Skip to main content
SpringerLink
Log in

A likelihood-based QUALIFLEX method with interval type-2 fuzzy sets for multiple criteria decision analysis

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

Abstract

The aim of this paper is to develop a likelihood-based QUALIFLEX method with interval type-2 fuzzy sets for multiple criteria decision analysis. This paper considers the context of interval type-2 trapezoidal fuzzy numbers and also introduces an extended concept of likelihoods of interval type-2 fuzzy preference relations. The concepts of lower and upper likelihoods are presented to serve as lower and upper bounds, respectively, of the possibility of preference relations and then to determine the likelihoods between interval type-2 trapezoidal fuzzy numbers. This paper uses a likelihood-based comparison between evaluative ratings to propose the concepts of concordance indices and comprehensive concordance indices for evaluating the permutations of alternatives corresponding to criterion-by-criterion consistency. By employing the signed distance-based method or the optimal membership-degree-determination method, the best permutation and its corresponding optimal ranking order of the alternatives can be acquired through a comparison of all of the comprehensive concordance indices. The applicability and effectiveness of the proposed method are illustrated with a medical decision-making problem that addresses the selection of treatment options. Additionally, a comparative analysis is performed with some relevant multiple criteria decision-making methods to demonstrate the advantages of the likelihood-based QUALIFLEX method. Finally, an analysis through computational experiments is conducted to examine the implementation efficiency of the proposed method.

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

Similar content being viewed by others

References

  • Baležentis T, Zeng S (2013) Group multi-criteria decision making based upon interval-valued fuzzy numbers: an extension of the MULTIMOORA method. Expert Syst Appl 40(2):543–550

    Article  Google Scholar 

  • Castillo O, Melin P (2012) Optimization of type-2 fuzzy systems based on bio-inspired methods: a concise review. Inform Sci 205:1–19

    Article  MathSciNet  Google Scholar 

  • Castillo O, Melin P, Pedrycz W (2011) Design of interval type-2 fuzzy models through optimal granularity allocation. Appl Soft Comput 11(8):5590–5601

    Article  Google Scholar 

  • Chen T-Y (2011a) An integrated approach for assessing criterion importance with interval type-2 fuzzy sets and signed distances. J Chin Inst Ind Eng 28(8):553–572

    Google Scholar 

  • Chen T-Y (2011b) Signed distanced-based TOPSIS method for multiple criteria decision analysis based on generalized interval-valued fuzzy numbers. Int J Inform Technol Decis Making 10(6):1131–1159

    Article  Google Scholar 

  • Chen T-Y (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  Google Scholar 

  • Chen T-Y (2013a) An interactive method for multiple criteria group decision analysis based on interval type-2 fuzzy sets and its application to medical decision making. Fuzzy Optim Decis Making 12(3):323–356

    Article  Google Scholar 

  • Chen T-Y (2013b) A signed-distance-based approach to importance assessment and multi-criteria group decision analysis based on interval type-2 fuzzy set. Knowl Inform Syst 35(1):193–231

    Article  Google Scholar 

  • Chen T-Y (2013c) A linear assignment method for multiple-criteria decision analysis with interval type-2 fuzzy sets. Appl Soft Comput 13(5):2735–2748

    Article  Google Scholar 

  • Chen T-Y (2013d) Data construction process and QUALIFLEX-based method for multiple-criteria group decision making with interval-valued intuitionistic fuzzy sets”. Int J Inform Technol Decis Making 12(3):425–467

    Article  Google Scholar 

  • Chen T-Y (2014a) Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis. Inform Sci 261:149–169

    Article  MathSciNet  Google Scholar 

  • Chen T-Y (2014b) An ELECTRE-based outranking method for multiple criteria group decision making using interval type-2 fuzzy sets. Inform Sci 263:1–21

    Article  MathSciNet  Google Scholar 

  • Chen T-Y, Chang C-H, Lu J-FR (2013) The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making. Eur J Oper Res 226(3):615–625

