Aggregation operators with moving averages

  • José M. MerigóEmail author
  • Ronald R. Yager


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.


Weighted average OWA operator Moving average Aggregation operators 



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.

Compliance with ethical standards

Conflict of interest

The authors declare that they do not have any conflict of interest.

Ethical approval

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


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Manchester Business SchoolUniversity of ManchesterManchesterUK
  2. 2.Department of Management Control and Information Systems, School of Economics and BusinessUniversity of ChileSantiagoChile
  3. 3.School of Information, Systems and Modelling, Faculty of Engineering and Information TechnologyUniversity of Technology SydneyUltimoAustralia
  4. 4.Machine Intelligence InstituteIona CollegeNew RochelleUSA

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