Ideal Reference Method with Linguistic Labels: A Comparison with LTOPSIS

  • Elio H. CablesEmail author
  • María Teresa Lamata
  • José Luis Verdegay
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 377)


In many life situations we are in the presence of decision making problems, therefore it becomes necessary to study different theories, methods and tools to solve these kinds of problems as efficiently as possible. In this paper, we describe the elements that integrate a decision making model, as well as show some of the compensatory multicriteria decision making methods such as TOPSIS, VIKOR or RIM, that are most used. In particular, we identify the limitations of the RIM method to operate with linguistic labels. Next, the basic concepts of the Reference Ideal Method are described, and another variant is proposed to determine the minimum distance to the Reference Ideal, as well as the normalization function. We illustrate our method by means of an example and compare the results with those obtained by the LTOPSIS method. Finally, the conclusions are presented.


Multicriteria decision making Reference ideal method RIM 



This work has been partially funded by projects TIN2014-55024-P and TIN2017-86647-P from the Spanish Ministry of Economy and Competitiveness, P11-TIC-8001 from the Andalusian Government, and FEDER funds. Also, the support provided by the Antonio Nariño University, Colombia.


  1. 1.
    Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley, New York (1976)zbMATHGoogle Scholar
  2. 2.
    Saaty, T.L.: The analytic hierarchy process. McGraw-Hill, New York (1980)zbMATHGoogle Scholar
  3. 3.
    Saaty, T.L.: Fundamentals of the Analytic Network Process. ISAHP, Kobe, Japan (1999)Google Scholar
  4. 4.
    Edwards, W., Barron, F.H.: SMARTS and SMARTER: improves simple methods for multiattibute utility measurement. Organ. Behav. Hum. Decis. Process. 60, 306–325 (1994)CrossRefGoogle Scholar
  5. 5.
    Roy, B.: Classement et choix en présence de points de vue multiples (la méthode ELECTRE). Revue Francaise d’Informatique et de Recherche Opérationnelle 8, 57–75 (1968)CrossRefGoogle Scholar
  6. 6.
    Brans, J.P., Vincke, P., Mareschal, B.: How to select and how to rank projects: the PROMETHEE method. Eur. J. Oper. Res. 24, 228–238 (1986)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hwang, C.L., Yoon, K.: Multi-attribute Decision Making: Methods and Applications. Springer-Verlag, Berlin (1981)CrossRefGoogle Scholar
  8. 8.
    Opricovic, S.: Multi-criteria optimization of civil engineering systems. Faculty of Civil Engineering. Belgrade (1998)Google Scholar
  9. 9.
    Cables, E., Lamata, M.T., Verdegay, J.L.: RIM-reference ideal method in multicriteria decision making. Inf. Sci. 337, 1–10 (2016)CrossRefGoogle Scholar
  10. 10.
    Bozbura, F.T., Beskese, A., Kahraman, C.: Prioritization of human capital measurement indicators using fuzzy AHP. Expert Syst. Appl. 32, 1100–1112 (2007)CrossRefGoogle Scholar
  11. 11.
    Wang, Y.M., Luo, Y., Hua, Z.: On the extent analysis method for fuzzy AHP and its applications. Eur. J. Oper. Res. 186, 735–747 (2008)CrossRefGoogle Scholar
  12. 12.
    Dagdeviren, M., Yuksel, I.: Developing a fuzzy analytic hierarchy process (AHP) model for behavior-based safety management. Inf. Sci. 178, 1717–1733 (2008)CrossRefGoogle Scholar
  13. 13.
    Buyukozkan, G., Cifci, G., Guleryuz, S.: Strategic analysis of healthcare service quality using fuzzy AHP methodology. Expert Syst. Appl. 38, 9407–9424 (2011)CrossRefGoogle Scholar
  14. 14.
    Chou, C.H., Liang, G.S., Chang, H.C.: A fuzzy AHP approach based on the concept of possibility extent. Qual. Quant. 47, 1–14 (2013)CrossRefGoogle Scholar
  15. 15.