    Article  MathSciNet  Google Scholar 

  • Chen S-M, Chen J-H (2009) Fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers and interval-valued fuzzy number arithmetic operators. Expert Syst Appl 36(3–2):6309–6317

    Article  Google Scholar 

  • Chen S-M, Lee L-W (2010a) 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 

  • Chen S-M, Lee L-W (2010b) Fuzzy multiple criteria hierarchical group decision-making based on interval type-2 fuzzy sets. IEEE Trans Syst Man Cybern Part A Syst Hum 40(5):1120–1128

    Article  Google Scholar 

  • Chen S-M, Lee L-W (2010c) Fuzzy decision-making based on likelihood-based comparison relations. IEEE Trans Fuzzy Syst 18(3):613–628

    Article  Google Scholar 

  • Chen T-Y, Tsui C-W (2012) Intuitionistic fuzzy QUALIFLEX method for optimistic and pessimistic decision making. Adv Inform Sci Serv Sci 4(14):219–226

    Google Scholar 

  • Chen T-Y, Wang J-C (2009) Interval-valued fuzzy permutation method and experimental analysis on cardinal and ordinal evaluations. J Comput Syst Sci 75(7):371–387

    Article  Google Scholar 

  • Chen S-M, Wang C-Y (2013) Fuzzy decision making systems based on interval type-2 fuzzy sets. Inform Sci 242:1–21

    Article  MathSciNet  Google Scholar 

  • Chen T-Y, Wang J-C, Tsui C-W (2007) Decision model with permutation methods based on intuitionistic fuzzy sets. In: Proceedings of the 8th Asia Pacific Industrial Engineering and Management System and 2007 Chinese Institute of Industrial Engineers Conference (APIEMS and CIIE 2007), pp 243–250

  • Greco S, Kadziński M, Mousseau V, Słowiński R (2011) ELECTRE\(^{{\rm GKMS}}\): robust ordinal regression for outranking methods. Eur J Oper Res 214(1):118–135

    Article  Google Scholar 

  • Greenfield S, Chiclana F, Coupland S, John R (2009) The collapsing method of defuzzification for discretised interval type-2 fuzzy sets. Inform Sci 179(13):2055–2069

    Article  MathSciNet  Google Scholar 

  • Griffith DA, Paelinck JHP (2011) Qualireg, a qualitative regression method. Adv Geogr Inform Sci 1(2):227–233

    Article  Google Scholar 

  • Hidalgo D, Castillo O, Melin P (2009) Type-1 and type-2 fuzzy inference systems as integration methods in modular neural networks for multimodal biometry and its optimization with genetic algorithms. Inform Sci 179(13):2123–2145

    Article  Google Scholar 

  • Hokkanen J, Lahdelma R, Salminen P (2000) Multicriteria decision support in a technology competition for cleaning polluted soil in Helsinki. J Environ Manage 60(4):339–348

    Article  Google Scholar 

  • Lahdelma R, Miettinen K, Salminen P (2003) Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA). Eur J Oper Res 147(1):117–127

    Article  Google Scholar 

  • Lee L-W, Chen S-M (2009) A new method for fuzzy decision-making based on likelihood-based comparison relations. In: Proceedings of the Eighth International Conference on Machine Learning and Cybernetics, Baoding, China, July 12–15 2009, pp 3021–3025

  • Li D-F (2010a) Linear programming method for MADM with interval-valued intuitionistic fuzzy sets. Expert Syst Appl 37(8):5939–5945

    Article  Google Scholar 

  • Li D-F (2010b) TOPSIS-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 18(2):299–311

    Google Scholar 

  • Li D-F (2011) Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information. Appl Soft Comput 11(4):3402–3418

    Article  Google Scholar 

  • Li D-F, Wang Y-C, Liu S, Shan F (2009) Fractional programming methodology for multi-attribute group decision-making using IFS. Appl Soft Comput 9(1):219–225

