Soft Computing

, Volume 22, Issue 15, pp 4855–4878 | Cite as

Probabilistic OWA distances applied to asset management

  • José M. MerigóEmail author
  • Ligang Zhou
  • Dejian Yu
  • Nabil Alrajeh
  • Khalid Alnowibet


Average distances are widely used in many fields for calculating the distances between two sets of elements. This paper presents several new average distances by using the ordered weighted average, the probability and the weighted average. First, the work presents the probabilistic ordered weighted averaging weighted average distance (POWAWAD) operator. POWAWAD is a new aggregation operator that uses distance measures in a unified framework between the probability, the weighted average and the ordered weighted average (OWA) operator that considers the degree of importance that each concept has in the aggregation. The POWAWAD operator includes a wide range of particular cases including the maximum distance, the minimum distance, the normalized Hamming distance, the weighted Hamming distance and the ordered weighted average distance (OWAD). The article also presents further generalizations by using generalized and quasi-arithmetic means forming the generalized probabilistic ordered weighted averaging weighted average distance (GPOWAWAD) operator and the quasi-POWAWAD operator. The study ends analysing the applicability of this new approach in the calculation of the average fixed assets. Particularly, the work focuses on measuring the average distances between the ideal percentage of fixed assets that the companies of a specific country should have versus the real percentage of fixed assets they have. The illustrative example focuses on the Asian market.


Distance measures Aggregation operators OWA operator Average fixed asset Group decision-making 



We would like to thank the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Distinguished Scientist Fellowship Programme from King Saud University (Saudi Arabia) and the Chilean Government through the Fondecyt Regular Programme (Project Number 1160286) is gratefully acknowledged.

Compliance with ethical standards

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Conflict of interest

The authors declare that they have no conflict of interests.


