The Bonferroni mean-type pre-aggregation operators construction and generalization: Application to edge detection

Abstract

In recent years, immense interest in the exploration of the generalized version of the monotonicity condition has been significantly accomplished by the researchers. The intention behind generalizing the monotonicity condition is to envelop many prime functions which are of huge interest in the domain of mathematical applications such as classification problems, image processing, decision-making systems, etc. In this regard, the framework of the pre-aggregation operators was introduced to generalize the notion of monotonicity in the traditionally defined concept of aggregation operators. Such functions have extended the group of operators utilized for information accumulation by considering directional monotonicity with respect to a specified vector. This study emphasizes the systematized exploration of the theoretical framework of the Bonferroni mean-type (BM-type) pre-aggregation operators. We propose the construction methodology of the BM-type pre-aggregation operators by suitably befitting preferable functions to provide a descriptive arrangement, which is quite adaptable, understandable, and interpretable. First, a construction mechanism is proposed by utilizing a bivariate function M. To enhance the potentiality of the proposed operator, a generalized variation of it has been proposed by suitably using two functions M and M∗, respectively. The primary step for an object recognition problem is edge detection and is considered as an important tool in image processing systems. For the applicatory purpose, an edge detection algorithm based on the proposed BM-type pre-aggregation operator has been presented with more emphasis given to the feature image extraction. A comprehensive comparative study has been made to assess the results obtained through the proposed edge detection algorithm with some other well-known edge detectors extensively utilized in the literature.