Skip to main content
SpringerLink
Log in
Book cover

Intuitionistic Fuzzy Information Aggregation pp 189–248Cite as

Decision Making Models and Approaches Based on Intuitionistic Preference Relations

  • Chapter

Abstract

In real-life situations, such as partner selection in supply chain management, and performance assessment of military systems, a decision maker may be unable to express accurately his/her preferences for alternatives, because ① the decision maker may not possess a precise or sufficient level of knowledge (i.e., lack of knowledge to a certain degree (Mitchell, 2004), and ② he/she is unable to discriminate explicitly the degree to which one alternative is better than the others (Herrera-Viedma et al., 2007), and so there is a certain degree of hesitation (Szmidt and Kacprzyk, 2000). The decision maker may express, to a certain degree, his/her preferences for alternatives, but it is possible that he/she is not so sure about it (Deschrijver and Kerre, 2003a). In these problems, it is very suitable to study the decision maker’s preferences using IFNs rather than exact numerical values or linguistic variables (Dai et al., 2007; Herrera et al., 2005; Szmidt and Kacprzyk, 2003; 2002; Xu, 2007c; 2007f; Xu and Chen, 2007a).

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arbel A. 1989. Approximate articulation of preference and priority derivation. European Journal of Operational Research, 43: 317–326.

    Google Scholar 

  • Bordogna G, Fedrizzi M, Passi G. 1997. A linguistic modeling of consensus in group decision making based on OWA operator. IEEE Transactions on Systems, Man, and Cybernetics, 27: 126–132.

    Google Scholar 

  • Chen C Y, Xu L G. 2001. Partner selection model in supply chain management. Chinese Journal of Management Science, 9(Suppl.): 57–62.

    Google Scholar 

  • Chen Y, Fan Z P. 2005. Study on the adverse judgment problem for group decision making based on linguistic judgment matrices. Journal of Systems Engineering, 20(2): 211–215.

    Google Scholar 

  • Chiclana F, Herrera F, Herrera-Viedma E. 1998. Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets and Systems, 97: 33–48.

    Google Scholar 

  • Chiclana F, Herrera F, Herrera-Viedma E. 2001a. Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets and Systems, 122: 277–291.

    Google Scholar 

  • Chiclana F, Herrera F, Herrera-Viedma E. 2001b. Multiperson decision making based on multiplicative preference relations. European Journal of Operational Research, 129:372–385.

    Google Scholar 

  • Chiclana F, Herrera F, Herrera-Viedma E. 2002. A note on the internal consistency of various preference representations. Fuzzy Sets and Systems, 131: 75–78.

    Google Scholar 

  • Dai Y Q, Xu Z S, Da Q L. 2007. Approach to multiple attribute decision making based on different intuitionistic preference structures. Journal of Southeast University (Natural Science Edition), 37: 706–710.

    Google Scholar 

  • Deschrijver G, Kerre E E. 2003a. On the composition of intuitionistic fuzzy relations. Fuzzy Sets and Systems, 136: 333–361.

    Google Scholar 

  • Fan Z P, Ma J, Zhang Q. 2002. An approach to multiple attribute decision making based on fuzzy preference information on alternatives. Fuzzy Sets and Systems, 131: 101–106.

    Google Scholar 

  • Haines L M. 1998. A statistical approach to the analytic hierarchy process with interval judgments. European Journal of Operational Research, 110: 112–125.

    Google Scholar 

  • Herrera E, Martínez L. 2000b. An approach for combining linguistic and numerical information based on 2-tuple fuzzy linguistic representation model in decision-making. International Journal of Uncertainty, Fuzziness, Knowledge-based Systems, 8: 539–562.

    Google Scholar 

  • Herrera F, Herrera-Viedma E, Martínez L. 2000. A fusion approach for managing multigranularity linguistic term sets in decision making. Fuzzy Sets and Systems, 114:43–58.

    Google Scholar 

  • Herrera F, Herrera-Viedma E, Verdegay J L. 1996a. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets and Systems, 78: 73–87.

    Google Scholar 

  • Herrera F, Herrera-Viedma E, Verdegay J L. 1996b. Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets and Systems, 79: 175–190.

    Google Scholar 

  • Herrera F, Herrera-Viedma E, Verdegay J L. 1997. A rational consensus model in group decision making using linguistic assessments. Fuzzy Sets and Systems, 88: 31–49.

