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

Neuro-fuzzy techniques to optimize an FPGA embedded controller for robot navigation

This paper describes how low-cost embedded controllers for robot navigation can be obtained by using a small number of if-then rules (exploiting the connection in cascade of rule bases) that apply Takagi-Sugeno fuzzy inference method and employ fuzzy sets represented by normalized triangular functions. The rules comprise heuristic and fuzzy knowledge together with numerical data obtained from a geometric analysis of the control problem that considers the kinematic and dynamic constraints of the robot. Numerical data allow tuning the fuzzy symbols used in the rules to optimize the controller performance. From the implementation point of view, very few computational and memory resources are required: standard logical, addition, and multiplication operations and a few data that can be represented by integer values. This is illustrated with the design of a controller for the safe navigation of an autonomous car-like robot among possible obstacles toward a goal configuration. Implementation results of an FPGA embedded system based on a general-purpose soft processor confirm that percentage reduction in clock cycles is drastic thanks to applying the proposed neuro-fuzzy techniques. Simulation and experimental results obtained with the robot confirm the efficiency of the controller designed. Design methodology has been supported by the CAD tools of the environment Xfuzzy 3 and by the Embedded System Tools from Xilinx. © 2014 Elsevier B.V.Peer Reviewe

Evolution of Voronoi based Fuzzy Recurrent Controllers

A fuzzy controller is usually designed by formulating the knowledge of a human expert into a set of linguistic variables and fuzzy rules. Among the most successful methods to automate the fuzzy controllers development process are evolutionary algorithms. In this work, we propose the Recurrent Fuzzy Voronoi (RFV) model, a representation for recurrent fuzzy systems. It is an extension of the FV model proposed by Kavka and Schoenauer that extends the application domain to include temporal problems. The FV model is a representation for fuzzy controllers based on Voronoi diagrams that can represent fuzzy systems with synergistic rules, fulfilling the $\epsilon$-completeness property and providing a simple way to introduce a priory knowledge. In the proposed representation, the temporal relations are embedded by including internal units that provide feedback by connecting outputs to inputs. These internal units act as memory elements. In the RFV model, the semantic of the internal units can be specified together with the a priori rules. The geometric interpretation of the rules allows the use of geometric variational operators during the evolution. The representation and the algorithms are validated in two problems in the area of system identification and evolutionary robotics

On Information Granulation via Data Filtering for Granular Computing-Based Pattern Recognition: A Graph Embedding Case Study

Granular Computing is a powerful information processing paradigm, particularly useful for the synthesis of pattern recognition systems in structured domains (e.g., graphs or sequences). According to this paradigm, granules of information play the pivotal role of describing the underlying (possibly complex) process, starting from the available data. Under a pattern recognition viewpoint, granules of information can be exploited for the synthesis of semantically sound embedding spaces, where common supervised or unsupervised problems can be solved via standard machine learning algorithms. In this companion paper, we follow our previous paper (Martino et al. in Algorithms 15(5):148, 2022) in the context of comparing different strategies for the automatic synthesis of information granules in the context of graph classification. These strategies mainly differ on the specific topology adopted for subgraphs considered as candidate information granules and the possibility of using or neglecting the ground-truth class labels in the granulation process and, conversely, to our previous work, we employ a filtering-based approach for the synthesis of information granules instead of a clustering-based one. Computational results on 6 open-access data sets corroborate the robustness of our filtering-based approach with respect to data stratification, if compared to a clustering-based granulation stage

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

Spectral Pattern Recognition and Fuzzy Artmap Classification: Design Features, System Dynamics and Real World Simulation

Classification of terrain cover from satellite radar imagery represents an area of considerable current interest and research. Most satellite sensors used for land applications are of the imaging type. They record data in a variety of spectral channels and at a variety of ground resolutions. Spectral pattern recognition refers to classification procedures utilizing pixel-by-pixel spectral information as the basis for automated land cover classification. A number of methods have been developed in the past to classify pixels [resolution cells] from multispectral imagery to a priori given land cover categories. Their ability to provide land cover information with high classification accuracies is significant for work where accurate and reliable thematic information is needed. The current trend towards the use of more spectral bands on satellite instruments, such as visible and infrared imaging spectrometers, and finer pixel and grey level resolutions will offer more precise possibilities for accurate identification. But as the complexity of the data grows, so too does the need for more powerful tools to analyse them. It is the major objective of this study to analyse the capabilities and applicability of the neural pattern recognition system, called fuzzy ARTMAP, to generate high quality classifications of urban land cover using remotely sensed images. Fuzzy ARTMAP synthesizes fuzzy logic and Adaptive Resonance Theory (ART) by exploiting the formal similarity between the computations of fuzzy subsethood and the dynamics of category choice, search and learning. The paper describes design features, system dynamics and simulation algorithms of this learning system, which is trained and tested for classification (8 a priori given classes) of a multispectral image of a Landsat-5 Thematic Mapper scene (270 x 360 pixels) from the City of Vienna on a pixel-by-pixel basis. Fuzzy ARTMAP performance is compared with that of an error-based learning system based upon the multi-layer perceptron, and the Gaussian maximum likelihood classifier as conventional statistical benchmark on the same database. Both neural classifiers outperform the conventional classifier in terms of classification accuracy. Fuzzy ARTMAP leads to out-of-sample classification accuracies, very close to maximum performance, while the multi-layer perceptron--like the conventional classifier--shows difficulties to distinguish between some land use categories