[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

A hesitant fuzzy linguistic set is an extension of both a linguistic term set and a hesitant fuzzy set. It combines a quantitative evaluation with a qualitative evaluation, which can describe the real preferences of decision makers and reflect their uncertainty, hesitancy and inconsistency. The focus of this paper is those multi-criteria decision-making (MCDM) problems in which the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). Having reviewed the relevant literature, the Hausdorff distance for HFLNs is provided and some linguistic scale functions are applied. Subsequently, two hesitant fuzzy linguistic MCDM methods are proposed, which are based on the proposed distance measure and the TOPSIS and TODIM methods. The first of these MCDM methods is based on complete rationality, whilst the second is based on bounded rationality. Finally, an illustrative example is provided to verify the proposed methods, which are then compared to the existing approaches.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Abo-Sinna MA, Amer AH, Ibrahim AS (2008) Extensions of TOPSIS for large scale multi-objective non-linear programming problems with block angular structure. Appl Math Model 32:292–302

    Article  MathSciNet  MATH  Google Scholar 

  • Beg I, Rashid T (2013) TOPSIS for hesitant fuzzy linguistic term sets. Int J Intell Syst 28:1162–1171

    Article  Google Scholar 

  • Bellman R, Zadeh LA (1990) Decision making in a fuzzy environment. Manag Sci 17:141–164

    Article  MathSciNet  MATH  Google Scholar 

  • Bordogna G, Fedrizzi M, Pasi G (1997) A linguistic modeling of consensus in group decision making based on OWA operators. IEEE Trans Syst Man Cybern Part A Syst Hum 27:126–133

    Article  Google Scholar 

  • Chen N, Xu ZS, Xia MM (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37:2197–2211

    Article  MathSciNet  Google Scholar 

  • Delgado M, Verdegay JL, Vila MA (1992) Linguistic decision making models. Int J Intell Syst 7:479–492

    Article  MATH  Google Scholar 

  • Doukas H, Karakosta C, Psarras J (2010) Computing with words to assess the sustainability of renewable energy options. Expert Syst Appl 37:5491–5497

    Article  Google Scholar 

  • Farhadinia B (2014) Distance and similarity measures for higher order hesitant fuzzy sets. Knowl Based Syst 55:43–48

    Article  Google Scholar 

  • Gomes LFAM, Lima MMPP (1992) TODIM: basics and application to multicriteria ranking of ranking of projects with environment impacts. Found Comput Decis Sci 16:113–127

    MATH  Google Scholar 

  • Gomes LFAM, Rangel LAD (2009) An application of the TODIM method to the multicriteria rental evaluation of residential properties. Eur J Oper Res 193:204–211

    Article  MATH  Google Scholar 

  • Gomes LFAM, Rangel LAD, Maranhão FJC (2009) Multicriteria analysis of natural gas destination in brazil: an application of the TODIM method. Math Comput Model 50:92–100

    Article  MATH  Google Scholar 

  • Herrera F, Herrera-Viedma E, Martínez L (2000) A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst 114:43–58

    Article  MATH  Google Scholar 

  • Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8:46–52

  • Herrera F, Martínez L (2001) The 2-tuple linguistic computational model. Advantages of its linguistic description, accuracy and consistency. Int J Uncertain Fuzziness Knowl Based Syst 9:33–48

  • Hu JH, Zhang Y, Chen XH, Liu YM (2013) Multi-criteria decision-making method based on possibility degree of interval type-2 fuzzy number. Knowl Based Syst 43:21–29

    Article  Google Scholar 

  • Hwang CL, Yoon KP (1981) Multiple attributes decision making: methods and applications. Springer-Verlag, New York

    Book  MATH  Google Scholar 

  • Jiang YP, Fan ZP, Ma J (2008) A method for group decision making with multi-granularity linguistic assessment information. Inf Sci 178:1098–1109

    Article  MATH  Google Scholar 

  • Joshi D, Kumar S (2014) Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making. Egypt Inform J. doi:10.1016/j.eij.2014.03.002

  • Huttenlocher DP, Klanderman GA, Rucklidge WJ (1993) Comparing images using the Hausdorff distance. IEEE Trans Pattern Anal Mach Intell 15:850–863

    Article  Google Scholar 

  • Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47:263–291

    Article  MATH  Google Scholar 

  • Lai YJ, Liu TY, Hwang CL (1996) TOPSIS for MODM. Eur J Oper Res 76:486–500

    Article  MATH  Google Scholar 

  • Lan JB, Sun Q, Chen QG, Wang ZG (2013) Group decision making based on induced uncertain linguistic OWA operators. Decis Support Syst 55:296–303

    Article  Google Scholar 

  • Lee LW, Chen SM (2013) Intelligent information and database systems., Fuzzy decision making based on hesitant fuzzy linguistic term setsSpringer, Berlin

    Google Scholar 

  • Li DF, Chen GH, Huang ZG (2010) Linear programming method for multiattribute group decision making using IF sets. Inf Sci 180:1591–1609

