2,979 publications from this institution
Fuzzy decision trees (FDTs) have shown to be an effective solution in the framework of fuzzy classification. The approaches proposed so far to FDT learning, however, have generally neglected time and space requirements. In this paper, we propose a distributed FDT learning scheme shaped according to the MapReduce programming model for generating both binary and multiway FDTs from big data. The scheme relies on a novel distributed fuzzy discretizer that generates a strong fuzzy partition for each continuous attribute based on fuzzy information entropy. The fuzzy partitions are, therefore, used as an input to the FDT learning algorithm, which employs fuzzy information gain for selecting the attributes at the decision nodes. We have implemented the FDT learning scheme on the Apache Spark framework. We have used ten real-world publicly available big datasets for evaluating the behavior of the scheme along three dimensions: 1) performance in terms of classification accuracy, model complexity, and execution time; 2) scalability varying the number of computing units; and 3) ability to efficiently accommodate an increasing dataset size. We have demonstrated that the proposed scheme turns out to be suitable for managing big datasets even with a modest commodity hardware support. Finally, we have used the distributed decision tree learning algorithm implemented in the MLLib library and the Chi-FRBCS-BigData algorithm, a MapReduce distributed fuzzy rule-based classification system, for comparative analysis. © 1993-2012 IEEE.
This paper is concerned with an enhanced independent component analysis (ICA) and its application to face recognition. Typically, face representations obtained by ICA involve unsupervised learning and high-order statistics. In this paper, we develop an enhancement of the generic ICA by augmenting this method by the Fisher linear discriminant analysis (LDA); hence, its abbreviation, FICA. The FICA is systematically developed and presented along with its underlying architecture. A comparative analysis explores four distance metrics, as well as classification with support vector machines (SVMs). We demonstrate that the FICA approach leads to the formation of well-separated classes in low-dimension subspace and is endowed with a great deal of insensitivity to large variation in illumination and facial expression. The comprehensive experiments are completed for the facial-recognition technology (FERET) face database; a comparative analysis demonstrates that FICA comes with improved classification rates when compared with some other conventional approaches such as eigenface, fisherface, and the ICA itself.
This study is concerned with an evolutionary methodology of designing logic-based models. These models dwell on a logic fabric of granular computing and learning capabilities of fuzzy neural networks. The proposed design comprises two fundamental phases, namely an evolutionary optimization (via Genetic Programming, GP) of the generic structure of the model that is followed by its parametric refinement completed in the form of a detailed gradient-based learning. We discuss the underlying algorithm and elaborate on the way in which GP helps cope with high dimensionality of the modeling problem (it is known that a significant number of variables leads to the failure of the parametric learning). The study is illustrated with the aid of a numeric example that provides a detailed insight into the performance of the logic-oriented models and quantifies crucial design issues.
Federated learning addresses the issue of machine learning realized under constraints of privacy and security. While there have been intensive studies on building and analyzing federated regression models, this topic has not been analyzed so far in the area of fuzzy systems. To narrow down this gap, in this study, we formulate and solve a problem of unsupervised federated learning by designing an original federated FCM (F-FCM) clustering which could serve as a basis toward building a spectrum of fuzzy set constructs including rule-based models. Following a general client–server structure, where the local data residing with each client are not available globally and cannot be centralized (as commonly encountered in learning scenarios), the aim is to discover an overall structure across all data. The federated gradient-based optimization realized in the horizontal mode is developed. An overall learning process is derived, which is composed of communicating gradients coming from clients and providing updates of the prototypes at the server side and passing them on to the clients. It is also shown that the relevance of the globally constructed structure is conveniently assessed in terms of granular footprints of the prototypes constructed by the F-FCM. Some illustrative examples are covered to illustrate the efficiency of the developed federated algorithm.
The study is aimed at the development of neural networks useful in modelling processes of fuzzy decision-making. A variety of logic-oriented neurons (both aggregative and referential processing units) makes it possible to directly treat the efficacies of the decision problem at hand and handle them within the topology of the network. The learning capabilities of the decision networks are thoroughly investigated. Several aspects of these architectures including dynamical characteristics of the decision processes and representing and processing of incomplete or uncertain information are also addressed.
