Abstract
A moving average is an average that aggregates a subset of variables from the set and moves across the sample. It is widely used in time-series forecasting. This paper studies the use of moving averages in some representative aggregation operators. The ordered weighted averaging weighted moving averaging (OWAWMA) operator is introduced. It is a new approach based on the use of the moving average in a unified model between the weighted average and the ordered weighted average. Its main advantage is that it provides a parameterized family of moving aggregation operators between the moving minimum and the moving maximum. Moreover, it also includes the weighted moving average and the ordered weighted moving average as particular cases. This approach is further extended by using generalized aggregation operators, obtaining the generalized OWAWMA operator. The construction of interval and fuzzy numbers with these operators obtaining the concept of moving interval number and moving fuzzy number is also studied. The paper ends analyzing the applicability of this new approach in some key statistical concepts such as the variance and the covariance and with a numerical example regarding sales forecasting.
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Alfaro-García VG, Merigó JM, Gil-Lafuente AM, Kacprzyk J (2018) Logarithmic aggregation operators and distance measures. Int J Intell Syst 33:1488–1506
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
Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Berlin
Belles-Sampera J, Merigó JM, Guillén M, Santolino M (2014) Indicators for the characterization of discrete Choquet integrals. Inf Sci 267:201–216
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
Blanco-Mesa F, Merigó JM, Gil-Lafuente AM (2017) Fuzzy decision making: a bibliometric-based review. J Intell Fuzzy Syst 32:2033–2050
Blanco-Mesa F, León-Castro E, Merigó JM (2018) Bonferroni induced heavy operators in ERM decision-making: a case on large companies in Colombia. Appl Soft Comput 72:371–391
Cabrerizo FJ, Al-Hmouz R, Morfeq A, Balamash AS, Martinez MA, Herrera-Viedma E (2017) Soft consensus measures in group decision making using unbalanced fuzzy linguistic information. Soft Comput 21:3037–3050
Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York
Elliot G, Granger CWJ, Timmermann A (2006) Handbook of economic forecasting. North-Holland, Amsterdam
Emrouznejad A, Marra M (2014) Ordered weighted averaging operators 1988–2014: a citation based literature survey. Int J Intell Syst 29:994–1014
Evans MK (2002) Practical business forecasting. Blackwell, Hong Kong
Fodor J, Marichal JL, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3:236–240
Grabisch M, Marichal JL, Mesiar R, Pap E (2011) Aggregation functions: means. Inf Sci 181:1–22
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
Kacprzyk J, Yager RR, Merigó JM (2019) Towards human centric aggregation via the ordered weighted aggregation operators and linguistic data summaries: A new perspective on Zadeh’s inspirations. IEEE Comput Intell Mag 14(1):16–30
Karanik M, Peláez JI, Bernal R (2016) Selective majority additive ordered weighted averaging operator. Eur J Oper Res 250:816–826
Kaufmann A, Gupta MM (1985) Introduction to fuzzy arithmetic. Publications Van Nostrand, Rheinhold
León-Castro E, Avilés E, Merigó JM (2018a) Induced heavy moving averages. Int J Intell Syst 33:1823–1839
León-Castro E, Avilés-Ochoa E, Merigó JM, Gil-Lafuente AM (2018b) Heavy moving averages and their application in econometric forecasting. Cybern Syst 49:26–43
Merigó JM (2011) A unified model between the weighted average and the induced OWA operator. Expert Syst Appl 38:11560–11572
Merigó JM (2012) Probabilities in the OWA operator. Expert Syst Appl 39(13):11456–11467
Merigó JM, Gil-Lafuente AM (2009) The induced generalized OWA operator. Inf Sci 179:729–741
Merigó JM, Yager RR (2013) Generalized moving averages, distance measures and OWA operators. Int J Uncertain Fuzziness Knowl-Based Syst 21:533–559
Merigó JM, Casanovas M, Zeng SZ (2014) Distance measures with heavy aggregation operators. Appl Math Model 38:3142–3153
Merigó JM, Yang JB, Xu DL (2016) Demand analysis with aggregation operators. Int J Intell Syst 31:425–443
Merigó JM, Zhou LG, Yu D, Alrajeh N, Alnowibet K (2018) Probabilistic OWA distances applied to asset management. Soft Comput 22:4855–4878
Moore R (1966) Interval analysis. Prentice Hall, Englewood Cliffs
Morente-Molinera JA, Kou G, Pang C, Cabrerizo FJ, Herrera-Viedma E (2019) An automatic procedure to create fuzzy ontologies from users’ opinions using sentiment analysis procedures and multi-granular fuzzy linguistic modelling methods. Inf Sci 476:222–238
Peláez JI, Doña JM (2006) A majority model in group decision making using QMA-OWA operators. Int J Intell Syst 21:193–208
Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423
Torra V (1997) The weighted OWA operator. Int J Intell Syst 12:153–166
Traneva V, Tranev S, Stoenchev M, Atanassov K (2018) Scaled aggregation operators over two- and three- dimensional index matrices. Soft Comput 22:5115–5120
Tukey JW (1977) Exploratory data analysis. Addison-Wesley, Reading
Ureña R, Chiclana F, Melancon G, Herrera-Viedma E (2019) A social network based approach for consensus achievement in multiperson decision making. Inf Fusion 47:72–87
Xu ZS, Da QL (2003) An overview of operators for aggregating information. Int J Intell Syst 18:953–969
Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern B 18:183–190
Yager RR (1993) Families of OWA operators. Fuzzy Sets Syst 59:125–148
Yager RR (1996) Constrained OWA aggregation. Fuzzy Sets Syst 81:89–101
Yager RR (2002) Heavy OWA operators. Fuzzy Optim Decis Making 1:379–397
Yager RR (2004) Generalized OWA aggregation operators. Fuzzy Optim Decis Making 3:93–107
Yager RR (2008) Time series smoothing and OWA aggregation. IEEE Trans Fuzzy Syst 16:994–1007
Yager RR (2013) Exponential smoothing with credibility weighted observations. Inf Sci 252:96–105
Yu D (2015) A scientometrics review on aggregation operator research. Scientometrics 105:115–133
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
Zhao H, Xu ZS, Ni M, Liu S (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 24:1–30
Zhou LG, Chen HY (2010) Generalized ordered weighted logarithm aggregation operators and their applications to group decision making. Int J Intell Syst 25:683–707
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
Acknowledgements
We would like to thank the associate editor and the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Chilean Government through the Fondecyt Regular program (project number 1160286), the University of Chile and the European Commission through the project PIEF-GA-2011-300062 are gratefully acknowledged.
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Merigó, J.M., Yager, R.R. Aggregation operators with moving averages. Soft Comput 23, 10601–10615 (2019). https://doi.org/10.1007/s00500-019-03892-w
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DOI: https://doi.org/10.1007/s00500-019-03892-w