  1. Alfaro-García VG, Merigó JM, Gil-Lafuente AM, Kacprzyk J (2018) Logarithmic aggregation operators and distance measures. Int J Intell Syst 33:1488–1506CrossRefGoogle Scholar
  2. Aggarwal M (2015) Generalized compensative weighted averaging aggregation operators. Comput Ind Eng 87:81–90CrossRefGoogle Scholar
  3. Avilés-Ochoa E, León-Castro E, Pérez-Arellano LA, Merigó JM (2018) Government transparency measurement through prioritized distance operators. J Intell Fuzzy Syst 34:2783–2794CrossRefGoogle Scholar
  4. Bargiela A, Pedrycz W (2003) Granular computing: an introduction. Kluwer Academic Publishers, DordrechtCrossRefzbMATHGoogle Scholar
  5. Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, BerlinzbMATHGoogle Scholar
  6. Beliakov G, Bustince-Sola H, Calvo-Sánchez T (2016) A practical guide to averaging functions. Springer, HeidelbergCrossRefGoogle Scholar
  7. Belles-Sampera J, Merigó JM, Guillén M, Santolino M (2014) Indicators for the characterization of discrete Choquet integrals. Inf Sci 267:201–216MathSciNetCrossRefzbMATHGoogle Scholar
  8. Blanco-Mesa F, Merigó JM, Kacprzyk J (2016) Bonferroni means with distance measures and the adequacy coefficient in entrepreneurial group theory. Knowl Based Syst 111:217–227CrossRefGoogle Scholar
  9. Blanco-Mesa F, Merigó JM, Gil-Lafuente AM (2017) Fuzzy decision making: a bibliometric-based review. J Intell Fuzzy Syst 32:2033–2050CrossRefGoogle Scholar
  10. Casanovas M, Torres-Martínez A, Merigó JM (2016) Decision making in reinsurance with induced OWA operators and Minkowski distances. Cybern Syst 47:460–477CrossRefGoogle Scholar
  11. Emrouznejad A, Marra M (2014) Ordered weighted averaging operators 1988–2014. A citation based literature survey. Int J Intell Syst 29:994–1014CrossRefGoogle Scholar
  12. Engemann KJ, Filev DP, Yager RR (1996) Modelling decision making using immediate probabilities. Int J Gen Syst 24:281–294CrossRefzbMATHGoogle Scholar
  13. Figueira J, Greco S, Ehrgott M (2005) Multiple criteria decision analysis: state of the art surveys. Springer, BostonCrossRefzbMATHGoogle Scholar
  14. Fodor J, Marichal JL, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3(2):236–240CrossRefGoogle Scholar
  15. Gao JW, Liu HH (2017) Generalized ordered weighted reference dependent utility aggregation operators and their applications to group decision-making. Group Decis Negot 26:1173–1207CrossRefGoogle Scholar
  16. Gil-Aluja J (1999) Elements for a theory of decision under uncertainty. Kluwer Academic Publishers, DordrechtCrossRefzbMATHGoogle Scholar
  17. Grabisch M, Marichal JL, Mesiar R, Pap E (2011) Aggregation functions: means. Inf Sci 181:1–22MathSciNetCrossRefzbMATHGoogle Scholar
  18. Hamming RW (1950) Error-detecting and error-correcting codes. Bell Syst Tech J 29:147–160MathSciNetCrossRefGoogle Scholar
  19. He XR, Wu YY, Yu D, Merigó JM (2017) Exploring the ordered weighted averaging operator knowledge domain: a bibliometric analysis. Int J Intell Syst 32:1151–1166CrossRefGoogle Scholar
  20. Kacprzyk J, Pedrycz W (2015) Handbook of computational intelligence. Springer, BerlinCrossRefzbMATHGoogle Scholar
  21. Kahraman C, Onar SC, Oztaysi B (2015) Fuzzy multicriteria decision-making: a literature review. Int J Comput Intell Syst 8:637–666CrossRefzbMATHGoogle Scholar
  22. Kaufmann A (1975) Introduction to the theory of fuzzy subsets. Academic Press, New YorkzbMATHGoogle Scholar
  23. Laengle S, Loyola G, Merigó JM (2017) Mean-variance portfolio selection with the ordered weighted average. IEEE Trans Fuzzy Syst 25:350–362CrossRefGoogle Scholar
  24. León-Castro E, Avilés-Ochoa E, Merigó JM, Gil-Lafuente AM (2018) Heavy moving averages and their application in econometric forecasting. Cybern Syst 49:26–43CrossRefGoogle Scholar
  25. Liao HC, Xu ZS, Zeng XJ, Merigó JM (2015) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl Based Syst 76:127–138CrossRefGoogle Scholar
  26. Liu PD, Liu X (2017) Multi-attribute group decision-making method based on cloud distance operators with linguistic information. Int J Fuzzy Syst 19:1011–1024MathSciNetCrossRefGoogle Scholar
  27. Liu JP, Chen HY, Xu Q, Zhou LG, Tao ZF (2016a) Generalized ordered modular averaging operator and its application to group decision making. Fuzzy Sets Syst 299:1–25MathSciNetCrossRefzbMATHGoogle Scholar
  28. Liu PD, He L, Yu XC (2016b) Generalized hybrid aggregation operators based on the 2-dimension uncertain linguistic information for multiple attribute group decision making. Group Decis Negot 25:103–126CrossRefGoogle Scholar
  29. Maldonado S, Merigó JM, Miranda J (2018) Redefining support vector machines with the ordered weighted average. Knowl Based Syst 148:41–46CrossRefGoogle Scholar
  30. Merigó JM (2010) Fuzzy decision making with immediate probabilities. Comput Ind Eng 58:651–657CrossRefGoogle Scholar
  31. Merigó JM (2011) A unified model between the weighted average and the induced OWA operator. Expert Syst Appl 38:11560–11572CrossRefGoogle Scholar
  32. Merigó JM (2012) Probabilities in the OWA operator. Expert Syst Appl 39(13):11456–11467CrossRefGoogle Scholar
  33. Merigó JM, Casanovas M (2011a) Decision making with distance measures and induced aggregation operators. Comput Ind Eng 60:66–76CrossRefzbMATHGoogle Scholar
  34. Merigó JM, Casanovas M (2011b) A new Minkowski distance based on induced aggregation operators. Int J Comput Intell Syst 4(2):123–133CrossRefGoogle Scholar
  35. Merigó JM, Gil-Lafuente AM (2009) The induced generalized OWA operator. Inf Sci 179:729–741MathSciNetCrossRefzbMATHGoogle Scholar
