Skip to main content
SpringerLink
Log in

Some Intuitionistic Fuzzy Weighted Distance Measures and Their Application to Group Decision Making

  • Published:
Group Decision and Negotiation Aims and scope Submit manuscript

Abstract

Xu and Chen (J Syst Sci Syst Eng 17:432–445, 2008) introduced a new decision-making technique called the ordered weighted distance (OWD) measure, having been proved useful for the treatment of situation where the available information is represented in exact numerical values. In this paper, we consider the situations with intuitionistic fuzzy and interval-valued intuitionistic information, and develop some intuitionistic fuzzy weighted distance measures such as intuitionistic fuzzy ordered weighted distance (IFOWD) measure, interval-valued intuitionistic fuzzy ordered weighted distance (IVIFOWD) measure, intuitionistic fuzzy hybrid weighted distance (IFHWD) measure and interval-valued intuitionistic fuzzy hybrid weighted distance (IVIFHWD) measure. These developed weighted distance measures are very suitable to deal with the situation where the input data are represented in intuitionistic fuzzy numbers or interval-lvalued intuitionistic fuzzy numbers. Then we present a consensus reaching process for group decision making with intuitionistic fuzzy preference information based on the developed distance measures. Finally, a practical application of he developed approach to the problem of evaluating university faculty for tenure and promotion is given.

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

Similar content being viewed by others

References

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Berlin

    Google Scholar 

  • Bogart KP (1975) Preference structures II: distances between asymetric relations. SIAM Journal of Applied Mathematics 29: 254–262

    Article  Google Scholar 

  • Bolton J, Gader P, Wilson JN (2008) Choquet integral as a distance measure. IEEE Trans Fuzzy Syst 16: 1107–1110

    Article  Google Scholar 

  • Boran FE, Genc S, Kurt M, Akay D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36: 11363–11368

    Article  Google Scholar 

  • Bryson N, Mobolurin A (1995) An action learning evaluation procedure for multiple criteria decision making problems. Eur J Oper Res 96: 379–386

    Article  Google Scholar 

  • Chen SJ, Chen SM (2003) A new method for handling multi-criteria fuzzy decision-making problems using FN-IOWA operators. Cybern Syst 34: 109–137

    Article  Google Scholar 

  • Cheng CH, Wang JW, Wu MC (2009) OWA-weighted based clustering method for classification problem. Expert Syst Appl 36: 4988–4995

    Article  Google Scholar 

  • Hamming RW (1950) Error-detecting and error-correcting codes. Bell Syst Tech J 29: 147–160

    Google Scholar 

  • Herrera-Viedma E, Chiclana F, Herrera F, Alonso S (2007) Group decision making model with incomplete fuzzy preference relations based on additive consistency. IEEE Trans Syst Man Cybern B 37: 176–189

    Article  Google Scholar 

  • Kacprzyk J (1997) Multistage Fuzzy Control: A model-based approach to control and decision-making. Wiley, Chichester

    Google Scholar 

  • Karayiannis N (2000) Soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators. IEEE Trans Neural Netw 11: 1093–1105

    Article  Google Scholar 

  • Kaufmann A (1975) Introduction to the theory of fuzzy subsets. Academic Press, New York

    Google Scholar 

  • Liu X (2008) A general model of parameterized OWA aggregation with given orness level. Int J Approx Reason 48: 598–627

    Article  Google Scholar 

  • Liu PD (2009) A novel method for hybrid multiple attribute decision making. Knowl Based Syst 22: 388–391

    Article  Google Scholar 

  • Merigó JM, Casanovas M (2010) Decision making with distance measures and linguistic aggregation operators. Int J Fuzzy Syst 12: 190–198

    Google Scholar 

  • Merigó JM, Casanovas M (2011a) Decision making with distance measures and induced aggregation operators. Comput Ind Eng 60: 66–76

    Article  Google Scholar 

  • Merigó JM, Casanovas M (2011b) The uncertain induced quasi-arithmetic OWA operator. Int J Intell Syst 26: 1–24

    Article  Google Scholar 

  • Merigó JM, Gil-Lafuente AM (2008) Using the OWA operator in the Minkowski distance. Int J Electr Comput Eng 3: 149–157

    Google Scholar 

  • Merigó JM, Gil-Lafuente AM (2010) New decision making techniques and their application in the selection of financial products. Inf Sci 180: 2085–2094

    Article  Google Scholar 

  • Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114: 505–518

    Article  Google Scholar 

  • Szmidt E, Kacprzyk J (2002) Using intuitonistic fuzzy sets in group making. Control Cybern 31: 1017–1053

    Google Scholar 

  • Szmidt E, Kacprzyk J (2003) A consensus-reaching process under intuitionistic fuzzy preference relations. Int J Intell Syst 18: 837–852

