Skip to main content
SpringerLink
Log in

A survey of type-2 fuzzy aggregation and application for multiple criteria decision making

  • Original Paper
  • Published:
Journal of Data, Information and Management Aims and scope Submit manuscript

Abstract

Type-2 fuzzy sets (T2FSs) exhibit evident merits when it comes to representing the complex and high uncertainty, which has been encountered in fuzzy optimization and multiple criteria decision making (MCDM) problems. Since T2FSs theory was proposed by Zadeh in 1975, then a series of theories and methods were investigated by more scholars. Type-2 fuzzy aggregation operators, contributing to the fundamental information fusion theory, have been paid more attention and applied to different areas during the last two decades. In this paper, a survey of type-2 fuzzy aggregation and application for MCDM is carried out. We first review some basic knowledge including definitions, operations, type reduction and ranking methods of T2FSs. Then the definitions and properties of some main aggregation operators are introduced. Furthermore, some application categories under type-2 fuzzy environment are given. Finally, we identify some existing shortcomings and point at future research directions on this topic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Beliakov G (2003) How to build aggregation operators from data. Int J Intell Syst 18(8):903–923

    Article  MATH  Google Scholar 

  • Eriz M (2007) Aggregation functions: a guide for practitioners. Springer, Berlin Heidelberg

    Google Scholar 

  • Calvo T, Beliakov G (2010) Aggregation functions based on penalties. Fuzzy Sets Syst 161(10):1420–1436

    Article  MathSciNet  MATH  Google Scholar 

  • Mardani A, Nilashi M, Zavadskas EK, Awang SR, Zare H, Jamal NM (2018) Decision making methods based on fuzzy aggregation operators: three decades review from 1986 to 2017. Int J Inf Tech Dec Making 17(02):391–466

    Article  Google Scholar 

  • Qin JD (2017) Interval type-2 fuzzy Hamy Mean operators and their application in multiple criteria decision making. Gran Comput 2(7):1–21

    Google Scholar 

  • Ma X, Wu P, Zhou L, Chen H, Zheng T, Ge J (2016) Approaches based on interval type-2 fuzzy aggregation operators for multiple attribute group decision making. Inter J Fuzzy Syst 18(4):697–715

    Article  MathSciNet  Google Scholar 

  • Zhang Z (2018) Trapezoidal interval type-2 fuzzy aggregation operators and their application to multiple attribute group decision making. Neural Comput Appl 29(4):1039–1054

    Article  Google Scholar 

  • Qin JD, Liu XW (2014) Frank aggregation operators for triangular interval type-2 fuzzy set and its application in multiple attribute group decision making. J Appl Math 2014:1–24

    Google Scholar 

  • Zadeh LA (1975a) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199–249

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1975b) The concept of a linguistic variable and its application to approximate reasoning-ii. Inf Sci 8(4):301–357

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1975c) The concept of a linguistic variable and its application to approximate reason-III. Inf Sci 8(3):43–80

    Article  MATH  Google Scholar 

  • Karnik NN, Mendel JM (2001) Centroid of a type-2 fuzzy set. Inf Sci 132(1):195–220

    Article  MathSciNet  MATH  Google Scholar 

  • Liu X, Mendel JM (2011) Connect Karnik-Mendel algorithms to root-finding for computing the centroid of an interval type-2 fuzzy set. IEEE Trans Fuzzy Syst 19(4):652–665

    Article  Google Scholar 

  • Wu D, Mendel JM (2007a) Uncertainty measures for interval type-2 fuzzy sets. Inf Sci 177(23):5378–5393

    Article  MathSciNet  MATH  Google Scholar 

  • Chen T (2012) Multiple criteria group decision-making with generalized interval-valued fuzzy numbers based on signed distances and incomplete weights. Appl Math Model 36(7):3029–3052

    Article  MathSciNet  MATH  Google Scholar 

  • Sang X, Liu X (2016) Possibility mean and variation coefficient based ranking methods for type-1 fuzzy numbers and interval type-2 fuzzy numbers. J Intel Fuzzy Syst 30(4):2157–2168

    Article  MATH  Google Scholar 

  • Mendel JM, John RIB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127

    Article  Google Scholar 

  • Mendel JM, John RI, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14(6):808–821

    Article  Google Scholar 

  • Wu D, Mendel JM (2007b) Aggregation using the linguistic weighted average and interval type-2 fuzzy sets. IEEE Trans Fuzzy Syst 15(6):1145–1161

    Article  Google Scholar 

  • Wu T, Liu X (2016) An interval type-2 fuzzy clustering solution for large-scale multiple-criteria group decision-making problems. Knowl-Based Syst 114:118–127

    Article  Google Scholar 

  • Kundu P, Kar S, Maiti M (2017) A fuzzy multi-criteria group decision making based on ranking interval type-2 fuzzy variables and an application to transportation mode selection problem. Soft Comput 21(11):3051–3062

