Applying d-XChoquet integrals in classification problems

Several generalizations of the Choquet integral have been applied in the Fuzzy Reasoning Method (FRM) of Fuzzy Rule-Based Classification Systems (FRBCS's) to improve its performance. Additionally, to achieve that goal, researchers have searched for new ways to provide more flexibility to those generalizations, by restricting the requirements of the functions being used in their constructions and relaxing the monotonicity of the integral. This is the case of CT-integrals, CC-integrals, CF-integrals, CF1F2-integrals and dCF-integrals, which obtained good performance in classification algorithms, more specifically, in the fuzzy association rule-based classification method for high-dimensional problems (FARC-HD). Thereafter, with the introduction of Choquet integrals based on restricted dissimilarity functions (RDFs) in place of the standard difference, a new generalization was made possible: the d-XChoquet (d-XC) integrals, which are ordered directional increasing functions and, depending on the adopted RDF, may also be a pre-aggregation function. Those integrals were applied in multi-criteria decision making problems and also in a motor-imagery brain computer interface framework. In the present paper, we introduce a new FRM based on the d-XC integral family, analyzing its performance by applying it to 33 different datasets from the literature.Supported by Navarra de Servicios y Tecnologías, S.A. (NASERTIC), CNPq (301618/2019-4, 305805/2021-5), FAPERGS (19/2551-0001660-3), the Spanish Ministry of Science and Technology (TIN2016-77356-P, PID2019- 108392GB I00 (MCIN/AEI/10.13039/501100011033)

Classification System based on Fuzzy Rules and Vector-Valued Choquet Integral Model

If-Then形式のファジィルールで複数のクラスへの分類ルールを記述し, そのルールから各クラスと未分類, 重複分類, 矛盾のクラスへ所属度を計算するモデルを提案した. 本稿では, 3つの利用法のモデルを提案する. 1番目は, 分類先のクラス毎にルールを設定する方法であり, 重なる部分は, 重複分類として表示する方法である. 2番目は, 条件毎にルールを設定していき, 合計が1となるような相対的なルールを設定する. この場合, 重複分類は無い. 3番目は, 分類先は, 基本的に1つのみとし, ある条件で複数の分類に分類する場合は, 矛盾と考える方法である. また, これらのモデルに基づく集合関数（ファジィ測度）を同定するWeb上のシステムを開発した. ファジィルール間では制約がありその制約を満たすようにする. また, このWebシステムで同定した集合関数から, 実際に [0,1]区間の入力値から, 各クラスへの所属度を計算する表計算ソフトウエアの関数を作成した.We previously proposed a vector-valued Choquet integral model and a classification model based on the Choquet integral model. In this paper, we propose three application-oriented models. The first model describes the degrees of each class, overlapping degree, and unknown degree. The second model is the relative classification model. The third model is the strict classification model in which a condition of if–then rules has only one class. If there are two or more classes, the overlapping becomes contradictions. To use those models, we develop a web-based system that identifies set functions using the if–then rules interactively and spreadsheet macros that calculate the degrees of class using the identified set functions

Using Choquet integrals for kNN approximation and classification

k-nearest neighbors (kNN) is a popular method for function approximation and classification. One drawback of this method is that the nearest neighbors can be all located on one side of the point in question x. An alternative natural neighbors method is expensive for more than three variables. In this paper we propose the use of the discrete Choquet integral for combining the values of the nearest neighbors so that redundant information is canceled out. We design a fuzzy measure based on location of the nearest neighbors, which favors neighbors located all around x. <br /

Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks

Information fusion is an essential part of numerous engineering systems and biological functions, e.g., human cognition. Fusion occurs at many levels, ranging from the low-level combination of signals to the high-level aggregation of heterogeneous decision-making processes. While the last decade has witnessed an explosion of research in deep learning, fusion in neural networks has not observed the same revolution. Specifically, most neural fusion approaches are ad hoc, are not understood, are distributed versus localized, and/or explainability is low (if present at all). Herein, we prove that the fuzzy Choquet integral (ChI), a powerful nonlinear aggregation function, can be represented as a multi-layer network, referred to hereafter as ChIMP. We also put forth an improved ChIMP (iChIMP) that leads to a stochastic gradient descent-based optimization in light of the exponential number of ChI inequality constraints. An additional benefit of ChIMP/iChIMP is that it enables eXplainable AI (XAI). Synthetic validation experiments are provided and iChIMP is applied to the fusion of a set of heterogeneous architecture deep models in remote sensing. We show an improvement in model accuracy and our previously established XAI indices shed light on the quality of our data, model, and its decisions.Comment: IEEE Transactions on Fuzzy System

An Overview of Classifier Fusion Methods

A number of classifier fusion methods have been recently developed opening an alternative approach leading to a potential improvement in the classification performance. As there is little theory of information fusion itself, currently we are faced with different methods designed for different problems and producing different results. This paper gives an overview of classifier fusion methods and attempts to identify new trends that may dominate this area of research in future. A taxonomy of fusion methods trying to bring some order into the existing “pudding of diversities” is also provided

An Overview of Classifier Fusion Methods

A number of classifier fusion methods have been recently developed opening an alternative approach leading to a potential improvement in the classification performance. As there is little theory of information fusion itself, currently we are faced with different methods designed for different problems and producing different results. This paper gives an overview of classifier fusion methods and attempts to identify new trends that may dominate this area of research in future. A taxonomy of fusion methods trying to bring some order into the existing “pudding of diversities” is also provided