SpringerLink
Log in

Extension of the ELECTRE method based on interval-valued fuzzy sets

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Decision-making is the process of finding the best option among the feasible alternatives. In classical multiple criteria decision-making (MCDM) methods, the ratings and the weights of the criteria are known precisely. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper, the interval-valued fuzzy ELECTRE method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy set concepts. For the purpose of proving the validity of the proposed model, we present a numerical example and build a practical maintenance strategy selection problem.

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
EUR 32.99 /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 (Thailand)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Al-Najjar B (1999) An approach for continuous reduction in LLC when using integrated vibration-based maintenance: a case study, COMADEM 99, Sunderland University, Sunderland, England, pp 159–169

  • Benayoun R, Roy B, Sussman N (1966) Manual de reference du programme electre. Note De Synthese et Formaton, No. 25, Direction Scientifique SEMA, Paris, France

  • Bertolini M, Bevilacqua M (2006) A combined goal programming—AHP approach to maintenance selection problem. Reliab Eng Syst Saf Roach Maint Sel Probl 91(7):839–848

    Article  Google Scholar 

  • Bevilacqua M, Barglia M (2000) The analytic hierarchy process applied to maintenance strategy selection. Reliab Eng Syst Saf 70:71–83

    Article  Google Scholar 

  • Buckley JJ (1985) Fuzzy hierarchical analysis. Fuzzy Sets Syst 17:233–247

    Article  MATH  MathSciNet  Google Scholar 

  • Bustince H (1994) Conjuntos Intuicionistas e Intervalo valorados Difusos: Propiedades y Construcci_on, Relaciones Intuicionistas Fuzzy. Thesis, Universidad Publica de Navarra

  • Chan GK, Asgarpoor S (2006) Optimum maintenance policy with Markov process. Electron Power Syst Res 76:452–456

    Article  Google Scholar 

  • Chen C-T (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 114:1–9

    Article  MATH  Google Scholar 

  • Chen C-T, Lin C-T, Huang S-F (2006) A fuzzy approach for supplier evaluation and selection in supply chain management. Int J Prod Econ 102:289–301

    Google Scholar 

  • Cornelis C, Deschrijver G, Kerre EE (2006) Advances and challenges in interval-valued fuzzy logic. Fuzzy Sets Syst 157:622–627

    Article  MATH  MathSciNet  Google Scholar 

  • Dembczyński K, Greco S, Słowiński R (2009) Rough set approach to multiple criteria classification with imprecise evaluations and assignments. Eur J Oper Res 198(2):626–636

    Article  MATH  Google Scholar 

  • Dimova L, Sevastianov P, Sevastianov D (2006) MADM in a fuzzy setting: investment projects assessment application. Int J Prod Econ 100(1):10–29

    Article  Google Scholar 

  • Gal T, Hanne T (eds) (1999) Multicriteria decision making: advances in MCDM models, algorithms, theory, and applications. Kluwer Academic Publishers, New York

  • Gorzalczany MB (1987) A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 21:1–17

    Article  MATH  MathSciNet  Google Scholar 

  • Grattan-Guinness I (1975) Fuzzy membership mapped onto interval and many-valued quantities. Z Math Logik Grundlag Mathe 22:149–160

    Article  MathSciNet  Google Scholar 

  • Grzegorzewski P (2004) Distances between intuitionistic fuzzy sets and/or interval valued fuzzy sets based on the Hausdorff metric. Fuzzy Set Syst 148:319–328

    Article  MATH  MathSciNet  Google Scholar 

  • Halouani N, Chabchoub H, Martel J-M (2009) PROMETHEE-MD-2T method for project selection. Eur J Oper Res 195(3):841–849

    Article  MATH  MathSciNet  Google Scholar 

  • Hong DH, Lee S (2002) Some algebraic properties and a distance measure for interval valued fuzzy numbers. Inf Sci 148:1–10

    Article  MATH  MathSciNet  Google Scholar 

  • Ivy JS, Nembhard HB (2005) A modeling approach to maintenance decisions using statistical quality control and organization. Qual Reliab Eng Int 21:355–366

