We derive bounds on the variance of a random variable in terms of its arithmetic and harmonic means. Both discrete and continuous cases are considered, and an operator version is obtained. Some refinements of the Kantorovich inequality are obtained. Bounds for the largest and smallest eigenvalues of a positive definite matrix are also obtained.

We analyze different types of aggregation operators based on the use of probabilities, weighted averages (WAs) and generalized aggregation operators. We present the generalized probabilistic weighted averaging (GPWA) operator. It is a new aggregation operator that unifies the WA and the probability in the same formulation considering the degree of importance that each concept has in the analysi...

We introduce a new aggregation operator called the heavy ordered weighted averaging – weighted averaging (HOWAWA) operator. It is a new aggregation operator that uses the weighted average and the ordered weighted average in the same formulation and considering the degree of importance that each concept has in the analysis. Moreover, by using heavy aggregations, we are allowing the weighting vec...