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 ordered weighted averaging (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 and Mexican pesos is also presented.

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.

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.

The prioritized induced probabilistic ordered weighted average distance (PIPOWAD) has been developed. This new operator is an extension of the ordered weighted average (OWA) operator that can be used in cases where we have two sets of data that want to be compared. Some of the main characteristics of this new operator are: 1) Not all the decision makers are equally important, so the information needs to be prioritized, 2) The information has a probability to occur and 3) The decision makers can change the importance of the information based in an induced variable. Additionally, characteristics and families of the PIPOWAD operator are presented. Finally, an application of the PIPOWAD operator in order to measure government transparency in Mexico is presented.