Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 642165, 19 pages
http://dx.doi.org/10.1155/2014/642165
Research Article

Induced Unbalanced Linguistic Ordered Weighted Average and Its Application in Multiperson Decision Making

1Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda Països Catalans 26, 43007 Tarragona, Catalonia, Spain
2MBS Decision Solutions, Manchester Business School Decision and Cognitive Sciences Research Centre (DCSRC), The University of Manchester, Booth Street West, Manchester M15 4PB, UK

Received 23 February 2014; Accepted 10 June 2014; Published 17 July 2014

Academic Editor: Francisco J. Cabrerizo

Copyright © 2014 Lucas Marin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. Torra and Y. Narukawa, Modeling Decisions: Information Fusion and Aggregation Operators, Springer, Berlin, Germany, 2007.
  2. G. Beliakov, A. Pradera, and T. Calvo, Aggregation Functions: A Guide for Practitioners, Springer, Berlin, Germany, 2007.
  3. R. R. Yager, “On ordered weighted averaging aggregation operators in multicriteria decision making,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, no. 1, pp. 183–190, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. R. Yager and D. P. Filev, “Induced ordered weighted averaging operators,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 29, no. 2, pp. 141–150, 1999. View at Publisher · View at Google Scholar · View at Scopus
  5. F. J. Cabrerizo, I. J. Pérez, and E. Herrera-Viedma, “Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information,” Knowledge-Based Systems, vol. 23, no. 2, pp. 169–181, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. J. M. Merigó and M. Casanovas, “The uncertain induced quasi-arithmetic OWA operator,” International Journal of Intelligent Systems, vol. 26, no. 1, pp. 1–24, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. P. Bonissone and K. Decker, “Selecting uncertainty calculi and granularity: an experiment in trading-off precision and complexity,” in Proceedings of the 1st Annual Conference on Uncertainty in Artificial Intelligence (UAI '85), L. N. Kanal and J. F. Lemmer, Eds., pp. 217–248, New York, NY, USA, 1985.
  8. R. R. Yager, “Measures of specificity over continuous spaces under similarity relations,” Fuzzy Sets and Systems, vol. 159, no. 17, pp. 2193–2210, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Z. Xu, “On generalized induced linguistic aggregation operators,” International Journal of General Systems, vol. 35, no. 1, pp. 17–28, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. Z. S. Xu, “An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations,” Decision Support Systems, vol. 41, no. 2, pp. 488–499, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. Z. S. Xu and Q. L. Da, “An overview of operators for aggregating information,” International Journal of Intelligent Systems, vol. 18, no. 9, pp. 953–969, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. F. Herrera and L. Martínez, “A 2-tuple fuzzy linguistic representation model for computing with words,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 6, pp. 746–752, 2000. View at Google Scholar
  13. Z. S. Xu, “Linguistic aggregation operators: an overview,” in Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, H. Bustince, F. Herrera, and J. Montero, Eds., pp. 163–181, Springer, Berlin, Germany, 2008. View at Google Scholar
  14. F. Herrera, E. Herrera-Viedma, and L. Martínez, “A fuzzy linguistic methodology to deal with unbalanced linguistic term sets,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 2, pp. 354–370, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-I,” vol. 8, no. 3, pp. 199–249, 1975. View at Google Scholar · View at MathSciNet · View at Scopus
  16. Z. S. Xu, “An interactive approach to multiple attribute group decision making with multigranular uncertain linguistic information,” Group Decision and Negotiation, vol. 18, no. 2, pp. 119–145, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Isern, L. Marin, A. Valls, and A. Moreno, “The unbalanced linguistic ordered weighted averaging operator,” in Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ '10), pp. 1–8, Barcelona, Spain, July 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. Z. Xu, “Multi-period multi-attribute group decision-making under linguistic assessments,” International Journal of General Systems, vol. 38, no. 8, pp. 823–850, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. X. Yu, Z. S. Xu, and