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Probabilistic OWA distances applied to asset management

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Abstract

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.

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References

  • Alfaro-García VG, Merigó JM, Gil-Lafuente AM, Kacprzyk J (2018) Logarithmic aggregation operators and distance measures. Int J Intell Syst 33:1488–1506

    Article  Google Scholar 

  • Aggarwal M (2015) Generalized compensative weighted averaging aggregation operators. Comput Ind Eng 87:81–90

    Article  Google Scholar 

  • Avilés-Ochoa E, León-Castro E, Pérez-Arellano LA, Merigó JM (2018) Government transparency measurement through prioritized distance operators. J Intell Fuzzy Syst 34:2783–2794

    Article  Google Scholar 

  • Bargiela A, Pedrycz W (2003) Granular computing: an introduction. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Berlin

    MATH  Google Scholar 

  • Beliakov G, Bustince-Sola H, Calvo-Sánchez T (2016) A practical guide to averaging functions. Springer, Heidelberg

    Book  Google Scholar 

  • Belles-Sampera J, Merigó JM, Guillén M, Santolino M (2014) Indicators for the characterization of discrete Choquet integrals. Inf Sci 267:201–216

    Article  MathSciNet  MATH  Google Scholar 

  • Blanco-Mesa F, Merigó JM, Kacprzyk J (2016) Bonferroni means with distance measures and the adequacy coefficient in entrepreneurial group theory. Knowl Based Syst 111:217–227

    Article  Google Scholar 

  • Blanco-Mesa F, Merigó JM, Gil-Lafuente AM (2017) Fuzzy decision making: a bibliometric-based review. J Intell Fuzzy Syst 32:2033–2050

    Article  Google Scholar 

  • Casanovas M, Torres-Martínez A, Merigó JM (2016) Decision making in reinsurance with induced OWA operators and Minkowski distances. Cybern Syst 47:460–477

    Article  Google Scholar 

  • Emrouznejad A, Marra M (2014) Ordered weighted averaging operators 1988–2014. A citation based literature survey. Int J Intell Syst 29:994–1014

    Article  Google Scholar 

  • Engemann KJ, Filev DP, Yager RR (1996) Modelling decision making using immediate probabilities. Int J Gen Syst 24:281–294

    Article  MATH  Google Scholar 

  • Figueira J, Greco S, Ehrgott M (2005) Multiple criteria decision analysis: state of the art surveys. Springer, Boston

    Book  MATH  Google Scholar 

  • Fodor J, Marichal JL, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3(2):236–240

    Article  Google Scholar 

  • Gao JW, Liu HH (2017) Generalized ordered weighted reference dependent utility aggregation operators and their applications to group decision-making. Group Decis Negot 26:1173–1207

    Article  Google Scholar 

  • Gil-Aluja J (1999) Elements for a theory of decision under uncertainty. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Grabisch M, Marichal JL, Mesiar R, Pap E (2011) Aggregation functions: means. Inf Sci 181:1–22

    Article  MathSciNet  MATH  Google Scholar 

  • Hamming RW (1950) Error-detecting and error-correcting codes. Bell Syst Tech J 29:147–160

    Article  MathSciNet  Google Scholar 

  • He XR, Wu YY, Yu D, Merigó JM (2017) Exploring the ordered weighted averaging operator knowledge domain: a bibliometric analysis. Int J Intell Syst 32:1151–1166

    Article  Google Scholar 

  • Kacprzyk J, Pedrycz W (2015) Handbook of computational intelligence. Springer, Berlin

    Book  MATH  Google Scholar 

  • Kahraman C, Onar SC, Oztaysi B (2015) Fuzzy multicriteria decision-making: a literature review. Int J Comput Intell Syst 8:637–666

    Article  MATH  Google Scholar 

  • Kaufmann A (1975) Introduction to the theory of fuzzy subsets. Academic Press, New York

    MATH  Google Scholar 

  • Laengle S, Loyola G, Merigó JM (2017) Mean-variance portfolio selection with the ordered weighted average. IEEE Trans Fuzzy Syst 25:350–362

