José María Sarabia

The Ordered Weighted Average in the Variance and the Covariance

The ordered weighted average (OWA) is an aggregation operator that provides a parameterized family of aggregation operators between the minimum and the maximum. This paper analyzes the use of the OWA in the variance and the covariance. It presents several extensions by using a unified framework between the weighted average and the OWA. Furthermore, it also develops other generalizations with induced aggregation operators and by using quasi‐arithmetic means. Several measures of correlation by using the OWA are introduced including a new type of Pearson coefficient. The paper ends with some numerical examples focused on the construction of interval and fuzzy numbers with the variance and the covariance.

Missing Fundamental Illusion: A New Theory Based On Japanese Knowledge Management

AbstractWe propose the Fundamental Illusion Theory to explain knowledge creation in the case of Japanese companies. This theory is based on an analogy with a hearing illusion which explains that when two tones occur together a third lower pitched tone is heard. However, this last perceived pitch is a frequency (fundamental) for which there is no actual source vibration. If we make an analogy between fundamental frequency and knowledge, and between tones occurring together and learning + culture + leadership, we arrive at a new management model.

A Generalization of the Variance by Using the Ordered Weighted Average

The ordered weighted average is an aggregation operator that provides a parameterized family of aggregation operators between the minimum and the maximum. This paper analyzes the use of the ordered weighted average in the variance. It presents several extensions by using a unified framework between the weighted average and the ordered weighted average. Furthermore, it also develops other generalizations with induced aggregation operators and by using quasi-arithmetic means.