IMPROVING UNDERSTANDABILITY AND UNCERTAINTY MODELING OF DATA USING FUZZY LOGIC SYSTEMS

The need for automation, optimality and efficiency has made modern day control and monitoring systems extremely complex and data abundant. However, the complexity of the systems and the abundance of raw data has reduced the understandability and interpretability of data which results in a reduced state awareness of the system. Furthermore, different levels of uncertainty introduced by sensors and actuators make interpreting and accurately manipulating systems difficult. Classical mathematical methods lack the capability to capture human knowledge and increase understandability while modeling such uncertainty. Fuzzy Logic has been shown to alleviate both these problems by introducing logic based on vague terms that rely on human understandable terms. The use of linguistic terms and simple consequential rules increase the understandability of system behavior as well as data. Use of vague terms and modeling data from non-discrete prototypes enables modeling of uncertainty. However, due to recent trends, the primary research of fuzzy logic have been diverged from the basic concept of understandability. Furthermore, high computational costs to achieve robust uncertainty modeling have led to restricted use of such fuzzy systems in real-world applications. Thus, the goal of this dissertation is to present algorithms and techniques that improve understandability and uncertainty modeling using Fuzzy Logic Systems. In order to achieve this goal, this dissertation presents the following major contributions: 1) a novel methodology for generating Fuzzy Membership Functions based on understandability, 2) Linguistic Summarization of data using if-then type consequential rules, and 3) novel Shadowed Type-2 Fuzzy Logic Systems for uncertainty modeling. Finally, these presented techniques are applied to real world systems and data to exemplify their relevance and usage

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

Data granulation by the principles of uncertainty

Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference

Multi-criteria decision making with linguistic labels: a comparison of two methodologies applied to energy planning

This paper compares two multi-criteria decision making (MCDM) approaches based on linguistic label assessment. The first approach consists of a modified fuzzy TOPSIS methodology introduced by Kaya and Kahraman in 2011. The second approach, introduced by Agell et al. in 2012, is based on qualitative reasoning techniques for ranking multi-attribute alternatives in group decision-making with linguistic labels. Both approaches are applied to a case of assessment and selection of the most suitable types of energy in a geographical area.Peer ReviewedPostprint (published version

Data-Driven Induction of Shadowed Sets Based on Grade of Fuzziness

We propose a procedure devoted to the induction of a shadowed set through the post-processing of a fuzzy set, which in turn is learned from labeled data. More precisely, the fuzzy set is inferred using a modified support vector clustering algorithm, enriched in order to optimize the fuzziness grade. Finally, the fuzzy set is transformed into a shadowed set through application of an optimal alpha-cut. The procedure is tested on synthetic and real-world datasets

A new extension of fuzzy sets using rough sets: R-fuzzy sets

This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some examples are provided

Automated software quality visualisation using fuzzy logic techniques

In the past decade there has been a concerted effort by the software industry to improve the quality of its products. This has led to the inception of various techniques with which to control and measure the process involved in software development. Methods like the Capability Maturity Model have introduced processes and strategies that require measurement in the form of software metrics. With the ever increasing number of software metrics being introduced by capability based processes, software development organisations are finding it more difficult to understand and interpret metric scores. This is particularly problematic for senior management and project managers where analysis of the actual data is not feasible. This paper proposes a method with which to visually represent metric scores so that managers can easily see how their organisation is performing relative to quality goals set for each type of metric. Acting primarily as a proof of concept and prototype, we suggest ways in which real customer needs can be translated into a feasible technical solution. The solution itself visualises metric scores in the form of a tree structure and utilises Fuzzy Logic techniques, XGMML, Web Services and the .NET Framework. Future work is proposed to extend the system from the prototype stage and to overcome a problem with the masking of poor scores

A Historical Account of Types of Fuzzy Sets and Their Relationships

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used