Skip to main content
SpringerLink
Log in

Applying FARSJUM intelligent system to derive priorities in sparse hierarchical problems

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

Abstract

The analytic hierarchy process (AHP) is a decision analysis technique used to evaluate complex multi-criteria alternatives. In this paper, the fuzzy rule based system (FARSJUM) is introduced for especially sparse hierarchical problems to make decisions similar to AHP. The system is previously developed by the authors in sparse judgment matrices and in this paper an enhancement of the system in sparse hierarchical problems is brought. Numerical example is brought to show the applicability of the method and its advantages.

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

Similar content being viewed by others

References

  • Altuzarra A, Moreno-Jiménez JM, Salvador M (2007) A Bayesian priorization procedure for AHP group decision making. Eur J Oper Res 182(1):367–382

    Article  MATH  Google Scholar 

  • Bernroider EWN, Maier K, Stix V (2010) Incomplete information within relative pairwise comparisons as utilized by the AHP. Lect Notes Business Inf Process 57(1):39–50

    Article  Google Scholar 

  • Bozóki S, Fülöp J, Rónyai L (2010) On optimal completion of incomplete pairwise comparison matrices. Math Comput Model 52(1–2):318–333

    Article  MATH  Google Scholar 

  • Buckley JJ, Feuring T, Hayashi Y (1999) Fuzzy hierarchical analysis. IEEE int fuzzy syst proc 2:1009–1013

    Google Scholar 

  • Buyukozkan G, Ertay T, Kahraman C, Ruan Da (2004) Determining the importance weights for the design requirements in the house of quality using the fuzzy analytic network approach. Int J Intell Syst 19(5):443–461

    Article  Google Scholar 

  • Carmone FJ Jr, Kara A, Zanakis SH (1997) Monte Carlo investigation of incomplete pairwise comparison matrices in AHP. Eur J Oper Res 102(3):538–553

    Article  MATH  Google Scholar 

  • Dopazo E, González-Pachón J, Robles J (2005) A distance-based method for preference information retrieval in paired comparisons. Lect Notes Comput Sci 3646:66–73

    Article  Google Scholar 

  • Durkin J, Durkin J (1998) Expert systems: design and development. Prentice Hall, New Jersey

    Google Scholar 

  • Fattahi AA (2001) IUST’s faculties’ performance evaluation with integration of data envelopment analysis (DEA) and analytic hierarchical process (AHP). Industrial Engineering Department, IUST University

  • Fedrizzi M, Giove S (2007) Incomplete pairwise comparison and consistency optimization. Eur J Oper Res 183(1):303–313

    Article  MATH  Google Scholar 

  • Forman EH (1990) Random indices for incomplete pairwise comparison matrices. Eur J Oper Res 48(1):153–155

    Article  Google Scholar 

  • Forman EH (1993) Facts and fictions about the analytic hierarchy process. Math Comput Model 17(4–5):19–26

    Article  MATH  Google Scholar 

  • Forman EH, Selly MA (2002) Decision by objectives. World Scientific, New Jersey

    Google Scholar 

  • Gholamian MR, Fatemi Ghomi SMT, Ghazanfari M (2006) A hybrid intelligent system for multiobjective decision making problem. Comput Ind Eng 51(1):26–43

    Article  Google Scholar 

  • Gholamian MR, Fatemi Ghomi SMT (2007a) Meta knowledge of intelligent manufacturing: an overview of state-of-the-art. Appl Soft Comput 7(1):1–16

    Article  Google Scholar 

  • Gholamian MR, Fatemi Ghomi SMT, Ghazanfari M (2007b) FARSJUM, a fuzzy system for ranking sparse judgment matrices: a case study in soccer tournaments. Int J Uncertain, Fuzziness Knowl-Based Syst 15(1):115–129

    Article  Google Scholar 

  • Gomez-Ruiz JA, Karanik M, Peláez JA (2010) Estimation of missing judgments in AHP pairwise matrices using a neural network-based model. Appl Math Comput 216(10):2959–2975

    Article  MATH  MathSciNet  Google Scholar 

  • Harker PT (1987) Incomplete pairwise comparisons in the analytic hierarchy process. Math Model 9(11):837–848

    Article  MathSciNet  Google Scholar 

  • Hu Y-C, Tsai J-F (2006) Backpropagation multi-layer Perceptron for incomplete pairwise comparison matrices in analytic hierarchy process. Appl Math Comput 180(1):53–62

    Article  MATH  MathSciNet  Google Scholar 

  • Hwang CL, Masud AS (1979) Multiple attributes decision-making; methods and applications: A state of the art survey. Springer, Berlin

    Book  Google Scholar 

  • Jin X, Zhang Z, Wang C (2003) An improved AHP algorithm for scheme evaluation of a complex structure. In: Proceedings of the International Conference on Agile Manufacturing, Advances in Agile Manufacturing (ICAM 2003) (pp 139–144)

