Rule model simplification

Centre for Intelligent Systems and their ApplicationsDue to its high performance and comprehensibility, fuzzy modelling is becoming more and more popular in dealing with nonlinear, uncertain and complex systems for tasks such as signal processing, medical diagnosis and financial investment. However, there are no principal routine methods to obtain the optimum fuzzy rule base which is not only compact but also retains high prediction (or classification) performance. In order to achieve this, two major problems need to be addressed. First, as the number of input variables increases, the number of possible rules grows exponentially (termed curse of dimensionality). It inevitably deteriorates the transparency of the rule model and can lead to over-fitting, with the model obtaining high performance on the training data but failing to predict the unknown data successfully. Second, gaps may occur in the rule base if the problem is too compact (termed sparse rule base). As a result, it cannot be handled by conventional fuzzy inference such as Mamdani. This Ph.D. work proposes a rule base simplification method and a family of fuzzy interpolation methods to solve the aforementioned two problems. The proposed simplification method reduces the rule base complexity via Retrieving Data from Rules (RDFR). It first retrieves a collection of new data from an original rule base. Then the new data is used for re-training to build a more compact rule model. This method has four advantages: 1) It can simplify rule bases without using the original training data, but is capable of dealing with combinations of rules and data. 2) It can integrate with any rule induction or reduction schemes. 3) It implements the similarity merging and inconsistency removal approaches. 4) It can make use of rule weights. Illustrative examples have been given to demonstrate the potential of this work. The second part of the work concerns the development of a family of transformation based fuzzy interpolation methods (termed HS methods). These methods first introduce the general concept of representative values (RVs), and then use this to interpolate fuzzy rules involving arbitrary polygonal fuzzy sets, by means of scale and move transformations. This family consists of two sub-categories: namely, the original HS methods and the enhanced HS methods. The HS methods not only inherit the common advantages of fuzzy interpolative reasoning -- helping reduce rule base complexity and allowing inferences to be performed within simple and sparse rule bases -- but also have two other advantages compared to the existing fuzzy interpolation methods. Firstly, they provide a degree of freedom to choose various RV definitions to meet different application requirements. Secondly, they can handle the interpolation of multiple rules, with each rule having multiple antecedent variables associated with arbitrary polygonal fuzzy membership functions. This makes the interpolation inference a practical solution for real world applications. The enhanced HS methods are the first proposed interpolation methods which preserve piece-wise linearity, which may provide a solution to solve the interpolation problem in a very high Cartesian space in the mathematics literature. The RDFR-based simplification method has been applied to a variety of applications including nursery prediction, the Saturday morning problem and credit application. HS methods have been utilized in truck backer-upper control and computer hardware prediction. The former demonstrates the simplification potential of the HS methods, while the latter shows their capability in dealing with sparse rule bases. The RDFR-based simplification method and HS methods are further integrated into a novel model simplification framework, which has been applied to a scaled-up application (computer activity prediction). In the experimental studies, the proposed simplification framework leads to very good fuzzy rule base reductions whilst retaining, or improving, performance

Fuzzy interpolation with generalized representative values

Fuzzy interpolative reasoning offers the potential to model problems using sparse rule bases, as opposed to dense rule bases deployed in traditional fuzzy systems. It thus supports the simplification of complex fuzzy models in terms of rule number and facilitates inferences when limited knowledge is available. This paper presents an interpolative reasoning method by means of scale and move transformations

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

Models and modelling

When searching for nature rules we encounter a fundamental difficulty: for technical reasons we are not able to investigate the whole Nature - we have to explore its sections i.e. empirical systems (structures). However, even then it might happen that the system is too complex and its comprehensive, direct investigation is impossible. In this case we can study the system by means of its abstract model e.g. a mathematical model.Abstract models of empirical systems usually present simplified modelled systems, where simplification depends on different reasons, e.g. on the purpose of model construction or the state of our knowledge on a modelled system. As a rule we also exclude from the model those independent variables, whose influence on a dependent variable is insignificant. Simplification does not have to mean that the validity of the simplified heuristic model is lower than the validity of the same model before its simplification.Some remarks refer to certain methodological problems associated with models and modelling, as well as scientific research performed with those tools

Building Fuzzy Elevation Maps from a Ground-based 3D Laser Scan for Outdoor Mobile Robots

Mandow, A; Cantador, T.J.; Reina, A.J.; Martínez, J.L.; Morales, J.; García-Cerezo, A. "Building Fuzzy Elevation Maps from a Ground-based 3D Laser Scan for Outdoor Mobile Robots," Robot2015: Second Iberian Robotics Conference, Advances in Robotics, (2016) Advances in Intelligent Systems and Computing, vol. 418. This is a self-archiving copy of the author’s accepted manuscript. The final publication is available at Springer via http://link.springer.com/book/10.1007/978-3-319-27149-1.The paper addresses terrain modeling for mobile robots with fuzzy elevation maps by improving computational speed and performance over previous work on fuzzy terrain identification from a three-dimensional (3D) scan. To this end, spherical sub-sampling of the raw scan is proposed to select training data that does not filter out salient obstacles. Besides, rule structure is systematically defined by considering triangular sets with an unevenly distributed standard fuzzy partition and zero order Sugeno-type consequents. This structure, which favors a faster training time and reduces the number of rule parameters, also serves to compute a fuzzy reliability mask for the continuous fuzzy surface. The paper offers a case study using a Hokuyo-based 3D rangefinder to model terrain with and without outstanding obstacles. Performance regarding error and model size is compared favorably with respect to a solution that uses quadric-based surface simplification (QSlim).This work was partially supported by the Spanish CICYT project DPI 2011-22443, the Andalusian project PE-2010 TEP-6101, and Universidad de Málaga-Andalucía Tech

Integrating Transformer and Paraphrase Rules for Sentence Simplification

Sentence simplification aims to reduce the complexity of a sentence while retaining its original meaning. Current models for sentence simplification adopted ideas from machine translation studies and implicitly learned simplification mapping rules from normalsimple sentence pairs. In this paper, we explore a novel model based on a multi-layer and multi-head attention architecture and we propose two innovative approaches to integrate the Simple PPDB (A Paraphrase Database for Simplification), an external paraphrase knowledge base for simplification that covers a wide range of real-world simplification rules. The experiments show that the integration provides two major benefits: (1) the integrated model outperforms multiple stateof-the-art baseline models for sentence simplification in the literature (2) through analysis of the rule utilization, the model seeks to select more accurate simplification rules. The code and models used in the paper are available at https://github.com/ Sanqiang/text_simplification