    Article  Google Scholar 

  • León-Castro E, Avilés-Ochoa E, Merigó JM, Gil-Lafuente AM (2018) Heavy moving averages and their application in econometric forecasting. Cybern Syst 49:26–43

    Article  Google Scholar 

  • Liao HC, Xu ZS, Zeng XJ, Merigó JM (2015) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl Based Syst 76:127–138

    Article  Google Scholar 

  • Liu PD, Liu X (2017) Multi-attribute group decision-making method based on cloud distance operators with linguistic information. Int J Fuzzy Syst 19:1011–1024

    Article  MathSciNet  Google Scholar 

  • 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 299:1–25

    Article  MathSciNet  MATH  Google Scholar 

  • 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 25:103–126

    Article  Google Scholar 

  • Maldonado S, Merigó JM, Miranda J (2018) Redefining support vector machines with the ordered weighted average. Knowl Based Syst 148:41–46

    Article  Google Scholar 

  • Merigó JM (2010) Fuzzy decision making with immediate probabilities. Comput Ind Eng 58:651–657

    Article  Google Scholar 

  • Merigó JM (2011) A unified model between the weighted average and the induced OWA operator. Expert Syst Appl 38:11560–11572

    Article  Google Scholar 

  • Merigó JM (2012) Probabilities in the OWA operator. Expert Syst Appl 39(13):11456–11467

    Article  Google Scholar 

  • Merigó JM, Casanovas M (2011a) Decision making with distance measures and induced aggregation operators. Comput Ind Eng 60:66–76

    Article  MATH  Google Scholar 

  • Merigó JM, Casanovas M (2011b) A new Minkowski distance based on induced aggregation operators. Int J Comput Intell Syst 4(2):123–133

    Article  Google Scholar 

  • Merigó JM, Gil-Lafuente AM (2009) The induced generalized OWA operator. Inf Sci 179:729–741

    Article  MathSciNet  MATH  Google Scholar 

  • Merigó JM, Gil-Lafuente AM (2010) New decision-making techniques and their application in the selection of financial products. Inf Sci 180:2085–2094

    Article  MathSciNet  MATH  Google Scholar 

  • Merigó JM, Yager RR (2013) Generalized moving averages, distance measures and OWA operators. Int J Uncertain Fuzziness Knowl Based Syst 21:533–559

    Article  MathSciNet  MATH  Google Scholar 

  • Merigó JM, Lobato-Carral C, Carrilero-Castillo A (2012) Decision making in the European Union under risk and uncertainty. Eur J Int Manag 6:590–609

    Article  Google Scholar 

  • Merigó JM, Palacios-Marqués D, Zeng SZ (2016) Subjective and objective information in linguistic multi-criteria group decision making. Eur J Oper Res 248:522–531

    Article  MathSciNet  MATH  Google Scholar 

  • Merigó JM, Palacios-Marqués D, Soto-Acosta P (2017) Distance measures, weighted averages, OWA operators and Bonferroni means. Appl Soft Comput 50:356–366

    Article  Google Scholar 

  • Scherger V, Terceño A, Vigier H (2017) The OWA distance operator and its application in business failure. Kybernetes 46:114–130

    Article  Google Scholar 

  • Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423

    Article  MathSciNet  MATH  Google Scholar 

  • Torra V (1997) The weighted OWA operator. Int J Intell Syst 12:153–166

    Article  MATH  Google Scholar 

  • Xian SD, Sun WJ (2014) Fuzzy linguistic Euclidean OWA distance operator and its application in group linguistic decision making. Int J Intell Syst 29:478–491

    Article  Google Scholar 

  • 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 19:325–335

    Article  MathSciNet  Google Scholar 

  • Xu ZS, Chen J (2008) Ordered weighted distance measure. J Syst Sci Syst Eng 17:432–445

    Article  Google Scholar 

  • Xu ZS, Da QL (2003) An overview of operators for aggregating information. Int J Intell Syst 18:953–969