    Google Scholar 

  • Herrera F, Herrera-Viedma E. 2000a. Choice functions and mechanisms for linguistic preference relations. European Journal of Operational Research, 120: 144–161.

    Google Scholar 

  • Herrera F, Herrera-Viedma E. 2000b. Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets and Systems, 115: 67–82.

    Google Scholar 

  • Herrera F, Martínez L. 2000a. A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8: 746–752.

    Google Scholar 

  • Herrera F, Martinez L, Sanchez P J. 2005. Managing non-homogeneous information in group decision making. European Journal of Operational Research, 166: 115–132.

    Google Scholar 

  • Herrera-Viedma E, Chiclana F, Herrera F, Alonso S. 2007. A group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Transactions on Systems, Man and Cybernetics-Part B, 37: 176–189.

    Google Scholar 

  • Hwang C L, Yoon K. 1981. Multiple Attribute Decision Making: Methods and Applications. Berlin: Springer-Verlag.

    Google Scholar 

  • Igizio J P. 1976. Goal Programming and Extensions. Lexington: Health.

    Google Scholar 

  • Islam R, Biswal M P, Alam S S. 1997. Preference programming and inconsistent interval judgments. European Journal of Operational Research, 97: 53–62.

    Google Scholar 

  • Li X M, Min M, Tan C F. 2005. The functional assessment of agricultural ecosystems in Hubei Province, China. Ecological Modelling, 187: 352–360.

    Google Scholar 

  • Ma J, Fan Z P, Jiang Y P, Mao J Y, et al. 2006. A method for repairing the inconsistency of fuzzy preference relations. Fuzzy Sets and Systems, 157: 20–33.

    Google Scholar 

  • Mikhailov L. 2002. Fuzzy analytical approach to partnership selection in formation of virtual enterprises. Omega, 30: 393–401.

    Google Scholar 

  • Mikhailov L. 2003. Deriving priorities from fuzzy pairwise comparison judgements. Fuzzy Sets and Systems, 137: 365–385.

    Google Scholar 

  • Mitchell H B. 2004. A correlation coefficient for intuitionistic fuzzy sets. International Journal of Intelligent Systems, 19: 483–490.

    Google Scholar 

  • Orlovsky S A. 1978. Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems, 1: 155–167.

    Google Scholar 

  • Saaty T L, Vargas L G. 1987. Uncertainty and rank order in the analytic hierarchy process. European Journal of Operational Research, 32: 107–117.

    Google Scholar 

  • Saaty T L. 1980. The Analytic Hierarchy Process. New York: McGraw-Hill.

    Google Scholar 

  • Salo A, Hämäläinen R P. 1995. Preference programming through approximate ratio comparisons. European Journal of Operational Research, 82: 458–475.

    Google Scholar 

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

    Google Scholar 

  • Szmidt E, Kacprzyk J. 2002. Using intuitionistic fuzzy sets in group decision making. Control and Cybernetics, 31: 1037–1053.

    Google Scholar 

  • Szmidt E, Kacprzyk J. 2003. A consensus-reaching process under intuitionistic fuzzy preference relations. International Journal of Intelligent Systems, 18: 837–852.

    Google Scholar 

  • Szmidt E, Kacprzyk J. 2004. A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. Lecture Notes in Artificial Intelligence, 3070: 388–393.

    Google Scholar 

  • Tanino T. 1984. Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems, 12: 117–131.

    Google Scholar 

  • Wang L F, Xu S B. 1990. The Introduction to Analytic Hierarchy Process. Beijing: China Renmin University Press.

    Google Scholar 

  • Wang Y M, Xu D L. 2005. A two-stage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets and Systems, 152: 475–498.

    Google Scholar 

  • Xu Z S, Cai X Q. 2009. Incomplete interval-valued intuitionistic preference relations. International Journal of General Systems, 38: 871–886.

    Google Scholar 

  • Xu Z S, Chen J. 2007a. An approach to group decision making based on interval-valued intuitionistic judgment matrices. Systems Engineering-Theory & Practice, 27(4): 126–133.

    Google Scholar 

  • Xu Z S, Da Q L. 2003a. A possibility-based method for priorities of interval judgment matrices. Chinese Journal of Management Science, 11(1): 63–65.