  36. Merigó JM, Gil-Lafuente AM (2010) New decision-making techniques and their application in the selection of financial products. Inf Sci 180:2085–2094MathSciNetCrossRefzbMATHGoogle Scholar
  37. Merigó JM, Yager RR (2013) Generalized moving averages, distance measures and OWA operators. Int J Uncertain Fuzziness Knowl Based Syst 21:533–559MathSciNetCrossRefzbMATHGoogle Scholar
  38. Merigó JM, Lobato-Carral C, Carrilero-Castillo A (2012) Decision making in the European Union under risk and uncertainty. Eur J Int Manag 6:590–609CrossRefGoogle Scholar
  39. Merigó JM, Palacios-Marqués D, Zeng SZ (2016) Subjective and objective information in linguistic multi-criteria group decision making. Eur J Oper Res 248:522–531MathSciNetCrossRefzbMATHGoogle Scholar
  40. Merigó JM, Palacios-Marqués D, Soto-Acosta P (2017) Distance measures, weighted averages, OWA operators and Bonferroni means. Appl Soft Comput 50:356–366CrossRefGoogle Scholar
  41. Scherger V, Terceño A, Vigier H (2017) The OWA distance operator and its application in business failure. Kybernetes 46:114–130CrossRefGoogle Scholar
  42. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423MathSciNetCrossRefzbMATHGoogle Scholar
  43. Torra V (1997) The weighted OWA operator. Int J Intell Syst 12:153–166CrossRefzbMATHGoogle Scholar
  44. Xian SD, Sun WJ (2014) Fuzzy linguistic Euclidean OWA distance operator and its application in group linguistic decision making. Int J Intell Syst 29:478–491CrossRefGoogle Scholar
  45. Xian SD, Sun WJ, Xu SH, Gao YY (2016) Fuzzy linguistic induced OWA Minkowski distance operator and its application in group decision making. Pattern Anal Appl 19:325–335MathSciNetCrossRefGoogle Scholar
  46. Xu ZS, Chen J (2008) Ordered weighted distance measure. J Syst Sci Syst Eng 17:432–445CrossRefGoogle Scholar
  47. Xu ZS, Da QL (2003) An overview of operators for aggregating information. Int J Intell Syst 18:953–969CrossRefzbMATHGoogle Scholar
  48. Xue WT, Xian SD, Dong YF (2017) A novel intuitionistic fuzzy induced ordered weighted Euclidean distance operator and its application for group decision making. Int J Intell Syst 32:739–753CrossRefGoogle Scholar
  49. Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern B 18:183–190CrossRefzbMATHGoogle Scholar
  50. Yager RR (1993) Families of OWA operators. Fuzzy Sets Syst 59:125–148MathSciNetCrossRefzbMATHGoogle Scholar
  51. Yager RR (1996) Constrained OWA aggregation. Fuzzy Sets Syst 81:89–101MathSciNetCrossRefGoogle Scholar
  52. Yager RR (1998) Including importances in OWA aggregation using fuzzy systems modelling. IEEE Trans Fuzzy Syst 6:286–294CrossRefGoogle Scholar
  53. Yager RR (2002) Heavy OWA operators. Fuzzy Optim Decis Mak 1:379–397MathSciNetCrossRefzbMATHGoogle Scholar
  54. Yager RR (2004) Generalized OWA aggregation operators. Fuzzy Optim Decis Mak 3:93–107MathSciNetCrossRefzbMATHGoogle Scholar
  55. Yager RR, Engemann KJ, Filev DP (1995) On the concept of immediate probabilities. Int J Intell Syst 10:373–397CrossRefzbMATHGoogle Scholar
  56. Yager RR, Kacprzyk J, Beliakov G (2011) Recent developments on the ordered weighted averaging operators: theory and practice. Springer, BerlinCrossRefGoogle Scholar
  57. Yu D (2015) A scientometrics review on aggregation operator research. Scientometrics 105:115–133CrossRefGoogle Scholar
  58. Zadeh LA (2005) Toward a generalized theory of uncertainty (GTU): an outline. Inf Sci 172:1–40MathSciNetCrossRefzbMATHGoogle Scholar
  59. Zadeh LA, Abbasov AM, Yager RR, Shahbazova SN, Reformat MZ (2014) Recent developments and new directions in soft computing. Springer, SwitzerlandCrossRefzbMATHGoogle Scholar
  60. Zeng SZ (2016) An extension of OWAD operator and its application to uncertain multiple-attribute group decision-making. Cybern Syst 47:363–375CrossRefGoogle Scholar
  61. Zeng SZ, Su W (2012b) Linguistic induced generalized aggregation distance operators and their application to decision making. Econ Comput Econ Cybern Stud Res 46:155–172Google Scholar
  62. Zeng SZ, Su WH, Le A (2012a) Fuzzy generalized ordered weighted averaging distance operator and its application to decision making. Int J Fuzzy Syst 14:402–412MathSciNetGoogle Scholar
  63. Zeng SZ, Merigó JM, Su WH (2013) The uncertain probabilistic OWA distance operator and its application in group decision making. Appl Math Model 37:6266–6275MathSciNetCrossRefGoogle Scholar
  64. Zeng SZ, Merigó JM, Palacios-Marqués D, Jin HH, Gu FJ (2017) Intuitionistic fuzzy induced ordered weighted averaging distance operator and its application to decision making. J Intell Fuzzy Syst 32:11–22CrossRefzbMATHGoogle Scholar
  65. Zhou LG, Wu JX, Chen HY (2014) Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision making. Appl Soft Comput 25:266–276CrossRefGoogle Scholar
  66. Zhou LG, Tao ZF, Chen HY, Liu JP (2015) Generalized ordered weighted logarithmic harmonic averaging operators and their applications to group decision making. Soft Comput 19:715–730CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Management Control and Information Systems, School of Economics and BusinessUniversity of ChileSantiagoChile
  2. 2.Biomedical Technology Department, College of Applied Medical SciencesKing Saud UniversityRiyadhSaudi Arabia
  3. 3.School of Mathematical SciencesAnhui UniversityHefeiChina
  4. 4.Business SchoolNanjing Audit UniversityNanjingChina
  5. 5.Department of Statistics and Operations Research, College of ScienceKing Saud UniversityRiyadhSaudi Arabia

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