Consensus via penalty functions for decision making in ensembles in fuzzy rule-based classification systems

Distributivity of ordinal sum implications over overlap and grouping functions

“…In recent years, two kinds of binary aggregation functions, called overlap and grouping functions respectively, were introduced by Bustince et al [8,9]. Those two functions arise from problems in image processing, decision making and classification [6,9,19,20,21,23] based on fuzzy preference relations, where the associativity property is not strongly required in reality, and thus it's not necessary to consider t-norms and t-conorms as models of operations. In image processing, for example, in 2007, scholars such as Bustince et al used the so-called restricted equivalent function to calculate the threshold value of images [6].…”

“…In image processing, for example, in 2007, scholars such as Bustince et al used the so-called restricted equivalent function to calculate the threshold value of images [6]. In decision making, in 2017, Elkano et al [21] gave a consensus method via penalty functions for decision making in ensembles of fuzzy rule based classification systems and introduced a method for constructing confidence and support measures from overlap functions. In classification, in 2015, Elkano et al [20] adapted the inference system of fuzzy association rule classification model replacing the product triangular norm with n-dimensional overlap function for high-dimensional problems.…”

General Complex-Valued Grouping Functions

“…A grouping function measures the amount of evidence in favor of either of two choices in decision making. It plays an important role in many aspects of applications such as image processing [1,3], classification [4,5], and decision making [6,7].…”

Constructions of <i>n</i>-Dimensional Overlap Functions Based on Bivariate Overlap Functions

“…Overlap functions and grouping functions are two particular cases of bivariate continuous aggregation functions [4] [5]. Those two concepts have been applied to some interesting problems, for example, image processing [1] [6], classification [7] [8] and decision making [3] [9]. In recent years, some extended forms of overlap functions and grouping functions were presented, for example, n-Dimensional overlap functions and grouping functions [10], general overlap functions [11].…”