    Article  MATH  Google Scholar 

  • 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 32:739–753

    Article  Google Scholar 

  • Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern B 18:183–190

    Article  MATH  Google Scholar 

  • Yager RR (1993) Families of OWA operators. Fuzzy Sets Syst 59:125–148

    Article  MathSciNet  MATH  Google Scholar 

  • Yager RR (1996) Constrained OWA aggregation. Fuzzy Sets Syst 81:89–101

    Article  MathSciNet  Google Scholar 

  • Yager RR (1998) Including importances in OWA aggregation using fuzzy systems modelling. IEEE Trans Fuzzy Syst 6:286–294

    Article  Google Scholar 

  • Yager RR (2002) Heavy OWA operators. Fuzzy Optim Decis Mak 1:379–397

    Article  MathSciNet  MATH  Google Scholar 

  • Yager RR (2004) Generalized OWA aggregation operators. Fuzzy Optim Decis Mak 3:93–107

    Article  MathSciNet  MATH  Google Scholar 

  • Yager RR, Engemann KJ, Filev DP (1995) On the concept of immediate probabilities. Int J Intell Syst 10:373–397

    Article  MATH  Google Scholar 

  • Yager RR, Kacprzyk J, Beliakov G (2011) Recent developments on the ordered weighted averaging operators: theory and practice. Springer, Berlin

    Book  Google Scholar 

  • Yu D (2015) A scientometrics review on aggregation operator research. Scientometrics 105:115–133

    Article  Google Scholar 

  • Zadeh LA (2005) Toward a generalized theory of uncertainty (GTU): an outline. Inf Sci 172:1–40

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA, Abbasov AM, Yager RR, Shahbazova SN, Reformat MZ (2014) Recent developments and new directions in soft computing. Springer, Switzerland

    Book  MATH  Google Scholar 

  • Zeng SZ (2016) An extension of OWAD operator and its application to uncertain multiple-attribute group decision-making. Cybern Syst 47:363–375

    Article  Google Scholar 

  • Zeng SZ, Su W (2012b) Linguistic induced generalized aggregation distance operators and their application to decision making. Econ Comput Econ Cybern Stud Res 46:155–172

    Google Scholar 

  • Zeng SZ, Su WH, Le A (2012a) Fuzzy generalized ordered weighted averaging distance operator and its application to decision making. Int J Fuzzy Syst 14:402–412

    MathSciNet  Google Scholar 

  • Zeng SZ, Merigó JM, Su WH (2013) The uncertain probabilistic OWA distance operator and its application in group decision making. Appl Math Model 37:6266–6275

    Article  MathSciNet  Google Scholar 

  • 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 32:11–22

    Article  MATH  Google Scholar 

  • 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 25:266–276

    Article  Google Scholar 

  • 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 19:715–730

    Article  Google Scholar 

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Management Control and Information Systems, School of Economics and Business, University of Chile, Av. Diagonal Paraguay 257, 8330015, Santiago, Chile

    José M. Merigó

  2. Biomedical Technology Department, College of Applied Medical Sciences, King Saud University, Riyadh, Saudi Arabia

    José M. Merigó & Nabil Alrajeh

  3. School of Mathematical Sciences, Anhui University, 230601, Hefei, Anhui, China

    Ligang Zhou

  4. Business School, Nanjing Audit University, 211815, Nanjing, China

    Dejian Yu

  5. Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh, Saudi Arabia

    Khalid Alnowibet

Authors
  1. José M. Merigó
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  2. Ligang Zhou
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  3. Dejian Yu
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  4. Nabil Alrajeh
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  5. Khalid Alnowibet
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Correspondence to José M. Merigó.

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Communicated by C. Kahraman.

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Merigó, J.M., Zhou, L., Yu, D. et al. Probabilistic OWA distances applied to asset management. Soft Comput 22, 4855–4878 (2018). https://doi.org/10.1007/s00500-018-3263-1

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