  • Martel J-M, Matarazzo B (2005) Other outranking approaches. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state of the art surveys. Springer Science+Business Media, New York, pp 197–262

    Google Scholar 

  • Melin P, Castillo O (2013) A review on the applications of type-2 fuzzy logic in classification and pattern recognition. Expert Syst Appl 40(13):5413–5423

    Article  Google Scholar 

  • Mendel JM (2010) Type-2 fuzzy sets: a tribal parody. IEEE Comput Intell Mag 5(4):24–27

    Google Scholar 

  • Ngan S-C (2013) A type-2 linguistic set theory and its application to multi-criteria decision making. Comput Ind Eng 64(2):721–730

    Article  Google Scholar 

  • Paelinck JHP (1976) Qualitative multiple criteria analysis, environmental protection and multiregional development. Pap Reg Sci Assoc 36(1):59–74

    Article  Google Scholar 

  • Paelinck JHP (1977) Qualitative multicriteria analysis: an application to airport location. Environ Plann 9(8):883–895

    Article  Google Scholar 

  • Paelinck JHP (1978) QUALIFLEX: a flexible multiple-criteria method. Econ Lett 1(3):193–197

    Article  Google Scholar 

  • Sarabando P, Dias LC (2010) Simple procedures of choice in multicriteria problems without precise information about the alternatives’ values. Comput Oper Res 37(12):2239–2247

    Article  MathSciNet  Google Scholar 

  • Vahdani B, Hadipour H (2011) Extension of the ELECTRE method based on interval-valued fuzzy sets. Soft Comput 15(3):569–579

    Article  Google Scholar 

  • Vahdani B, Jabbari AHK, Roshanaei V, Zandieh M (2010) Extension of the ELECTRE method for decision-making problems with interval weights and data. Inte J Adv Manufact Technol 50(5–8):793 –800

  • 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

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

    Article  MathSciNet  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inform Sci 8(3):199–249

    Article  MathSciNet  Google Scholar 

  • Zhang Z (2013a) On characterization of generalized interval type-2 fuzzy rough sets. Inform Sci 219:124–150

    Article  MathSciNet  Google Scholar 

  • Zhang N (2013b) Method for aggregating correlated interval grey linguistic variables and its application to decision making. Technol Econ Dev Econ 19(2):189–202

    Article  Google Scholar 

  • Zhang X, Jin F, Liu P (2013) A grey relational projection method for multi-attribute decision making based on intuitionistic trapezoidal fuzzy number. Appl Math Model 37(5):3467–3477

    Article  MathSciNet  Google Scholar 

  • Zhang Z, Zhang S (2013) A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets. Appl Math Model 37(7):4948–4971

  • Zhao T, Xiao J (2014) General type-2 fuzzy rough sets based on \(\alpha \)-plane representation theory. Soft Comput 18(2):227–237

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors are very grateful to the respected editor and the anonymous referees for their insightful and constructive comments, which helped to improve the overall quality of the paper. The authors are grateful for the grant funding support of the Taiwan Ministry of Science and Technology (MOST 102-2410-H-182-013-MY3) during which the study was completed.

Author information

Authors and Affiliations

  1. Department of Information Management, College of Management, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan , 333, Taiwan

    Jih-Chang Wang

  2. Department of Industrial and Business Management, College of Management, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan , 333, Taiwan

    Chueh-Yung Tsao

  3. Department of Industrial and Business Management, Graduate Institute of Business and Management, College of Management, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan , 333, Taiwan

    Ting-Yu Chen

Authors
  1. Jih-Chang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chueh-Yung Tsao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ting-Yu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ting-Yu Chen.

Additional information

Communicated by V. Loia.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (docx 45 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, JC., Tsao, CY. & Chen, TY. A likelihood-based QUALIFLEX method with interval type-2 fuzzy sets for multiple criteria decision analysis. Soft Comput 19, 2225–2243 (2015). https://doi.org/10.1007/s00500-014-1404-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-014-1404-8

Keywords

Search

Navigation