    Article  Google Scholar 

  • Karnik NN, Mendel JM (2001) Operations on type-2 fuzzy sets. Fuzzy Sets Syst 122:327–348

    Article  MATH  MathSciNet  Google Scholar 

  • Kohout LJ, Bandler W (1996) Fuzzy interval inference utilizing the checklist paradigm and BK-relational products. In: Kearfort RB et al (eds) Applications of interval computations. Kluwer, Dordrecht, pp 291–335

    Google Scholar 

  • Mann L, Saxena A, Knapp G (1995) Statistical-based or condition-based maintenance? J Qual Maint Eng 1(1):46–59

    Article  Google Scholar 

  • Mechaefske CK (2003) Using linguistics to select optimum maintenance and condition monitoring strategies. Mech Syst Process 17(2):305–316

    Google Scholar 

  • Mobley RK (2004) Maintenance fundamentals, 2nd edn. Elsevier Inc, Amsterdam

  • Moore RE (1979) Methods and applications of interval analysis. SIAM, Philadelphia

  • Mustajoki J, Hamalainen RP, Salo A (2005) Decision support by interval SMART/SWING—incorporating imprecision in the SMART and SWING methods. Decis Sci 36(2):317–339

    Google Scholar 

  • Opricovic S, Tzeng GH (2007) Extended VIKOR method in comparison with outranking methods. Eur J Oper Res 178(2):514–529

    Article  MATH  Google Scholar 

  • Roy B (1968) Classement et choix en presence de points de vue multiples: La methode ELECTRE. RIRO 8:57–75

    Google Scholar 

  • Roy B, Bertier P (1971) La methode ELECTRE II: Une methode de classement en presence de critteres multiples. SEMA (Metra International), Direction Scientifique, Note de Travail No. 142, Paris, 25p

  • Sambuc R (1975) Fonctions f-floues. Application a` l’aide au diagnostic en pathologie thyroidienne. Ph.D. Thesis, University of Marseille

  • Triantaphyllou E (2000) Multi-criteria decision making methods: a comparative study. Kluwer Academic Publishers, London

  • Turksen IB (1986) Interval-valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20:191–210

    Article  MATH  MathSciNet  Google Scholar 

  • Turksen IB (1992) Interval-valued fuzzy sets and compensatory. Fuzzy Sets Syst 51:295–307

    Article  MathSciNet  Google Scholar 

  • Turksen IB (1996) Interval-valued strict preference with Zadeh triples. Fuzzy Sets Syst 78:183–195

    Article  MathSciNet  Google Scholar 

  • Wang G, Li X (1998) The applications of interval-valued fuzzy numbers and interval-distribution numbers. Fuzzy Sets Syst 98:331–335

    Article  MATH  Google Scholar 

  • Wang L, Chu J, Wu J (2007) Selection of optimum maintenance strategies based on a fuzzy analytic hierarchy process. Int J Prod Econ 107:151–163

    Article  Google Scholar 

  • Yao JS, Yu MM (2004) Decision making based on statistical data, signed distance and compositional rule of inference. Int J Uncertain Fuzziness Knowl Based Syst 12(2):161–190

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning, Inf Sci 8:301–357(a), 199–249

    Google Scholar 

  • Zavadskas EK, Turskis Z, Tamošaitiené J, Marina V (2008) Multicriteria selection of project managers by applying grey criteria. Technol Econ Dev Econ 14(4):462–477

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial and Mechanical Engineering, Islamic Azad University Qazvin Branch, Qazvin, Iran

    Behnam Vahdani & Hasan Hadipour

Authors
  1. Behnam Vahdani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hasan Hadipour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Behnam Vahdani.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vahdani, B., Hadipour, H. Extension of the ELECTRE method based on interval-valued fuzzy sets. Soft Comput 15, 569–579 (2011). https://doi.org/10.1007/s00500-010-0563-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-010-0563-5

Keywords

Search

Navigation