Nonparametric regression analysis of uncertain and imprecise data using belief functions

AbstractThis paper introduces a new approach to regression analysis based on a fuzzy extension of belief function theory. For a given input vector x, the method provides a prediction regarding the value of the output variable y, in the form of a fuzzy belief assignment (FBA), defined as a collection of fuzzy sets of values with associated masses of belief. The output FBA is computed using a nonparametric, instance-based approach: training samples in the neighborhood of x are considered as sources of partial information on the response variable; the pieces of evidence are discounted as a function of their distance to x, and pooled using Dempster’s rule of combination. The method can cope with heterogeneous training data, including numbers, intervals, fuzzy numbers, and, more generally, fuzzy belief assignments, a convenient formalism for modeling unreliable and imprecise information provided by experts or multi-sensor systems. The performances of the method are compared to those of standard regression techniques using several simulated data sets

A review of associative classification mining

Associative classification mining is a promising approach in data mining that utilizes the association rule discovery techniques to construct classification systems, also known as associative classifiers. In the last few years, a number of associative classification algorithms have been proposed, i.e. CPAR, CMAR, MCAR, MMAC and others. These algorithms employ several different rule discovery, rule ranking, rule pruning, rule prediction and rule evaluation methods. This paper focuses on surveying and comparing the state-of-the-art associative classification techniques with regards to the above criteria. Finally, future directions in associative classification, such as incremental learning and mining low-quality data sets, are also highlighted in this paper

A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels

In this paper, a systematic data-driven fuzzy modelling methodology is proposed, which allows to construct Mamdani fuzzy models considering both accuracy (precision) and transparency (interpretability) of fuzzy systems. The new methodology employs a fast hierarchical clustering algorithm to generate an initial fuzzy model efficiently; a training data selection mechanism is developed to identify appropriate and efficient data as learning samples; a high-performance Particle Swarm Optimisation (PSO) based multi-objective optimisation mechanism is developed to further improve the fuzzy model in terms of both the structure and the parameters; and a new tolerance analysis method is proposed to derive the confidence bands relating to the final elicited models. This proposed modelling approach is evaluated using two benchmark problems and is shown to outperform other modelling approaches. Furthermore, the proposed approach is successfully applied to complex high-dimensional modelling problems for manufacturing of alloy steels, using ‘real’ industrial data. These problems concern the prediction of the mechanical properties of alloy steels by correlating them with the heat treatment process conditions as well as the weight percentages of the chemical compositions

Large-scale Parallel Stratified Defeasible Reasoning

We are recently experiencing an unprecedented explosion of available data from the Web, sensors readings, scientific databases, government authorities and more. Such datasets could benefit from the introduction of rule sets encoding commonly accepted rules or facts, application- or domain-specific rules, commonsense knowledge etc. This raises the question of whether, how, and to what extent knowledge representation methods are capable of handling huge amounts of data for these applications. In this paper, we consider inconsistency-tolerant reasoning in the form of defeasible logic, and analyze how parallelization, using the MapReduce framework, can be used to reason with defeasible rules over huge datasets. We extend previous work by dealing with predicates of arbitrary arity, under the assumption of stratification. Moving from unary to multi-arity predicates is a decisive step towards practical applications, e.g. reasoning with linked open (RDF) data. Our experimental results demonstrate that defeasible reasoning with millions of data is performant, and has the potential to scale to billions of facts

Coalition structure generation in cooperative games with compact representations

This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well