  • Kosko B (1997) Fuzzy engineering. Prentice Hal, New Jersey

    MATH  Google Scholar 

  • Lim KH, Swenseth SR (1993) An iterative procedure for reducing problem size in large scale AHP problems. Eur J Oper Res 67(1):64–74

    Article  MATH  Google Scholar 

  • Mikhaikov L, Singh S (2003) Fuzzy analytic network process and its application to the development of decision support systems. IEEE Trans Syst Man Cybern Part C Appl Rev 33(1):33–41

    Article  Google Scholar 

  • Millet I, Saaty TL (2000) On the relativity of relative measures-accommodating both rank preservation and rank reversals in the AHP. Eur J Oper Res 121:205–212

    Article  MATH  Google Scholar 

  • Millet I, Harker PT, Patrick T (1990) Globally effective questioning in the analytic hierarchy process. Eur J Oper Res 48(1):88–97

    Article  Google Scholar 

  • Nauck D, Kruse R (1998) How the learning of rule weights affects the interpretability of fuzzy systems. IEEE Int Conf Fuzzy Syst 2:1235–1240

    Google Scholar 

  • Raharjo H, Endah D (2006) Evaluating relationship of consistency ratio and number of alternatives on rank reversal in the AHP. Qual Eng 18(1):39–46

    Article  Google Scholar 

  • Saaty TL (1994) Highlights and critical points in the theory and application of the analytic hierarchy process. Eur J Oper Res 74(3):426–447

    Article  MATH  Google Scholar 

  • Saaty TL (1996) Multicriteria decision making. RWS Publishing, Boston

    Google Scholar 

  • Saaty TL (2001) The Analytic network process: decision making with dependence and feedback, 2nd edn. RWS Publishing, Boston

    Google Scholar 

  • Saaty TL (2003) Decision-making with the AHP: why is the principal eigenvector necessary. Eur J Oper Res 145(1):85–91

    Article  MATH  MathSciNet  Google Scholar 

  • Saaty TL (2004) The analytic network process: Dependence and feedback in decision making (Part 1) theory and validation examples. In: The Proceedings of XVIIth International Conference on Multiple Criteria Decision Making (MCDM 2004), Whistler, BC, Canada

  • Saaty TL, Tran LT (2007) On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process. Math Comput Model 46(7–8):962–975

    Article  MATH  MathSciNet  Google Scholar 

  • Saaty TL, Vargas LG (2000) Models, methods, concepts & applications of the analytic hierarchy process. International series in operations research and management science, vol 34. Kluwer, Boston

    Google Scholar 

  • Siraj S, Mikhailov L, Keane JA (2012) Enumerating all spanning trees for pairwise comparisons. Comput Oper Res 39(2):191–199

    Google Scholar 

  • Sugihara K, Ishii H, Tanaka H (2001) Fuzzy AHP with incomplete information. In: The proceedings of IFSA World Congress and 20th NAFIPS International Conference 5:2730–2733

  • Totsenko VG (2006) On problem of reversal of alternatives ranks while multicriteria estimating. J Autom Inf Sci 38(6):1–11

    Article  Google Scholar 

  • Wang HF (2000) Fuzzy multicriteria decision making-an overview. J Intell Fuzzy Syst 9:61–83

    Google Scholar 

  • Wang Y-M, Elhag TMS (2006) An approach to avoiding rank reversal in AHP. Decis Support Syst 42(3):1474–1480

    Article  Google Scholar 

  • Wang T-C, Lin Y-L (2007) Incomplete fuzzy preference relations and the consistency. WSEAS Trans Inf Sci Applications 4(5):982–987

    Google Scholar 

  • Wedley WC, Schoner B, Tang TS (1993) Starting rules for incomplete comparisons in the analytic hierarchy process. Math Comput Model 17(4–5):93–100

    Article  MATH  Google Scholar 

  • Zgurovsky MZ, Totsenko VG, Tsyganok VV (2004) Group incomplete paired comparisons with account of expert competence. Math Comput Model 39(4–5):349–361

    Article  MathSciNet  Google Scholar 

  • Zimmermann HJ (1996) Fuzzy set theory and its applications, 3rd edn. Kluwer, Boston

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Industrial Engineering, Iran University of Science and Technology, Narmak, 16844, Tehran, Iran

    M. R. Gholamian & M. Ghazanfari

  2. Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Avenue, Tehran, Iran

    S. M. T. Fatemi Ghomi

Authors
  1. M. R. Gholamian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. M. T. Fatemi Ghomi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Ghazanfari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. R. Gholamian.

Additional information

Communicated by G. Acampora.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gholamian, M.R., Fatemi Ghomi, S.M.T. & Ghazanfari, M. Applying FARSJUM intelligent system to derive priorities in sparse hierarchical problems. Soft Comput 18, 299–311 (2014). https://doi.org/10.1007/s00500-013-1058-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-013-1058-y

Keywords

Search

Navigation