On the usage of the probability integral transform to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems

We present a new distributed fuzzy partitioning method to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems. The proposed algorithm builds a fixed number of fuzzy sets for all variables and adjusts their shape and position to the real distribution of training data. A two-step process is applied : 1) transformation of the original distribution into a standard uniform distribution by means of the probability integral transform. Since the original distribution is generally unknown, the cumulative distribution function is approximated by computing the q-quantiles of the training set; 2) construction of a Ruspini strong fuzzy partition in the transformed attribute space using a fixed number of equally distributed triangular membership functions. Despite the aforementioned transformation, the definition of every fuzzy set in the original space can be recovered by applying the inverse cumulative distribution function (also known as quantile function). The experimental results reveal that the proposed methodology allows the state-of-the-art multi-way fuzzy decision tree (FMDT) induction algorithm to maintain classification accuracy with up to 6 million fewer leaves.Comment: Appeared in 2018 IEEE International Congress on Big Data (BigData Congress). arXiv admin note: text overlap with arXiv:1902.0935

Use of idempotent functions in the aggregation of different filters for noise removal

The majority of existing denoising algorithms obtain good results for a specific noise model, and when it is known previously. Nonetheless, there is a lack in denoising algorithms that can deal with any unknown noisy images. Therefore, in this paper, we study the use of aggregation functions for denoising purposes, where the noise model is not necessary known in advance; and how these functions affect the visual and quantitative results of the resultant images

Interval-valued contractive fuzzy negations

In this work we consider the concept of contractive interval-valued fuzzy negation, as a negation such that it does not increase the length or amplitude of an interval. We relate this to the concept of Lipschitz function. In particular, we prove that the only strict (strong) contractive interval-valued fuzzy negation is the one generated from the standard (Zadeh's) negation

Consensus image method for unknown noise removal

Noise removal has been, and it is nowadays, an important task in computer vision. Usually, it is a previous task preceding other tasks, as segmentation or reconstruction. However, for most existing denoising algorithms the noise model has to be known in advance. In this paper, we introduce a new approach based on consensus to deal with unknown noise models. To do this, different filtered images are obtained, then combined using multifuzzy sets and averaging aggregation functions. The final decision is made by using a penalty function to deliver the compromised image. Results show that this approach is consistent and provides a good compromise between filters.This work is supported by the European Commission under Contract No. 238819 (MIBISOC Marie Curie ITN). H. Bustince was supported by Project TIN 2010-15055 of the Spanish Ministry of Science

Automatic histogram threshold using fuzzy measures

In this paper, an automatic histogram threshold approach based on a fuzziness measure is presented. This work is an improvement of an existing method. Using fuzzy logic concepts, the problems involved in finding the minimum of a criterion function are avoided. Similarity between gray levels is the key to find an optimal threshold. Two initial regions of gray levels, located at the boundaries of the histogram, are defined. Then, using an index of fuzziness, a similarity process is started to find the threshold point. A significant contrast between objects and background is assumed. Previous histogram equalization is used in small contrast images. No prior knowledge of the image is required.info:eu-repo/semantics/publishedVersio

Means on discrete product lattices

We investigate the problem of averaging values on lattices, and in particular on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme, need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties. We also discuss which of them coincide with the Cartesian product of the standard mean and median

A Compact Evolutionary Interval-Valued Fuzzy Rule-Based Classification System for the Modeling and Prediction of Real-World Financial Applications with Imbalanced Data

The current financial crisis has stressed the need of obtaining more accurate prediction models in order to decrease the risk when investing money on economic opportunities. In addition, the transparency of the process followed to make the decisions in financial applications is becoming an important issue. Furthermore, there is a need to handle the real-world imbalanced financial data sets without using sampling techniques which might introduce noise in the used data. In this paper, we present a compact evolutionary interval-valued fuzzy rule-based classification system, which is based on IVTURSFARC-HD (Interval-Valued fuzzy rulebased classification system with TUning and Rule Selection) [22]), for the modeling and prediction of real-world financial applications. This proposed system allows obtaining good predictions accuracies using a small set of short fuzzy rules implying a high degree of interpretability of the generated linguistic model. Furthermore, the proposed system deals with the financial imbalanced datasets with no need for any preprocessing or sampling method and thus avoiding the accidental introduction of noise in the data used in the learning process. The system is also provided with a mechanism to handle examples that are not covered by any fuzzy rule in the generated rule base. To test the quality of our proposal, we will present an experimental study including eleven realworld financial datasets. We will show that the proposed system outperforms the original C4.5 decision tree, type-1 and interval-valued fuzzy counterparts which use the SMOTE sampling technique to preprocess data and the original FURIA, which is a fuzzy approximative classifier. Furthermore, the proposed method enhances the results achieved by the cost sensitive C4.5 and it gives competitive results when compared with FURIA using SMOTE, while our proposal avoids pre-processing techniques and it provides interpretable models that allow obtaining more accurate results.Spanish Government TIN2011-28488 TIN2013-40765-