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This paper presents the induced heavy ordered weighted moving average (IHOWMA) operator. It is an aggregation operator that uses the main characteristics of three well‐known techniques: the moving average, induced operator, and heavy aggregation operator. This operator provides a parameterized family of aggregation operators that include the minimum, the maximum, and total operator as special cases. It can be used in a selection process, considering that not all decision makers have the same knowledge and expectations of the future. The main properties of this operator are studied including a wide range of families of IHOWMA operators, such as the heavy ordered weighted moving average operator and uncertain induced heavy ordered weighted moving average operator. The IHOWMA operator is also extended using generalized and quasi‐arithmetic means. An example in an investment selection process is also presented.

This paper presents the heavy ordered weighted moving average (HOWMA) operator. It is an aggregation operator that uses the main characteristics of two well-known techniques: the heavy OWA and the moving averages.Therefore, this operator provides a parameterized family of aggregation operators from the minimum to the total operator and includes the OWA operator as a special case. It uses a heavy weighting vector in the moving average formulation and it represents the information available and the knowledge of the decision maker about the future scenarios of the phenomenon, according to his attitudinal character. Some of the main properties of this operator are studied, including a wide range of families of HOWMA operators such as the heavy moving average and heavy weighted moving average operators. The HOWMA operator is also extended using generalized and quasi-arithmetic means. An example concerning the foreign exchange rate between US dollars (USD) and Mexican pesos (MXN) is also presented. JEL Classification: C43, C44, C53, C58. * Corresponding author Emails: ernesto.leon@udo.mx − +1 * the jth weight of the AOWA operator. Heavy aggregation operatorsThe heavy OWA (HOWA) operator (Yager, 2002) is an extension of the OWA operator. This operator is useful when the available information is not bounded by the maximum or the minimum operator of the usual OWA operator. The main difference between the OWA and HOWA operators is that the sum of the weights of the OWA operator must be 1. This restriction does not exist for the HOWA operator: the sum of the weights can range from 1 to n. In the following, we provide the definition of the HOWMA operator suggested by Yager (2002).

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The induced ordered weighted average is an averaging aggregation operator that provides a parameterized family of aggregation operators between the minimum and the maximum. This paper presents some new generalizations by using Bonferroni means (BM) forming induced BM. The main advantage of this approach is the possibility of reordering the results according to complex ranking processes based on order‐inducing variables. The work also presents some additional extensions by using the weighted ordered weighted average, immediate weights, and hybrid averages. Some further generalizations with generalized and quasi‐arithmetic means are also developed to consider a wide range of particular cases including quadratic and geometric aggregations. The article also considers the applicability of the new approach in‐group decision‐making developing an application in sales forecasting.