    Dabbaghian, M., Hewage, K., Reza, B., et al.: Sustainability performance assessment of green roof systems using fuzzy-analytical hierarchy process (FAHP). Int. J. Sustain. Build. Technol. Urban Dev. 5, 1–17 (2014)CrossRefGoogle Scholar
  16. 16.
    Kubler, S., Voisin, A., Derigent, W., et al.: Group fuzzy AHP approach to embed relevant data on communicating material. Comput. Ind. 65, 675–692 (2014)CrossRefGoogle Scholar
  17. 17.
    Sánchez-Lozano, M., García-Cascales, M.S., Lamata, M.T.: Evaluation of optimal sites to implant solar thermoelectric power plants: case study of the coast of the Region of Murcia, Spain. Comput. Ind. Eng. 87, 343–355 (2015)CrossRefGoogle Scholar
  18. 18.
    Ayag, Z., Ozdemir, R.: An intelligent approach to ERP software selection through fuzzy ANP. Int. J. Prod. Res. 45, 2169–2194 (2007)CrossRefGoogle Scholar
  19. 19.
    Onut, S., Tuzkaya, U.R., Torun, E.: Selecting container port via a fuzzy ANP-based approach: a case study in the Marmara Region, Turkey. Trans. Policy 18, 182–193 (2011)CrossRefGoogle Scholar
  20. 20.
    Kang, H.Y., Lee, A.H., Yang, C.Y.: A fuzzy ANP model for supplier selection as applied to IC packaging. J. Intell. Manuf. 23, 1477–1488 (2012)CrossRefGoogle Scholar
  21. 21.
    Vahdani, B., Hadipour, H., Tavakkoli-Moghaddam, R.: Soft computing based on interval valued fuzzy ANP-A novel methodology. J. Intell. Manuf. 23, 1529–1544 (2012)CrossRefGoogle Scholar
  22. 22.
    Roy, B.: ELECTRE III: Un algorithme de rangement fondé sur une représentation floue des préférences en présence de critéres multiples. Cahiers du Centre d´Etudes de recherche operationnelle, 20, 3–24 (1978)Google Scholar
  23. 23.
    Montazer, G.A., Saremi, H.Q., Ramezani, M.: Design a new mixed expert decision aiding system using fuzzy ELECTRE III method for vendor selection. Expert Syst. Appl. 36, 10837–10847 (2009)CrossRefGoogle Scholar
  24. 24.
    Roy, B., Skalka, J.: ELECTRE IS, aspects méthodologiques et guide d´utilisation. Université Paris-Dauphine, Paris, Cahier du LAMSADE (1985)Google Scholar
  25. 25.
    Yu, W.: ELECTRE TRI: Aspects methodologiques et manuel d´utilisation. Universite Paris-Dauphine, Document du LAMSADE (1992)Google Scholar
  26. 26.
    Sevkli, M.: An application of the fuzzy ELECTRE method for supplier selection. Int. J. Prod. Res. 48, 3393–3405 (2010)CrossRefGoogle Scholar
  27. 27.
    Wu, M.-C., Chen, T.-Y.: The ELECTRE multicriteria analysis approach based on Atanassov’s intuitionistic fuzzy sets. Expert Syst. Appl. 38, 12318–12327 (2011)CrossRefGoogle Scholar
  28. 28.
    Hatami-Marbini, A., Tavana, M., Moradi, M., et al.: A fuzzy group Electre method for safety and health assessment in hazardous waste recycling facilities. Saf. Sci. 51, 414–426 (2013)CrossRefGoogle Scholar
  29. 29.
    Devi, K., Yadav, S.P.: A multicriteria intuitionistic fuzzy group decision making for plant location selection with ELECTRE method. Int. J. Adv. Manuf. Technol. 66, 1219–1229 (2013)CrossRefGoogle Scholar
  30. 30.
    Sánchez-Lozano, J.M., García-Cascales, M.S., Lamata, M.T.: Comparative TOPSIS-ELECTRE TRI methods for optimal sites for photovoltaic solar farms: case study in Spain. J. Clean. Prod. 127, 387–398 (2016)CrossRefGoogle Scholar
  31. 31.
    Behzadian, M., Kazemzadeh, R.B., Albadvi, A., et al.: PROMETHEE: a comprehensive literature review on methodologies and applications. Eur. J. Oper. Res. 200, 198–215 (2010)CrossRefGoogle Scholar
  32. 32.
    Chen, Y.T., Wang, T.-C., Wu, C.-Y.: Strategic decisions using the fuzzy PROMETHEE for IS outsourcing. Expert Syst. Appl. 38, 13216–13222 (2011)CrossRefGoogle Scholar
  33. 33.
    Gupta, R., Sachdeva, A., Bhardwaj, A.: Selection of logistic service provider using fuzzy PROMETHEE for a cement industry. J. Manuf. Technol. Manag. 23, 899–921 (2012)CrossRefGoogle Scholar
  34. 34.