    Article  MathSciNet  MATH  Google Scholar 

  • Li LG, Peng DH (2014) Interval-valued hesitant fuzzy Hamacher synergetic weighted aggregation operators and their application to shale gas areas selection. Math Probl Eng. doi:10.1155/2014/181050

  • Li M, Jin L, Wang J (2014) A new MCDM method combining QFD with TOPSIS for knowledge management system selection from the user’s perspective in intuitionistic fuzzy environment. Appl Soft Comput 21:28–37

    Article  Google Scholar 

  • Lin R, Zhao XF, Wei GW (2014) Models for selecting an ERP system with hesitant fuzzy linguistic information. J Intell Fuzzy Syst 26:2155–2165

    MathSciNet  MATH  Google Scholar 

  • Liu PD (2013) Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making. Appl Math Model 37:2430–2444

    Article  MathSciNet  Google Scholar 

  • Liu QH (2014) An extended TOPSIS method for multiple attribute decision making problems with unknown weight based on 2-dimension uncertain linguistic variables. J Intell Fuzzy Syst. doi:10.3233/IFS-141186

  • Liu PD, Jin F (2012) Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Inf Sci 205:58–71

    Article  MathSciNet  MATH  Google Scholar 

  • Liu HB, Rodríguez RM (2014) A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making. Inf Sci 258:220–238

    Article  MathSciNet  MATH  Google Scholar 

  • Lourenzutti R, Krohling RA (2013) A study of TODIM in a intuitionistic fuzzy and random environment. Expert Syst Appl 40:6468–6495

  • Martínez L, Herrera F (2012) An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Inf Sci 207:1–18

    Article  MathSciNet  Google Scholar 

  • Martínez L, Ruan D, Herrera F (2010) Computing with words in decision support systems: an overview on models and applications. Int J Comput Intell Syst 3:382–395

    Article  Google Scholar 

  • Martínez L, Ruan D, Herrera F, Herrera-Viedma E, Wang PP (2009) Linguistic decision making: tools and applications. Inf Sci 179:2297–2298

    Article  Google Scholar 

  • Meng FY, Chen XH, Zhang Q (2014a) Multi-attribute decision analysis under a linguistic hesitant fuzzy environment. Inf Sci 267:287–305

  • Meng FY, Tan CQ, Zhang Q (2014b) An approach to multi-attribute group decision making under uncertain linguistic environment based on the Choquet aggregation operators. J Intell Fuzzy Syst 26:769–780

    MathSciNet  MATH  Google Scholar 

  • Nadler SB Jr (1978) Hyperspaces of sets. Marcel Dekker, New York

    MATH  Google Scholar 

  • Olson CF (1998) A probabilistic formulation for Hausdorff matching. In: 1998 IEEE computer society conference on computer vision and pattern recognition, pp 150–156

  • Pedrycz W (1990) Fuzzy sets in pattern recognition: methodology and methods. Pattern Recognit 23:121–146

    Article  Google Scholar 

  • Pedrycz W, Park BJ, Oh SK (2008) The design of granular classifiers: a study in the synergy of interval calculus and fuzzy sets in pattern recognition. Pattern Recognit 41:3720–3735

    Article  MATH  Google Scholar 

  • Peng DH, Gao CY, Gao ZF (2013) Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making. Appl Math Model 37:5837–5850

    Article  MathSciNet  MATH  Google Scholar 

  • Peng DH, Wang H (2014) Dynamic hesitant fuzzy aggregation operators in multi-period decision making. Kybernetes 43:715–736

    Article  MathSciNet  Google Scholar 

  • Peng DH, Wang TD, Gao CY, Wang H (2014) Continuous hesitant fuzzy aggregation operators and their application to decision making under interval-valued hesitant fuzzy setting. Sci World J. doi:10.1155/2014/897304

  • Peng JJ, Wang JQ, Zhou H, Chen XH (2015) A multi-criteria decision-making approach based on TODIM and Choquet integral within a multiset hesitant fuzzy environment. Appl Math Inf Sci 9:1–11

    Google Scholar 

  • Rodríguez RM, Martínez L (2013) An analysis of symbolic linguistic computing models in decision making. Int J Gen Syst 42:121–136

    Article  MathSciNet  MATH  Google Scholar 

  • Rodríguez RM, Martínez L, Herrera F (2013) A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inf Sci 241:28–42

    Article  MathSciNet  MATH  Google Scholar 

  • Rodríguez RM, Martínez L, Herrera F (2012a) Hesitant fuzzy linguistic term sets. Found Intell Syst (Springer, Berlin) 122:287–295

    Google Scholar 

  • Rodríguez RM, Martínez L, Herrera F (2012b) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20:109–119

    Article  Google Scholar 

  • Rodríguez RM, Martínez L, Torra V, Xu ZS, Herrera F (2014) Hesitant fuzzy sets: state of the art and future directions. Int J Intell Syst 29:495–524

    Article  Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539

    MATH  Google Scholar 

  • Wang JQ, Zhang Z (2009) Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. J Syst Eng Electron 20:321–326

    Google Scholar 

  • Wang JQ, Nie RR, Zhang HY, Chen XH (2013) Intuitionistic fuzzy multi-criteria decision-making method based on evidential reasoning. Appl Soft Comput 13:1823–1831

