogle Scholar
  15. Merigó JM, Casanovas M (2011a) Induced and uncertain heavy OWA operators. Comput Ind Eng 60(1):106–116CrossRefMATHGoogle Scholar
  16. Merigó JM, Casanovas M (2011b) The uncertain induced quasi-arithmetic OWA operator. Int J Intell Syst 26(1):1–24CrossRefMATHGoogle Scholar
  17. Merigó JM, Casanovas M, Martìnez L (2010) Linguistic aggregation operators for linguistic decision making based on the Dempster–Shafer theory of evidence. Int J Uncertain Fuzziness Knowl Based Syst 18(3):287–304MathSciNetCrossRefMATHGoogle Scholar
  18. Verma R (2015) Generalized Bonferroni mean operator for fuzzy number intuitionistic fuzzy sets and their application to multiattribute decision making. Int J Intell Syst 30(5):499–519CrossRefGoogle Scholar
  19. Verma R, Sharma BD (2013) Intuitionistic fuzzy Jensen-Rényi divergence: applications to multiple-attribute decision-making. Inform Int J Comput Inform 37(4):399–409Google Scholar
  20. Verma R, Sharma BD (2014a) Fuzzy generalized prioritized weighted average operator and its application to multiple attribute decision making. Int J Intell Syst 29:26–49CrossRefGoogle Scholar
  21. Verma R, Sharma BD (2014b) Trapezoid fuzzy linguistic prioritized weighted average operators and their application to multiple attribute group decision making. J Uncertain Anal Appl 2:1–19CrossRefGoogle Scholar
  22. Wang JQ (2008) Overview on fuzzy multi-criteria decision-making approach. Control Decis 23:601–606MathSciNetMATHGoogle Scholar
  23. Wang JQ, Li JJ (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Sci Technol Inf 33:8–9 (in Chinese)Google Scholar
  24. Xu ZS (2004a) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166:19–30MathSciNetCrossRefMATHGoogle Scholar
  25. Xu ZS (2004b) Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci 168:171–184CrossRefMATHGoogle Scholar
  26. Xu ZS (2004c) Uncertain multiple attribute decision making methods and application. Tsinghua University Press, BeijingGoogle Scholar
  27. Xu ZS (2005) Deviation measures of linguistic preference relations in group decision making. Omega 33:249–254CrossRefGoogle Scholar
  28. Xu ZS (2006) Induced uncertain linguistic OWA operators applied to group decision making. Inf Fusion 7:231–238CrossRefGoogle Scholar
  29. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):179–1187Google Scholar
  30. Xu ZS, Da QL (2003) Possibility degree method for ranking interval numbers and its application. J Syst Eng 18:67–70Google Scholar
  31. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433MathSciNetCrossRefMATHGoogle Scholar
  32. Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18(1):183–190CrossRefMATHGoogle Scholar
  33. Yi PT, Guo YJ, Zhang DN (2007) Density weighted averaging middle operator and application in multiple attribute decision making. Control Decis 22:515–524MATHGoogle Scholar
  34. Yi PT, Li WW, Guo YJ (2012) Two-tuple linguistic density operator and its application in multiple attribute decision making. Control Decis 27:757–760MathSciNetGoogle Scholar
  35. Yu XH, Xu ZS, Liu SS, Chen Q (2012) Multi-criteria decision making with 2-dimension linguistic aggregation techniques. Int J Intell Syst 27:539–562CrossRefGoogle Scholar
  36. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefMATHGoogle Scholar
  37. Zadeh LA (1975) The concept of a linguistic variable and its applications to approximate reasoning. Inf Sci 8:199–249MathSciNetCrossRefMATHGoogle Scholar
  38. Zhang X, Liu PD (2010) Method for aggregating triangular intuitionistic fuzzy information and its application to decision making. Technol Econ Dev Econ 16:280–290CrossRefGoogle Scholar
  39. Zhao H, Xu ZS, Ni MF, Liu SS (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30Google Scholar
  40. Zhou LG, Chen HY (2012) A generalization of the power aggregation operators for linguistic environment and its application in group decision making. Knowl Based Syst 26:216–224CrossRefGoogle Scholar
  41. Zhu WD, Zhou GZ, Yang SL (2009) An approach to group decision making based on 2-dimension linguistic assessment information. Syst Eng 27:113–118Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Management Science and EngineeringShandong University of Finance and EconomicsJinanChina

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