    Article  Google Scholar 

  • Tan CQ, Chen XH (2010) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37: 149–157

    Article  Google Scholar 

  • Wang P (2009) Qos-aware web services selection with intuitionistic fuzzy set under consumer’s vague perception. Expert Syst Appl 36: 4460–4466

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Wei GW (2009) Uncertain linguistic hybrid geometric mean operator and its application to group decision making under uncertain linguistic environment. Int J Uncertain Fuzziness Knowl Based Syst 17: 251–267

    Article  Google Scholar 

  • Wei GW (2010a) 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 

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

    Article  Google Scholar 

  • Wei GW, Zhao X, Lin R (2010) Some induced aggregating operators with fuzzy number intuitionistic fuzzy information and their applications to group decision making. Int J Comput Intell Syst 3: 84–95

    Article  Google Scholar 

  • Xu ZS (2005) An overview of methods for determining OWA weights. Int J Intell Syst 20: 843–865

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Xu ZS (2007b) Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Mak 6: 109–121

    Article  Google Scholar 

  • Xu ZS (2007c) Multi-person multi-attribute decision making models under intuitionistic fuzzy environment. Fuzzy Optim Decis Mak 6: 221–236

    Article  Google Scholar 

  • Xu ZS (2007d) Intuitionistic preference relations and their application in group decision making. Info Sci 177: 2363–2379

    Article  Google Scholar 

  • Xu ZS (2007e) Models for multiple attribute decision making with intuitionistic fuzzy information. Int J Uncertain Fuzziness Knowl Based Syst 15: 285–297

    Article  Google Scholar 

  • Xu ZS (2007f) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22: 215–219

    Google Scholar 

  • Xu ZS (2008) Dependent uncertain ordered weighted averaging operators. Info Fusion 9: 310–316

    Article  Google Scholar 

  • Xu ZS (2010a) A method based on distance measure for interval-valued intuitionistic fuzzy group decision making. Info Sci 180: 181–190

    Article  Google Scholar 

  • Xu ZS (2010b) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negotiat 19: 57–76

    Article  Google Scholar 

  • Xu ZS, Cai XQ (2009) Incomplete interval-valued intuitionistic preference relations. Int J Gen Syst 38: 871–886

    Article  Google Scholar 

  • Xu ZS, Cai XQ (2010) Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. Int J Intell Syst 25: 489–513

    Google Scholar 

  • Xu ZS, Chen J (2007) An approach to group decision making based on interval-valued intuitionistic judgment matrices. Syst Eng Theory Pract 27: 126–133

    Article  Google Scholar 

  • Xu ZS, Chen J (2008) Ordered weighted distance measure. J Syst Sci Syst Eng 17: 432–445

    Article  Google Scholar 

  • Xu ZS, Xia M (2010) Induced generalized intuitionistic fuzzy operators. Knowledge-Based Systems in press,

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

    Article  Google Scholar 

  • Xu ZS, Yager RR (2008) Dynamic intuitionistic fuzzy multiple attribute decision making. Int J Approx Reason 48: 246–262

    Article  Google Scholar 

  • Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8: 123–139

    Article  Google Scholar 

  • Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern B 18: 183–190

    Article  Google Scholar 

  • Yager RR (2003) Induced aggregation operators. Fuzzy Sets Syst 137: 59–69

    Article  Google Scholar 

  • Yager RR (2007) Centered OWA operators. Soft Comput 11: 631–639

    Article  Google Scholar 

  • Yager RR (2009a) Weighted maximum entropy OWA aggregation with applications to decision making under risk. IEEE Trans Syst Man Cybern A 39: 555–564

    Article  Google Scholar 

  • Yager RR (2009b) Prioritized OWA aggregation. Fuzzy Optim Decis Mak 8: 245–262

    Article  Google Scholar 

  • Yager RR (2010) Norms induced from OWA operators. IEEE Trans Fuzzy Syst 18: 57–66

    Article  Google Scholar 

  • Ye J (2009) Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Syst Appl 36: 6899–6902

    Article  Google Scholar 

  • Ye J (2010) Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. Eur J Oper Res 205: 202–204

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Zarghami M, Szidarovszky F (2009) Revising the OWA operator for fuzzy stochastic multi criteria decision making. Eur J Oper Res 198: 259–265

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Compute and Information, Zhejiang Wanli University, Ningbo, 315100, China

    Shouzhen Zeng

  2. College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China

    Shouzhen Zeng

Authors
  1. Shouzhen Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shouzhen Zeng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zeng, S. Some Intuitionistic Fuzzy Weighted Distance Measures and Their Application to Group Decision Making. Group Decis Negot 22, 281–298 (2013). https://doi.org/10.1007/s10726-011-9262-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10726-011-9262-6

Keywords

Search

Navigation