X. Zhang, “Uniformization of multigranular linguistic labels and their application to group decision making,” Journal of Systems Science and Systems Engineering, vol. 19, no. 3, pp. 257–276, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. F. Herrera, E. Herrera-Viedma, and J. L. Verdegay, “Direct approach processes in group decision making using linguistic OWA operators,” Fuzzy Sets and Systems, vol. 79, no. 2, pp. 175–190, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Z. Xu, “Induced uncertain linguistic OWA operators applied to group decision making,” Information Fusion, vol. 7, no. 2, pp. 231–238, 2006. View at Publisher · View at Google Scholar · View at Scopus
  22. J. M. Merigó and M. Casanovas, “Decision-making with distance measures and induced aggregation operators,” Computers and Industrial Engineering, vol. 60, no. 1, pp. 66–76, 2011. View at Publisher · View at Google Scholar · View at Scopus
  23. X. Liu and S. Han, “Orness and parameterized RIM quantifier aggregation with OWA operators: a summary,” International Journal of Approximate Reasoning, vol. 48, no. 1, pp. 77–97, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. Z. S. Xu, “An overview of methods for determining OWA weights,” International Journal of Intelligent Systems, vol. 20, no. 8, pp. 843–865, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. R. R. Yager, “Quantifier guided aggregation using OWA operators,” International Journal of Intelligent Systems, vol. 11, no. 1, pp. 49–73, 1996. View at Publisher · View at Google Scholar · View at Scopus
  26. J. Kacprzyk, “Group decision making with a fuzzy linguistic majority,” Fuzzy Sets and Systems, vol. 18, no. 2, pp. 105–118, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. J. M. Merigó and M. Casanovas, “The uncertain generalized OWA operator and its application to financial decision making,” International Journal of Information Technology and Decision Making, vol. 10, no. 2, pp. 221–230, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. G. Beliakov and S. James, “Induced ordered weighted averaging operators,” in Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice, R. R. Yager, J. Kacprzyk, and G. Beliakov, Eds., vol. 265, pp. 29–47, Springer, Berlin, Germany, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. G. Pasi and R. R. Yager, “Modeling the concept of majority opinion in group decision making,” Information Sciences, vol. 176, no. 4, pp. 390–414, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. J. M. Merigó and M. Casanovas, “Decision making with distance measures and linguistic aggregation operators,” International Journal of Fuzzy Systems, vol. 12, no. 3, pp. 190–198, 2010. View at Google Scholar · View at Scopus
  31. G. Wei, X. Zhao, and R. Lin, “Some induced aggregating operators with fuzzy number intuitionistic fuzzy information and their applications to group decision making,” International Journal of Computational Intelligence Systems, vol. 3, no. 1, pp. 84–95, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. M. Xia and Z. S. Xu, “Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment,” Information Fusion, vol. 13, no. 1, pp. 31–47, 2012. View at Publisher · View at Google Scholar · View at Scopus
  33. B. Arfi, “Linguistic fuzzy-logic decision-making process,” in Linguistic Fuzzy Logic Methods in Social Sciences, pp. 43–62, Springer, Berlin, Germany, 2010. View at Google Scholar
  34. R. Wang and S. J. Chuu, “Group decision-making using a fuzzy linguistic approach for evaluating the flexibility in a manufacturing system,” European Journal of Operational Research, vol. 154, no. 3, pp. 563–572, 2004. View at Publisher · View at Google Scholar · View at Scopus
  35. Z. Pei, Y. Xu, D. Ruan, and K. Qin, “Extracting complex linguistic data summaries from personnel database via simple linguistic aggregations,” Information Sciences, vol. 179, no. 14, pp. 2325–2332, 2009. View at Publisher · View at Google Scholar
  36. E. Herrera-Viedma, F. J. Cabrerizo, I. J. Pérez, M. J. Cobo, S. Alonso, and F. Herrera, “Applying linguistic OWA operators in consensus models under unbalanced linguistic information,” in Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice, R. Yager, J. Kacprzyk, and G. Beliakov, Eds., vol. 265 of Studies in Fuzziness and Soft Computing, pp. 167–186, Springer, Berlin, Germany, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. F. Herrera and L. Martínez, “A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 31, no. 2, pp. 227–234, 2001. View at Publisher · View at Google Scholar · View at Scopus