    Article  Google Scholar 

  • Wang JQ, Peng L, Zhang HY, Chen XH (2014a) Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information. Inf Sci 274:177–191

  • Wang JQ, Wang DD, Zhang HY, Chen XH (2014b) Multi-criteria outranking approach with hesitant fuzzy sets. OR Spectr 36:1001–1019

  • Wang JQ, Wang J, Chen QH, Zhang HY, Chen XH (2014c) An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. Inf Sci 280:338–351

  • Wang JQ, Wang P, Wang J, Zhang HY, Chen XH (2014d) Atanassov’s interval-valued intuitionistic linguistic multi-criteria group decision-making method based on trapezium cloud model. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2014.2317500

  • Wang JQ, Wu JT, Wang J, Zhang HY, Chen XH (2014e) Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf Sci 288:55–72

  • Wang XF, Wang JQ, Yang WE (2014f) Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators. J Intell Fuzzy Syst 26:115–125

  • Wang JQ, Peng JJ, Zhang HY, Liu T, Chen XH (2015a) An uncertain linguistic multi-criteria group decision-making method based on a cloud model. Group Decis Negot 24:171–192

  • Wang JQ, Wang DD, Zhang HY, Chen XH (2015b) Multi-criteria group decision making method based on interval 2-tuple linguistic information and Choquet integral aggregation operators. Soft Comput 19:389–405

  • Wei CP, Zhao N, Tang XJ (2014) Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst 22:575–585

    Article  Google Scholar 

  • Wei GW (2012) Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl Based Syst 31:176–182

    Article  Google Scholar 

  • Wei GW (2008) Two-tuple linguistic multiple attribute group decision making with incomplete attribute weight information. Syst Eng Electron 30:273–277

    MATH  Google Scholar 

  • Wei GW, Zhao XF, Lin R, Wang HJ (2013) Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making. Appl Math Model 37:5277–5285

    Article  MathSciNet  Google Scholar 

  • Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reas 52:395–407

    Article  MathSciNet  MATH  Google Scholar 

  • Xia MM, Xu ZS, Chen N (2013) Some hesitant fuzzy aggregation operators with their application in group decision making. Group Decis Negot 22:259–279

    Article  Google Scholar 

  • Xu YJ, Wang HM (2011) Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment. Appl Soft Comput 11:3988–3997

    Article  Google Scholar 

  • Xu ZS (2002) A method based on fuzzy linguistic assessments and linguistic ordered weighted averaging operator for multi-attribute group decision-making problems. Syst Eng 20:79–82

    Google Scholar 

  • Xu ZS (2004a) A method based on linguistic aggregation operators for group decision making with linguistic preference relation. Inf Sci 166:19–30

    Article  MATH  Google Scholar 

  • Xu ZS (2004b) Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci 168:171–184

    Article  MATH  Google Scholar 

  • Xu ZS (2008) Group decision making based on multiple types of linguistic preference relations. Inf Sci 178:452–467

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS, Xia MM (2011a) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128–2138

    Article  MathSciNet  MATH  Google Scholar 

  • Xu ZS, Xia MM (2011b) On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 26:410–425

    Article  MATH  Google Scholar 

  • Xu ZS, Zhang XL (2013) Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowl Based Syst 52:53–64

    Article  Google Scholar 

  • Yager RR (1997) Multiple objective decision-making using fuzzy sets. Int J Man Mach Stud 9:375–382

    Article  MATH  Google Scholar 

  • Yang WE, Wang JQ (2013) Multi-criteria semantic dominance: a linguistic decision aiding technique based on incomplete preference information. Eur J Oper Res 231:171–181

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1975a) Fuzzy logic and approximate reasoning. Synthese 30:407–428

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

  • Zhang HM (2013a) Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making. Appl Math Model 37:4269–4282

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang N, Wei GW (2013) Extension of VIKOR method for decision making problem based on hesitant fuzzy set. Appl Math Model 37:4938–4947

  • Zhang X (2013b) A grey relational projection method for multi-attribute decision making based on intuitionistic trapezoidal fuzzy number. Appl Math Model 37:3436–3477

  • Zhang XL, Xu ZS (2014) The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowl Based Syst 61:48–58

  • Zhang ZM (2013c) Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Inf Sci 234:150–181

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang ZM, Wu C (2014) Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making. J Intell Fuzzy Syst 26:2185–2202

    MathSciNet  MATH  Google Scholar 

  • Zhu B, Xu ZS (2014) Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst 22:35–45

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors thank the editors and anonymous reviewers for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China (Nos. 71271218, 71431006 and 71221061).

Author information

Authors and Affiliations

  1. School of Business, Central South University, Changsha, 410083, China

    Jian-qiang Wang, Jia-ting Wu, Jing Wang, Hong-yu Zhang & Xiao-hong Chen

Authors
  1. Jian-qiang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jia-ting Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hong-yu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiao-hong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian-qiang Wang.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Jq., Wu, Jt., Wang, J. et al. Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers. Soft Comput 20, 1621–1633 (2016). https://doi.org/10.1007/s00500-015-1609-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-015-1609-5

Keywords

Search

Navigation