A new fuzzy set merging technique using inclusion-based fuzzy clustering

This paper proposes a new method of merging parameterized fuzzy sets based on clustering in the parameters space, taking into account the degree of inclusion of each fuzzy set in the cluster prototypes. The merger method is applied to fuzzy rule base simplification by automatically replacing the fuzzy sets corresponding to a given cluster with that pertaining to cluster prototype. The feasibility and the performance of the proposed method are studied using an application in mobile robot navigation. The results indicate that the proposed merging and rule base simplification approach leads to good navigation performance in the application considered and to fuzzy models that are interpretable by experts. In this paper, we concentrate mainly on fuzzy systems with Gaussian membership functions, but the general approach can also be applied to other parameterized fuzzy sets

Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

We propose an automatic methodology framework for short- and long-term prediction of time series by means of fuzzy inference systems. In this methodology, fuzzy techniques and statistical techniques for nonparametric residual variance estimation are combined in order to build autoregressive predictive models implemented as fuzzy inference systems. Nonparametric residual variance estimation plays a key role in driving the identification and learning procedures. Concrete criteria and procedures within the proposed methodology framework are applied to a number of time series prediction problems. The learn from examples method introduced by Wang and Mendel (W&M) is used for identification. The Levenberg–Marquardt (L–M) optimization method is then applied for tuning. The W&M method produces compact and potentially accurate inference systems when applied after a proper variable selection stage. The L–M method yields the best compromise between accuracy and interpretability of results, among a set of alternatives. Delta test based residual variance estimations are used in order to select the best subset of inputs to the fuzzy inference systems as well as the number of linguistic labels for the inputs. Experiments on a diverse set of time series prediction benchmarks are compared against least-squares support vector machines (LS-SVM), optimally pruned extreme learning machine (OP-ELM), and k-NN based autoregressors. The advantages of the proposed methodology are shown in terms of linguistic interpretability, generalization capability and computational cost. Furthermore, fuzzy models are shown to be consistently more accurate for prediction in the case of time series coming from real-world applications.Ministerio de Ciencia e Innovación TEC2008-04920Junta de Andalucía P08-TIC-03674, IAC07-I-0205:33080, IAC08-II-3347:5626

Identification of Evolving Rule-based Models.

An approach to identification of evolving fuzzy rule-based (eR) models is proposed. eR models implement a method for the noniterative update of both the rule-base structure and parameters by incremental unsupervised learning. The rule-base evolves by adding more informative rules than those that previously formed the model. In addition, existing rules can be replaced with new rules based on ranking using the informative potential of the data. In this way, the rule-base structure is inherited and updated when new informative data become available, rather than being completely retrained. The adaptive nature of these evolving rule-based models, in combination with the highly transparent and compact form of fuzzy rules, makes them a promising candidate for modeling and control of complex processes, competitive to neural networks. The approach has been tested on a benchmark problem and on an air-conditioning component modeling application using data from an installation serving a real building. The results illustrate the viability and efficiency of the approach. (c) IEEE Transactions on Fuzzy System

An Incremental Construction of Deep Neuro Fuzzy System for Continual Learning of Non-stationary Data Streams

Existing FNNs are mostly developed under a shallow network configuration having lower generalization power than those of deep structures. This paper proposes a novel self-organizing deep FNN, namely DEVFNN. Fuzzy rules can be automatically extracted from data streams or removed if they play limited role during their lifespan. The structure of the network can be deepened on demand by stacking additional layers using a drift detection method which not only detects the covariate drift, variations of input space, but also accurately identifies the real drift, dynamic changes of both feature space and target space. DEVFNN is developed under the stacked generalization principle via the feature augmentation concept where a recently developed algorithm, namely gClass, drives the hidden layer. It is equipped by an automatic feature selection method which controls activation and deactivation of input attributes to induce varying subsets of input features. A deep network simplification procedure is put forward using the concept of hidden layer merging to prevent uncontrollable growth of dimensionality of input space due to the nature of feature augmentation approach in building a deep network structure. DEVFNN works in the sample-wise fashion and is compatible for data stream applications. The efficacy of DEVFNN has been thoroughly evaluated using seven datasets with non-stationary properties under the prequential test-then-train protocol. It has been compared with four popular continual learning algorithms and its shallow counterpart where DEVFNN demonstrates improvement of classification accuracy. Moreover, it is also shown that the concept drift detection method is an effective tool to control the depth of network structure while the hidden layer merging scenario is capable of simplifying the network complexity of a deep network with negligible compromise of generalization performance.Comment: This paper has been published in IEEE Transactions on Fuzzy System