    Google Scholar 

  • Xu Z S, Da Q L. 2003c. Possibility degree method for ranking interval numbers and its application. Journal of Systems Engineering, 18: 67–70.

    Google Scholar 

  • Xu Z S, Da Q L. 2005. A least deviation method to obtain a priority vector of a fuzzy preference relation. European Journal of Operational Research, 164: 206–216.

    Google Scholar 

  • Xu Z S, Yager R R. 2009. Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optimization and Decision Making, 8: 123–139.

    Google Scholar 

  • Xu Z S. 1999. Study on the Relation between two classes of scales in AHP. Systems Engineering-Theory & Practice, 19(7): 97–101.

    Google Scholar 

  • Xu Z S. 2001a. Algorithm for priority of fuzzy complementary judgment matrix. Journal of Systems Engineering, 16(4): 311–314.

    Google Scholar 

  • Xu Z S. 2001b. The least variance Priority method (LVM) for fuzzy complementary judgment matrix. Systems Engineering-Theory and Practice, 21(10): 93–96.

    Google Scholar 

  • Xu Z S. 2004a. A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Information Sciences, 166: 19–30.

    Google Scholar 

  • Xu Z S. 2004b. EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12: 791–810.

    Google Scholar 

  • Xu Z S. 2004c. Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation. International Journal of Approximate Reasoning, 36: 261–270.

    Google Scholar 

  • Xu Z S. 2004e. Uncertain Multiple Attribute Decision Making: Methods and Applications. Beijing: Tsinghua University Press.

    Google Scholar 

  • Xu Z S. 2005b. Deviation measures of linguistic preference relations in group decision making. Omega, 33: 249–254.

    Google Scholar 

  • Xu Z S. 2005d. On method for uncertain multiple attribute decision making problems with uncertain preference information on alternatives. Fuzzy Optimization and Decision Making, 4: 131–139.

    Google Scholar 

  • Xu Z S. 2006a. A C-OWA operator based approach to decision making with interval fuzzy preference relation. International Journal of Intelligent Systems, 21: 1289–1298.

    Google Scholar 

  • Xu Z S. 2006c An approach based on the uncertain LOWG and the induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations. Decision Support Systems, 41: 488–499.

    Google Scholar 

  • Xu Z S. 2006e. Group decision making method based on different types of incomplete judgment matrices. Control and Decision, 21(1): 28–33.

    Google Scholar 

  • Xu Z S. 2006f. Incomplete linguistic preference relations and their fusion. Information Fusion, 7: 331–337.

    Google Scholar 

  • Xu Z S. 2007b A survey of preference relations. International Journal of General Systems, 36: 179–203.

    Google Scholar 

  • Xu Z S. 2007c Approaches to multiple attribute decision making with intuitionistic fuzzy preference information. Systems Engineering-Theory and Practice, 27(11): 62–71.

    Google Scholar 

  • Xu Z S. 2007f. Intuitionistic preference relations and their application in group decision making. Information Sciences, 177: 2363–2379.

    Google Scholar 

  • Xu Z S. 2007g. Linguistic aggregation operators: an overview, In: Bustince H, Herrera F, Montero J, eds. Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Berlin: Springer: 163–181.

    Google Scholar 

  • Xu Z S. 2007j. Multiple attribute group decision making with different formats of preference information on attributes. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 37(6): 1500–1511.

    Google Scholar 

  • Xu Z S. 2008b. Group decision making based on multiple types of linguistic preference relations. Information Sciences, 178: 3775–3790.

    Google Scholar 

  • Yager R R, Xu Z S. 2006. The continuous ordered weighted geometric operator and its application to decision making. Fuzzy Sets and Systems, 157: 1393–1402.

    Google Scholar 

  • Zadeh L A. 2005. Toward a generalized theory of uncertainty (GTU)-an outline. Information Sciences, 172: 1–40.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Sciences, PLA University of Science and Technology, Room 2609, Building 5, No.2, Biaoying, Yudao Street, 210007, Nanjing, Jiangsu, P.R. China

    Zeshui Xu

  2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Xiaoqiang Cai

Authors
  1. Zeshui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoqiang Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Science Press Beijing and Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Xu, Z., Cai, X. (2012). Decision Making Models and Approaches Based on Intuitionistic Preference Relations. In: Intuitionistic Fuzzy Information Aggregation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29584-3_4

Download citation

Publish with us

Policies and ethics

Search

Navigation