    Article  MATH  Google Scholar 

  • Qin JD, Liu XW, Pedrycz W (2017) An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment. Eur J Oper Res 258(2):626–638

    Article  MathSciNet  MATH  Google Scholar 

  • John R, Hagras Hani, Castillo O (2018) Type-2 fuzzy logic and systems. doi: https://doi.org/10.1007/978-3-319- 72892-6_1

  • Zhou S, Chiclana F, John RI, Garibaldi JM (2008) Type-2 OWA operators - aggregating type-2 fuzzy sets in soft decision making. IEEE international conference on fuzzy systems

  • Zhou S, John RI, Chiclana F, Garibaldi JM (2010) On aggregating uncertain information by type-2 OWA operators for soft decision making. Int J Intel Syst 25(6)

  • Wang J, Yu S, Wang J, Chen Q, Zhang H, Chen X (2015) An interval type-2 fuzzy number based approach for multi-criteria group decision-making problems. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 23(04):565–588

    Article  MathSciNet  MATH  Google Scholar 

  • Liu X, Tao Z, Chen H, Zhou L (2017) A new interval-valued 2-tuple linguistic Bonferroni mean operator and its application to multiattribute group decision making. Int J Fuzzy Syst 19(1):86–108

    Article  MathSciNet  Google Scholar 

  • Gou X, Xu Z, Liao H (2017) Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information. Soft Comput 21(21):6515–6529

    Article  MATH  Google Scholar 

  • Gong Y, Hu N, Zhang J, Liu G, Deng J (2015) Multi-attribute group decision making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers. Comput Ind Eng 81(C):167–176

    Article  Google Scholar 

  • Wu Q, Wang F, Zhou L, Chen H (2017) Method of multiple attribute group decision making based on 2-dimension interval type-2 fuzzy aggregation operators with multi-granularity linguistic information. Int. J. Fuzzy Syst. 19(6):1880–1903

    Article  MathSciNet  Google Scholar 

  • Havens TC, Anderson DT, Keller JM (2010) A fuzzy Choquet integral with an interval type-2 fuzzy number-valued integrand, IEEE International Conference on Fuzzy Systems 1–8

  • Bustince H, Galar M, Bedregal B, Kolesarova A, Mesiar R (2013) A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy set applications. IEEE Trans Fuzzy Syst 21(6):1150–1162

    Article  Google Scholar 

  • Lee L, Chen S (2008) A new method for fuzzy multiple attributes group decision-making based on the arithmetic operations of interval type-2 fuzzy sets. Proceedings of the seventh international conference on machine learning and cybernetics 12–15

  • Andelkovic M, Saletic DZ (2012) A novel approach for generalizing weighted averages for trapezoidal interval type-2 fuzzy sets. IEEE Jubilee International symposium on intelligent systems & informatics

  • Chen S, Lee L (2010) Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert Syst Appl 37(1):824–833

    Article  Google Scholar 

  • Wang W, Liu X, Qin Y (2012) Multi-attribute group decision making models under interval type-2 fuzzy environment. Knowl-Based Syst 30:121–128

    Article  Google Scholar 

  • Li J, John R, Coupland S, Kendall G (2018) On Nie-tan operator and type-reduction of interval type-2 fuzzy sets. IEEE Trans Fuzzy Syst 26(2):1036–1039

    Article  Google Scholar 

  • Mo H, Wang FY, Zhou M, Li R, Xiao Z (2014) Footprint of uncertainty for type-2 fuzzy sets. Inf Sci 272:96–110

    Article  MathSciNet  MATH  Google Scholar 

  • Mendel JM, Rajati MR, Sussner P (2016) On clarifying some definitions and notations used for type-2 fuzzy sets as well as some recommended changes. Inf Sci 340:337–345

    Article  MathSciNet  MATH  Google Scholar 

  • Mo H, Wang FY (2017) Representation for general type-2 fuzzy sets. International Conference on Information, Cybernetics and Computational Social Systems:389–394

  • Kahraman C, Öztayşi B, Uçal Sİ, Turanoğlu E (2014) Fuzzy analytic hierarchy process with interval type-2 fuzzy sets. Knowl-Based Syst 59:48–57

    Article  Google Scholar 

  • Liu XW, Mendel JM, Wu D (2012) Analytical solution methods for the fuzzy weighted average. Infor Sci 187:151–170

    Article  MathSciNet  MATH  Google Scholar 

  • Liu XW, Wang YM (2013) An analytical solution method for the generalized fuzzy weighted average problem. Int J Uncertainty Fuzziness Knowl Based Syst 21(3):455–480

    Article  MathSciNet  MATH  Google Scholar 

  • Dong WM, Wong FS (1987) Fuzzy weighted averages and implementation of the extension principle. Fuzzy Sets Syst 21(2):183–199

    Article  MathSciNet  MATH  Google Scholar 

  • Liou TS, Wang MJJ (1992) Fuzzy weighted average: an improved algorithm. Fuzzy Sets Syst 49:307–315