  38. L. Garmendia, R. R. Yager, E. Trillas, and A. Salvador, “A t-norm based specificity for fuzzy sets on compact domains,” International Journal of General Systems, vol. 35, no. 6, pp. 687–698, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  39. G. J. Klir, “Developments in uncertainty-based information,” in Advances in Computers, C. Y. Marshall, Ed., pp. 255–332, Elsevier, New York, NY, USA, 1993. View at Google Scholar
  40. R. R. Yager, “Ordinal measures of specificity,” International Journal of General Systems, vol. 17, no. 1, pp. 57–72, 1990. View at Publisher · View at Google Scholar
  41. A. de Luca and S. Termini, “A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory,” Information and Computation, vol. 20, pp. 301–312, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  42. G. J. Klir and B. Yuan, “On nonspecificity of fuzzy sets with continuous membership functions,” in Proceedings of the 15th IEEE International Conference on Systems, Man and Cybernetics (SMC '95), pp. 25–29, Vancouver, Canada, October 1995. View at Scopus
  43. R. R. Yager, “Including importances in OWA aggregations using fuzzy systems modeling,” IEEE Transactions on Fuzzy Systems, vol. 6, no. 2, pp. 286–294, 1998. View at Publisher · View at Google Scholar · View at Scopus
  44. R. R. Yager, “On the dispersion measure of {OWA} operators,” Information Sciences, vol. 179, no. 22, pp. 3908–3919, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  45. F. Chiclana, E. Herrera-Viedma, F. Herrera, and S. Alonso, “Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations,” European Journal of Operational Research, vol. 182, no. 1, pp. 383–399, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  46. A. Valls, J. Pijuan, M. Schuhmacher, A. Passuello, M. Nadal, and J. Sierra, “Preference assessment for the management of sewage sludge application on agricultural soils,” International Journal of Multicriteria Decision Making, vol. 1, pp. 4–24, 2010. View at Publisher · View at Google Scholar
  47. J. Pijuan, A. Valls, A. Passuello, and M. Schuhmacher, “Evaluating the impact of sewage sludge application on agricultural soils,” in 15th Congreso español sobre tecnologías y lógica fuzzy (ESTYLF '10), pp. 369–374, Huelva, Spain, 2010.
  48. T. Kaya and C. Kahraman, “An integrated fuzzy AHP-ELECTRE methodology for environmental impact assessment,” Expert Systems with Applications, vol. 38, no. 7, pp. 8553–8562, 2011. View at Publisher · View at Google Scholar · View at Scopus
  49. A. Passuello, M. Schuhmacher, M. Mari, O. Cadiach, and M. Nadal, “A spatial multicriteria decision analysis to manage sewage sludge application on agriculatural soils,” in Environmental Modeling for Susteinable Regional Development: System Approaches and Advanced Methods, V. Olej, I. Obršálová, and J. Krupka, Eds., pp. 221–241, 2011. View at Google Scholar
  50. R. R. Yager, “A game theoretic approach to decision making under uncertainty,” International Journal of Intelligent Systems in Accounting, Finance and Management, vol. 8, no. 2, pp. 131–143, 1999. View at Publisher · View at Google Scholar
  51. V. Torra, “The WOWA operator: a review,” in Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice, pp. 17–28, Springer, Berlin, Germany, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  52. F. Herrera, E. Herrera-Viedma, and J. L. Verdegay, “A model of consensus in group decision making under linguistic assessments,” Fuzzy Sets and Systems, vol. 78, no. 1, pp. 73–87, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  53. L. Marin, A. Moreno, and D. Isern, “Automatic preference learning on numeric and multi-valued categorical attributes,” Knowledge-Based Systems, vol. 56, no. 1, pp. 201–215, 2014. View at Google Scholar
  54. L. Marin, D. Isern, and A. Moreno, “Dynamic adaptation of numerical attributes in a user profile,” Applied Intelligence, vol. 39, no. 2, pp. 421–437, 2013. View at Publisher · View at Google Scholar · View at Scopus
  55. A. Moreno, A. Valls, D. Isern, L. Marin, and J. Borràs, “SigTur/E-Destination: ontology-based personalized recommendation of Tourism and Leisure Activities,” Engineering Applications of Artificial Intelligence, vol. 26, no. 1, pp. 633–651, 2013. View at Publisher · View at Google Scholar · View at Scopus