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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.

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In this paper, we develop two new theorems relating to the series of floor and ceiling functions. We then use these two theorems to develop more than forty distinct novel results. Furthermore, we provide specific cases for the theorems and corollaries which show that our results constitute a generalisation of the currently available results such as the summation of first n Fibonacci numbers and Pascal’s identity. Finally, we provide three miscellaneous examples to showcase the vast scope of our developed theorems.

The variance is a statistical measure frequently used for analysis of dispersion in the data. This paper presents new types of variances that use Bonferroni means and ordered weighted averages in the aggregation process of the variance. The main advantage of this approach is that we can underestimate or overestimate the variance according to the attitudinal character of the decisionmaker. The work considers several particular cases including the minimum and the maximum variance and presents some numerical examples. The article also develops some extensions and generalizations by using induced aggregation operators and generalized and quasi-arithmetic means. These approaches provide a more general framework that can consider a lot of other particular cases and a complex attitudinal character that could be affected by a wide range of variables. The study ends with an application of the new approach in a business decision-making problem regarding strategic analysis in enterprise risk management. K E Y W O R D S asymmetric information, Bonferroni means, OWA operator, strategy decision-making, varianceStatistics is a science that collects, organizes, presents, analyzes, and interprets data to provide information to make decisions more effectively. Among its diverse applications is statistics applied to business and the economy, in which studies focus on descriptive statistics and statistical inference. On the one hand, descriptive statistics allows organizing, summarizing, and presenting data in an informative manner. On the other hand, statistical inference uses methods to describe or determine a specific property of a population based on a sample of it. For both approaches, it is important to highlight the origin of the data, which must be measurable and countable to be treated with different methods, allowing filtering to obtain objective information. Thus, statistics allows obtaining specific measures and conjectures about these. Among the most used procedures and measures are the frequency distribution (to organize the data), the average (the central location of a group of numeric data), measures of central tendency and dispersion (to observe the proximity of a set of data around the average) and other more complex measures related to probability and test statistics.However, statistics, although quite useful to describe, explain, and verify various phenomena within business and economic studies, is not able to capture nonnumerical aspects, such as semantics, linguistic meaning, approximate reasoning, intuition, and attitude. This is because these types of data do not follow formal patterns and largely respond to human behavior and subjectivity, which makes them more complex to measure. 1 Perhaps, this is the first difficulty in their mathematical treatment, as they try to measure with high-precision, data that in their nature have a high degree of complexity. According to Zadeh 2 human reasoning is related to possibility and uncertainty, which is different from probability, that is, high complexity is incompatibl...