    Article  MathSciNet  MATH  Google Scholar 

  • Lee DH, Park D (1997) An efficient algorithm for fuzzy weighted average. Fuzzy Sets Syst 87:39–45

    Article  MathSciNet  Google Scholar 

  • Liu F, Mendel JM (2008) Aggregation using the fuzzy weighted average as computed by the Karnik–Mendel algorithms. IEEE Trans Fuzzy Syst 16(1):1–12

    Article  Google Scholar 

  • Wu D, Mendel JM (2009) Enhanced Karnik-Mendel algorithms. IEEE Trans Fuzzy Syst 17(4):923–934

    Article  Google Scholar 

  • Kao C, Liu ST (2001) Fractional programming approach to fuzzy weighted average. Fuzzy Sets Syst 120(3):435–444

    Article  MathSciNet  MATH  Google Scholar 

  • Yager RR, Kacprzyk J, Beliakov G (2011) Recent developments in the ordered weighted averaging operators: theory and practice, Springer

  • Mendel JM (2008) Tutorial on the uses of the interval type-2 fuzzy set’s wavy slice representation theorem. Fuzzy Information Processing Society, Nafips Meeting of the North American 1–6

  • Xu Z, Yager RR (2011) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man Cyber Part B 41(2):568–578

    Article  Google Scholar 

  • Zhu B, Xu ZS (2013) Hesitant fuzzy Bonferroni means for multi-criteria decision making. J Oper Res Soc 64(12):1831–1840

    Article  Google Scholar 

  • Zhu B, Xu Z, Xia M (2012) Hesitant fuzzy geometric Bonferroni means. Inf Sci 205:72–85

    Article  MathSciNet  MATH  Google Scholar 

  • Chen S, Kuo L (2017) Autocratic decision making using group recommendations based on interval type-2 fuzzy sets, enhanced Karnik–Mendel algorithms, and the ordered weighted aggregation operator. Info Sci 412-413:174–193

    Article  MathSciNet  Google Scholar 

  • Chen TY (2017) Multiple criteria decision analysis using prioritised interval type-2 fuzzy aggregation operators and its application to site selection. Technol Econ Dev Eco 23(1):1–21

    Article  Google Scholar 

  • 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 86:116–130

    Article  Google Scholar 

  • Abdullah L, Zulkifli N (2015) Integration of fuzzy AHP and interval type-2 fuzzy DEATEL: an application to human resource management. Expert Syst Appl 42(9):4397–4409

    Article  Google Scholar 

  • Yang MS, Lin DC (2009) On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. Comput Math Appl 57(6):896–907

    Article  MathSciNet  MATH  Google Scholar 

  • Own CM (2009) Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis. Appl Intell 31(3):283

    Article  Google Scholar 

  • Wagner C, Hagras H (2008) zSlices — towards bridging the gap between interval and general type-2 fuzzy logic. IEEE International Conference on Fuzzy Systems 489–497

  • Wagner C, Hagras H (2010) Toward general type-2 fuzzy logic systems based on zslices. IEEE Trans Fuzzy Syst 18(4):637–660

    Article  Google Scholar 

  • Bilgin A, Hagras H, Malibari A, Alhaddad MJ, Alghazzawi D (2013) Towards a linear general type-2 fuzzy logic based approach for computing with words. Soft Comput 17(12):2203–2222

    Article  Google Scholar 

  • Kumbasar T, Hagras H (2015) A self-tuning zslices-based general type-2 fuzzy pi controller. IEEE Trans Fuzzy Syst 23(4):991–1013

    Article  Google Scholar 

  • Pedrycz W, Song M (2012) Granular fuzzy models: a study in knowledge management in fuzzy modeling. Int J Approx Reason 53(7):1061–1079

    Article  MathSciNet  Google Scholar 

  • Yao J, Vasilakos AV, Pedrycz W (2013) Granular computing: perspectives and challenges. IEEE Trans Cybern 43(6):1977–1989

    Article  Google Scholar 

  • Cabrerizo FJ, Herrera-Viedma E, Pedrycz W (2013) A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts. Eur J Oper Res 230(3):624–633

    Article  MathSciNet  MATH  Google Scholar 

  • Ben TN (1998) Robust convex optimization. Math Oper Res 23(4):769–805

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

We thank Professor Witold Pedrycz very much for his valuable suggestions and comments. The work was supported by the National Natural Science Foundation of China (NSFC) under Project 71701158, MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Project No. 17YJC630114) and the Fundamental Research Funds for the Central Universities 2018IVB036.

Author information

Authors and Affiliations

  1. School of Management, Wuhan University of Technology, Wuhan, 430070, Hubei, China

    Jindong Qin

Authors
  1. Jindong Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jindong Qin.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qin, J. A survey of type-2 fuzzy aggregation and application for multiple criteria decision making. J. of Data, Inf. and Manag. 1, 17–32 (2019). https://doi.org/10.1007/s42488-019-00002-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42488-019-00002-1

Keywords

Search

Navigation