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

An artificial immune systems based predictive modelling approach for the multi-objective elicitation of Mamdani fuzzy rules: a special application to modelling alloys

In this paper, a systematic multi-objective Mamdani fuzzy modeling approach is proposed, which can be viewed as an extended version of the previously proposed Singleton fuzzy modeling paradigm. A set of new back-error propagation (BEP) updating formulas are derived so that they can replace the old set developed in the singleton version. With the substitution, the extension to the multi-objective Mamdani Fuzzy Rule-Based Systems (FRBS) is almost endemic. Due to the carefully chosen output membership functions, the inference and the defuzzification methods, a closed form integral can be deducted for the defuzzification method, which ensures the efficiency of the developed Mamdani FRBS. Some important factors, such as the variable length coding scheme and the rule alignment, are also discussed. Experimental results for a real data set from the steel industry suggest that the proposed approach is capable of eliciting not only accurate but also transparent FRBS with good generalization ability

Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets

Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures of similarity which preserve all the common properties (i.e. reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013

Formal presentation of fuzzy systems with multiple sensor inputs

The paper addresses the problems of complexity in fuzzy rule based systems with multiple sensor inputs. The number of fuzzy rules in this case is an exponential function of the number of inputs. Some of the existing methods for rule base reductions are reviewed and their drawbacks summarized. As an alternative, a novel methodology for complexity management in fuzzy systems is presented which is based on formal presentation techniques such as integer tables. A Matlab example is shown illustrating the presentation of a fuzzy rule base with an integer table. Finally, some future research directions are outlined within the framework of the proposed methodology

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

Improving Transparency in Approximate Fuzzy Modeling Using Multi-objective Immune-Inspired Optimisation

In this paper, an immune inspired multi-objective fuzzy modeling (IMOFM) mechanism is proposed specifically for high-dimensional regression problems. For such problems, prediction accuracy is often the paramount requirement. With such a requirement in mind, however, one should also put considerable efforts in eliciting models which are as transparent as possible, a ‘tricky’ exercise in itself. The proposed mechanism adopts a multi-stage modeling procedure and a variable length coding scheme to account for the enlarged search space due to simultaneous optimisation of the rule-base structure and its associated parameters. We claim here that IMOFM can account for both Singleton and Mamdani Fuzzy Rule-Based Systems (FRBS) due to the carefully chosen output membership functions, the inference scheme and the defuzzification method. The proposed modeling approach has been compared to other representatives using a benchmark problem, and was further applied to a high-dimensional problem, taken from the steel industry, which concerns the prediction of mechanical properties of hot rolled steels. Results confirm that IMOFM is capable of eliciting not only accurate but also transparent FRBSs from quantitative data

An Ontology-Based Interpretable Fuzzy Decision Support System for Diabetes Diagnosis

Diabetes is a serious chronic disease. The importance of clinical decision support systems (CDSSs) to diagnose diabetes has led to extensive research efforts to improve the accuracy, applicability, interpretability, and interoperability of these systems. However, this problem continues to require optimization. Fuzzy rule-based systems are suitable for the medical domain, where interpretability is a main concern. The medical domain is data-intensive, and using electronic health record data to build the FRBS knowledge base and fuzzy sets is critical. Multiple variables are frequently required to determine a correct and personalized diagnosis, which usually makes it difficult to arrive at accurate and timely decisions. In this paper, we propose and implement a new semantically interpretable FRBS framework for diabetes diagnosis. The framework uses multiple aspects of knowledge-fuzzy inference, ontology reasoning, and a fuzzy analytical hierarchy process (FAHP) to provide a more intuitive and accurate design. First, we build a two-layered hierarchical and interpretable FRBS; then, we improve this by integrating an ontology reasoning process based on SNOMED CT standard ontology. We incorporate FAHP to determine the relative medical importance of each sub-FRBS. The proposed system offers numerous unique and critical improvements regarding the implementation of an accurate, dynamic, semantically intelligent, and interpretable CDSS. The designed system considers the ontology semantic similarity of diabetes complications and symptoms concepts in the fuzzy rules' evaluation process. The framework was tested using a real data set, and the results indicate how the proposed system helps physicians and patients to accurately diagnose diabetes mellitusThis work was supported by National Research Foundation of Korea-Grant funded by the Korean Government (Ministry of Science, ICT and Future Planning)-NRF-2017R1A2B2012337)S

On-Line Construction and Rule Base Simplification by Replacement in Fuzzy Systems Applied to a Wastewater Treatment Plant

Evolving Takagi-Sugeno (eTS) fuzzy models are used to build a computational model for the WasteWater Treatment Plant (WWTP) in a paper mill. The fuzzy rule base is constructed on-line from data using a recursive fuzzy clustering algorithm that develops the model structure and parameters. In order to avoid some redundancy in the fuzzy rule base mechanisms for merging membership functions and simplifying fuzzy rules are introduced. The rule base simplification is done by replacement allowing the preservation of the rule (cluster) centres as data points belonging to the original data set. Results for the WWTP show that it is possible to build less complex models and preserve a good balance between accuracy and transparency. Copyright © 2005 IFA

Trade-off between accuracy and interpretability: Experience-oriented fuzzy modeling via reduced-set vectors

AbstractThis paper focuses on accuracy and interpretability issue of fuzzy model approaches. In order to balance the trade-off between both of the aspects, a new fuzzy model based on experience-oriented learning algorithm is proposed. Firstly, support vector regression (SVR) with presented Mercer kernels is employed to generate the initial fuzzy model and the available experience on the training data. Secondly, a bottom-up simplification algorithm is introduced to generate reduced-set vectors for simplifying the structure of the initial fuzzy model, at the same time the parameters of the simplified model derived are adjusted by a hybrid learning algorithm including linear ridge regression algorithm and gradient descent method based on a new performance measure. Finally, taking the results from two-dimensional sinc function approximation and fuzzy control of the bar and beam system, the proposed fuzzy model preserves nice accuracy and interpretability