New perspectives on realism, tractability, and complexity in economics

Fuzzy logic and genetic algorithms are used to rework more realistic (and more complex) models of competitive markets. The resulting equilibria are significantly different from the ones predicted from the usual static analysis; the methodology solves the Walrasian problem of how markets can reach equilibrium, starting with firms trading at disparate prices. The modified equilibria found in these complex market models involve some mutual self-restraint on the part of the agents involved, relative to economically rational behaviour. Research (using similar techniques) into the evolution of collaborative behaviours in economics, and of altruism generally, is summarized; and the joint significance of these two bodies of work for public policy is reviewed. The possible extension of the fuzzy/ genetic methodology to other technical aspects of economics (including international trade theory, and development) is also discussed, as are the limitations to the usefulness of any type of theory in political domains. For the latter purpose, a more differentiated concept of rationality, appropriate to ill-structured choices, is developed. The philosophical case for laissez-faire policies is considered briefly; and the prospects for change in the way we ‘do economics’ are analysed

MODELLING EXPECTATIONS WITH GENEFER- AN ARTIFICIAL INTELLIGENCE APPROACH

Economic modelling of financial markets means to model highly complex systems in which expectations can be the dominant driving forces. Therefore it is necessary to focus on how agents form their expectations. We believe that they look for patterns, hypothesize, try, make mistakes, learn and adapt. AgentsÆ bounded rationality leads us to a rule-based approach which we model using Fuzzy Rule-Bases. E. g. if a single agent believes the exchange rate is determined by a set of possible inputs and is asked to put their relationship in words his answer will probably reveal a fuzzy nature like: "IF the inflation rate in the EURO-Zone is low and the GDP growth rate is larger than in the US THEN the EURO will rise against the USD". æLowÆ and ælargerÆ are fuzzy terms which give a gradual linguistic meaning to crisp intervalls in the respective universes of discourse. In order to learn a Fuzzy Fuzzy Rule base from examples we introduce Genetic Algorithms and Artificial Neural Networks as learning operators. These examples can either be empirical data or originate from an economic simulation model. The software GENEFER (GEnetic NEural Fuzzy ExplorER) has been developed for designing such a Fuzzy Rule Base. The design process is modular and comprises Input Identification, Fuzzification, Rule-Base Generating and Rule-Base Tuning. The two latter steps make use of genetic and neural learning algorithms for optimizing the Fuzzy Rule-Base.

New perspectives on realism, tractability, and complexity in economics

Fuzzy logic and genetic algorithms are used to rework more realistic (and more complex) models of competitive markets. The resulting equilibria are significantly different from the ones predicted from the usual static analysis; the methodology solves the Walrasian problem of how markets can reach equilibrium, starting with firms trading at disparate prices. The modified equilibria found in these complex market models involve some mutual self-restraint on the part of the agents involved, relative to economically rational behaviour. Research (using similar techniques) into the evolution of collaborative behaviours in economics, and of altruism generally, is summarized; and the joint significance of these two bodies of work for public policy is reviewed. The possible extension of the fuzzy/ genetic methodology to other technical aspects of economics (including international trade theory, and development) is also discussed, as are the limitations to the usefulness of any type of theory in political domains. For the latter purpose, a more differentiated concept of rationality, appropriate to ill-structured choices, is developed. The philosophical case for laissez-faire policies is considered briefly; and the prospects for change in the way we ‘do economics’ are analysed.Fuzzy logic; genetic algorithms; complexity; emergence; rationality; ill-structured choice; equilibrium; Walrasian Crier; paradigm change;

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.

Curvature-based sparse rule base generation for fuzzy rule interpolation

Fuzzy logic has been successfully widely utilised in many real-world applications. The most common application of fuzzy logic is the rule-based fuzzy inference system, which is composed of mainly two parts including an inference engine and a fuzzy rule base. Conventional fuzzy inference systems always require a rule base that fully covers the entire problem domain (i.e., a dense rule base). Fuzzy rule interpolation (FRI) makes inference possible with sparse rule bases which may not cover some parts of the problem domain (i.e., a sparse rule base). In addition to extending the applicability of fuzzy inference systems, fuzzy interpolation can also be used to reduce system complexity for over-complex fuzzy inference systems. There are typically two methods to generate fuzzy rule bases, i.e., the knowledge driven and data-driven approaches. Almost all of these approaches only target dense rule bases for conventional fuzzy inference systems. The knowledge-driven methods may be negatively affected by the limited availability of expert knowledge and expert knowledge may be subjective, whilst redundancy often exists in fuzzy rule-based models that are acquired from numerical data. Note that various rule base reduction approaches have been proposed, but they are all based on certain similarity measures and are likely to cause performance deterioration along with the size reduction. This project, for the first time, innovatively applies curvature values to distinguish important features and instances in a dataset, to support the construction of a neat and concise sparse rule base for fuzzy rule interpolation. In addition to working in a three-dimensional problem space, the work also extends the natural three-dimensional curvature calculation to problems with high dimensions, which greatly broadens the applicability of the proposed approach. As a result, the proposed approach alleviates the ‘curse of dimensionality’ and helps to reduce the computational cost for fuzzy inference systems. The proposed approach has been validated and evaluated by three real-world applications. The experimental results demonstrate that the proposed approach is able to generate sparse rule bases with less rules but resulting in better performance, which confirms the power of the proposed system. In addition to fuzzy rule interpolation, the proposed curvature-based approach can also be readily used as a general feature selection tool to work with other machine learning approaches, such as classifiers