Probability weighting function (PWF) is the psychological probability of a decision-maker for objective probability, which reflects and predicts the risk preferences of decision-maker in behavioral decisionmaking. The existing approaches to PWF estimation generally include parametric methodologies to PWF construction and nonparametric elicitation of PWF. However, few of them explores the combination of parametric and nonparametric elicitation approaches to approximate PWF. To describe quantitatively risk preferences, the Newton interpolation, as a well-established mathematical approximation approach, is introduced to task-specifically match PWF under the frameworks of prospect theory and cumulative prospect theory with descriptive psychological analyses. The Newton interpolation serves as a nonparametric numerical approach to the estimation of PWF by fitting experimental preference points without imposing any specific parametric form assumptions. The elaborated nonparametric PWF model varies in accordance with the number of the experimental preference points elicitation in terms of its functional form. The introduction of Newton interpolation to PWF estimation into decision-making under risk will benefit to reflect and predict the risk preferences of decision-makers both at the aggregate and individual levels. The Newton interpolation-based nonparametric PWF model exhibits an inverse S-shaped PWF and obeys the fourfold pattern of decision-makers’ risk preferences as suggested by previous empirical analyses.
In group decision making (GDM), consensus level is regarded as a critical criterion to measure the effectiveness and availability of the final group decision solution. Consensus model is aimed at conducting the decision group to reach agreement through the process of group negotiation, advice feedback, and opinion modification, which is time-consuming and rests with the willingness and behavior of individual decision makers. Thus, to guide the shift in the opinions of decision makers within a limited time, it is essential to design an effective, interpretable, and fair consensus mechanism in GDM, which is particularly vital when a mass of decision makers (e.g., more than 30) are involved in the decision process, viz., we encounter a large-scale GDM (LSGDM). With the involvement of information granulation, this study presents a rule-based consensus model in LSGDM by optimally allocating the level of information granularity to each decision maker. The opinions of decision makers in LSGDM are divided into different clusters by engaging the fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> -means method. Inspired by a generic fuzzy rule-based model, the radius of the individual preference granule (PG) is calculated by a weighted linear combination of the granularity levels allocated to the clusters. Then, a consensus model with the optimal allocation of information granularity (CMOIG) is built to determine the granularity level for each cluster by minimizing the sum of radii of individual PG. An interactive consensus reaching process is proposed with the proposed CMOIG and fuzzy modification rules. The CMOIG and fuzzy modification rules simultaneously guarantees high efficiency and interpretability, and the generation method of PGs leads to high fairness due to low discrepancy among the decision group. Finally, numerical and comparative experiments are conducted in detail to verify the validity and superiority of the presented models in terms of the efficiency, interpretability, and fairness.
Strong analogies between relational structures involving some composition operators and a certain class of neural networks are described. The problem of learning the connections of the structure is addressed, and relevant learning procedures are proposed. An optimized performance index which has a strong logical flavor is proposed. Some significant implementation details are studied. Numerical examples illustrate various schemes of learning in relational structures of different levels of complexity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
A fuzzy rulebase is a model of a system, expressed as a collection of fuzzy if/then rules, whose predicates are words in nature language, given mathematical meaning by associating each word with a fuzzy set fuzzy rulebases have been proven to be powerful and intuitive tools for modeling a wide range of phenomena. The problem of how to construct fuzzy rulebases has been extensively explored. However, the problem of how to defined operations on fuzzy rulebases is still an open question. This paper addressed the second question. The purpose of this research project was to develop an algorithm for detecting and quantifying structure similarity between two fuzzy rulebases, which in turn give an approximate measure of the similarity between two systems. The proposed algorithm is based on linguistic gradient, which is a linguistic analogue of the gradient operator from calculus. For each of the two fuzzy rulebases, the gradient vector can be computed at each point in the linguistic space. Each n-dimension gradient vector is converted to a 2ndimension 3-level vector by thresholding its magnitude on each axis. Vectors lie on each axis are added to compute projection. The projection vectors of the two fuzzy rulebases are regranulated to the same granularity using weighted sum. The regranulated vectors are then compared using Euclidean distance formula. The Euclidean distance is normalized so that results of different pair of rulebases are directly comparable. Programs have been developed for C++ and Matlab to implement this algorithm.
Fuzzy measures and Choquet integral are efficient aggregation operators utilised intensively in decision-making theory. To produce sound classification results based on a family of classifiers, the parameters of the fuzzy measure (especially, so-called fuzzy densities) have to be determined. In this study, we propose a method based on particle swarm optimisation (PSO) and discuss in detail a new concept of a so-called positive and negative optimisation to fully utilise specific properties of classifiers to carry out efficient classification. A suite of experiments is conducted to illustrate this approach and discuss its scope of applicability.
