On the orness of Bonferroni mean and its variants

Abstract

This article addresses orness measures to reflect the orlike degree of the Bonferroni mean (BM) and its variants. Some properties of these operators associated with their orness measures are portrayed analytically. However, the general orness measure involves the multiple integrals with the integral fold number being the number of the aggregated elements and as a result, the computation becomes complicated when the number of the aggregated elements is large. Furthermore, the analytical formula of the orness measure often cannot be obtained. For this reason, this study concentrates on Monte Carlo simulation to validate the result. We estimate the two parameters of the BM for a predefined orness value and a fixed length of the input vector. Besides the theoretical study of orness measure related to BM and its variants, the article also explores the simulation-based results. To support this, we provide four numerical examples. K E Y W O R D S aggregation operator, Bonferroni mean, decision-making, Monte Carlo simulation, orness measure

Neutrosophic cubic Maclaurin symmetric mean aggregation operators with applications in multi‐criteria decision‐making

“…As noted by Dutta et al. (2019), the arithmetical average represent neutral attitude character, which can compensate the inferior performance on certain criteria through the superior criteria performance. The orness of this average aggregation is 0.5.…”

“…When p 1 = 10, p 2 = 10 for W NCGMSM (m,p 1 ,p 2 ) , the aggregation is compensated where the superior performance of alternatives on some criteria can balance the inferior performance on criteria. As noted by Dutta et al (2019), the arithmetical average represent neutral attitude character, which can compensate the inferior performance on certain criteria through the superior criteria performance. The orness of this average aggregation is 0.5.…”

Aggregating Interrelated Attributes in Multi-Attribute Decision-Making With ELICIT Information Based on Bonferroni Mean and Its Variants

“…In nutshell, we can conclude that present ranking results are robust and not much sensitive to the parameters. Note that the exact estimation of the appropriate parameters associated with ELICITEBM could also be stem from the decision maker's perceived view towards aggregation process [22,46]. As we have emphasized on the fact that capturing the underlying interrelationship pattern in the aggregated ELICIT information is vital to make a reliable decision, it is worthy here to investigate the consequence if we do not consider the interrelationship in the information fusion process.…”