A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis

© 2014 Elsevier B.V. Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.Lynn D’eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765 and P10-TIC-6858, and by project PYR-2014-8 of the Genil Program of CEI BioTic GRANADA and Lluis Godo has been partially supported by the Spanish MINECO project EdeTRI TIN2012-39348-C02-01Peer Reviewe

Systems Statistical Engineering – Hierarchical Fuzzy Constraint Propagation

Driven by a growing requirement during the 21st century for the integration of rigorous statistical analyses in engineering research, there has been a movement within the statistics and quality communities to evolve a unified statistical engineering body of knowledge (Hoerl & Snee, 2010). Systems Statistical Engineering research seeks to integrate causal Bayesian hierarchical modeling (Pearl, 2009) and cybernetic control theory within Beer\u27s Viable System Model (S Beer, 1972; Stafford Beer, 1979, 1985) and the Complex Systems Governance framework (Keating, 2014; Keating & Katina, 2015, 2016) to produce multivariate systemic models for robust dynamic systems mission performance. (Cotter & Quigley, 2018) set forth the Bayesian systemic hierarchical constraint propagation theoretical basis for modeling the amplification and attenuation effects of environmental constraints propagated into systemic variability and variety. In their theoretical development, they simplified the analysis to only deterministic constraints, which models only the effect of statistical risks of failure. Imprecision and uncertainty in the assessment of environmental constraints will induce additional variance components in systemic variability and variety. To make causal Bayesian hierarchical modeling more capable of capturing and representing the imprecise and uncertain nature of environments, we must incorporate rough or fuzzy functions and boundaries to model imprecision and grey boundaries to model uncertainty in constraint propagation at each system level to measure the overall impact on the organization variability and variety. This paper sets forth a proposed research method to incorporate rough, fuzzy, and Grey set theories into Systems Statistical Engineering causal Bayesian hierarchical constraints modeling

Rough sets theory for travel demand analysis in Malaysia

This study integrates the rough sets theory into tourism demand analysis. Originated from the area of Artificial Intelligence, the rough sets theory was introduced to disclose important structures and to classify objects. The Rough Sets methodology provides definitions and methods for finding which attributes separates one class or classification from another. Based on this theory can propose a formal framework for the automated transformation of data into knowledge. This makes the rough sets approach a useful classification and pattern recognition technique. This study introduces a new rough sets approach for deriving rules from information table of tourist in Malaysia. The induced rules were able to forecast change in demand with certain accuracy

Scalable approximate FRNN-OWA classification

Fuzzy Rough Nearest Neighbour classification with Ordered Weighted Averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbour search. In practice, the query time complexity of exact nearest neighbour search algorithms in more than a handful of dimensions is near-linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbours returned by Hierarchical Navigable Small Worlds (HNSW), a recent approximative nearest neighbour search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW, and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster

Robust and fully automated segmentation of mandible from CT scans

Mandible bone segmentation from computed tomography (CT) scans is challenging due to mandible's structural irregularities, complex shape patterns, and lack of contrast in joints. Furthermore, connections of teeth to mandible and mandible to remaining parts of the skull make it extremely difficult to identify mandible boundary automatically. This study addresses these challenges by proposing a novel framework where we define the segmentation as two complementary tasks: recognition and delineation. For recognition, we use random forest regression to localize mandible in 3D. For delineation, we propose to use 3D gradient-based fuzzy connectedness (FC) image segmentation algorithm, operating on the recognized mandible sub-volume. Despite heavy CT artifacts and dental fillings, consisting half of the CT image data in our experiments, we have achieved highly accurate detection and delineation results. Specifically, detection accuracy more than 96% (measured by union of intersection (UoI)), the delineation accuracy of 91% (measured by dice similarity coefficient), and less than 1 mm in shape mismatch (Hausdorff Distance) were found.Comment: 4 pages, 5 figures, IEEE International Symposium on Biomedical Imaging (ISBI) 201

Smart Traction Control Systems for Electric Vehicles Using Acoustic Road-type Estimation

The application of traction control systems (TCS) for electric vehicles (EV) has great potential due to easy implementation of torque control with direct-drive motors. However, the control system usually requires road-tire friction and slip-ratio values, which must be estimated. While it is not possible to obtain the first one directly, the estimation of latter value requires accurate measurements of chassis and wheel velocity. In addition, existing TCS structures are often designed without considering the robustness and energy efficiency of torque control. In this work, both problems are addressed with a smart TCS design having an integrated acoustic road-type estimation (ARTE) unit. This unit enables the road-type recognition and this information is used to retrieve the correct look-up table between friction coefficient and slip-ratio. The estimation of the friction coefficient helps the system to update the necessary input torque. The ARTE unit utilizes machine learning, mapping the acoustic feature inputs to road-type as output. In this study, three existing TCS for EVs are examined with and without the integrated ARTE unit. The results show significant performance improvement with ARTE, reducing the slip ratio by 75% while saving energy via reduction of applied torque and increasing the robustness of the TCS.Comment: Accepted to be published by IEEE Trans. on Intelligent Vehicles, 22 Jan 201