    Sanayei, A., Mousavi, S.F., Yazdankhah, A.: Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Syst. Appl. 37, 24–30 (2010)CrossRefGoogle Scholar
  35. 35.
    Opricovic, S.: Fuzzy VIKOR with an application to water resources planning. Expert Syst. Appl. 38, 12983–12990 (2011)CrossRefGoogle Scholar
  36. 36.
    Park, J.H., Cho, H.J., Kwun, Y.C.: Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information. Fuzzy Optim. Decis. Making 10, 233–253 (2011)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Jeya, R., Vinodh, S.: Application of fuzzy VIKOR and environmental impact analysis for material selection of an automotive component. Mater. Des. 37, 478–486 (2012)CrossRefGoogle Scholar
  38. 38.
    Yucenur, G.N., Demirel, N.C.: Group decision making process for insurance company selection problem with extended VIKOR method under fuzzy environment. Expert Syst. Appl. 39, 3702–3707 (2012)CrossRefGoogle Scholar
  39. 39.
    Kim, Y., Chung, E.S.: Fuzzy VIKOR approach for assessing the vulnerability of the water supply to climate change and variability in South Korea. Appl. Math. Model. 37, 9419–9430 (2013)CrossRefGoogle Scholar
  40. 40.
    Wan, S.P., Wang, O.Y., Dong, J.-Y.: The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers. Knowl.-Based Syst. 52, 65–77 (2013)CrossRefGoogle Scholar
  41. 41.
    Mokhtarian, M.N., Sadi-Nezhad, S., Makui, A.: A new flexible and reliable interval valued fuzzy VIKOR method based on uncertainty risk reduction in decision making process: an application for determining a suitable location for digging some pits for municipal wet waste landfill. Comput. Ind. Eng. 78, 213–233 (2014)CrossRefGoogle Scholar
  42. 42.
    Chang, T.H.: Fuzzy VIKOR method: a case study of the hospital service evaluation in Taiwan. Inf. Sci. 271, 196–212 (2014)CrossRefGoogle Scholar
  43. 43.
    Antucheviciene, J.: Evaluation of alternatives applying TOPSIS method in a fuzzy environment. Technol. Econ. Dev. Econ. 11, 242–247 (2005)Google Scholar
  44. 44.
    Mahdavi, I., Mahdavi-Amiri, N., Heidarzade, A., et al.: Designing a model of fuzzy TOPSIS in multiple criteria decision making. Appl. Math. Comput. 206, 607–617 (2008)MathSciNetzbMATHGoogle Scholar
  45. 45.
    Ashtiani, B., Haghighirad, F., Makui, A.: Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets. Appl. Soft Comput. 9, 457–461 (2009)CrossRefGoogle Scholar
  46. 46.
    Afshar, A., Marino, M.A., Saadatpour, M.: Fuzzy TOPSIS multicriteria decision analysis applied to Karun reservoirs system. Water Resour. Manag. 25, 545–563 (2011)CrossRefGoogle Scholar
  47. 47.
    García-Cascales, M.S., Lamata, M.T.: Multi-criteria analysis for a maintenance management problem in an engine factory: rational choice. J. Intell. Manuf. 22, 779–788 (2011)CrossRefGoogle Scholar
  48. 48.
    Arslan, M., Cunkas, M.: Performance evaluation of sugar plants by fuzzy technique for order performance by similarity to ideal solution (TOPSIS). Cybern. Syst. 43, 529–548 (2012)CrossRefGoogle Scholar
  49. 49.
    Ceballos, B., Lamata, M.T., Pelta, D.A.: Fuzzy multicriteria decision-making methods: a comparative analysis. Int. J. Intell. Syst. 32(7), 722–738 (2017)CrossRefGoogle Scholar
  50. 50.
    Cables, E., Garcia-Cascales, M.S., Lamata, M.T.: The LTOPSIS: an alternative to TOPSIS decision-making approach for linguistic variables. Expert Syst. Appl. 39, 2119–2126 (2012)CrossRefGoogle Scholar
  51. 51.
    Garcia-Cascales, M.S., Lamata, M.T.: Selection of a cleaning system for engine maintenance based on the analytic hierarchy process. Comput. Ind. Eng. 56(4), 1442–1451 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Elio H. Cables
    • 1
    Email author
  • María Teresa Lamata
    • 2
  • José Luis Verdegay
    • 2
  1. 1.Universidad Antonio NariñoBogotáColombia
  2. 2.Universidad de GranadaGranadaSpain

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