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Fuzzy rule-based systems are one of the most important areas of application of fuzzy sets and fuzzy logic. Constituting an extension of classical rule-based systems, these have been successfully applied to a wide range of problems in different domains for which uncertainty and vagueness emerge in multiple ways. In a broad sense, fuzzy rule-based systems are rule-based systems, where fuzzy sets and fuzzy logic are used as tools for representing different forms of knowledge about the problem at hand, as well as for modeling the interactions and relationships existing between its variables. The use of fuzzy statements as one of the main constituents of the rules allows capturing and handling the potential uncertainty of the represented knowledge. On the other hand, thanks to the use of fuzzy logic, inference methods have become more robust and flexible. This chapter will mainly analyze what is a fuzzy rule-based system (from both conceptual and structural points of view), how is it built, and how can be used. The analysis will start by considering the two main conceptual components of these systems, knowledge, and reasoning, and how they are represented. Then, a review of the main structural approaches to fuzzy rule-based systems will be considered. Hierarchical fuzzy systems will also be analyzed. Once defined the components, structure and approaches to those systems, the question of design will be considered. Finally, some conclusions will be presented.

The popularity of modern online social networks has grown up so quickly in the last few years that, nowadays, social network analysis has become one of the hottest research lines in the world. It is important to highlight that social network analysis is not limited to the analysis of networks connecting people. Indeed, it is strongly connected with the classical methods widely recognized in the context of graph theory. Thus, social network analysis is applied to many different areas like for instance economics, bibliometrics, and so on. This contribution shows how it can also be successfully applied in the context of designing interpretable fuzzy systems. The key point consists of looking at the rule base of a fuzzy system as a fuzzy inference-gram (fingram), i.e., as a social network made of nodes representing fuzzy rules. In addition, nodes are connected through edges that represent the interaction between rules, at inference level, in terms of co-fired rules, i.e., rules fired at the same time by a given input vector. In short, fingram analysis consists of studying the interaction among nodes in the network for the purpose of understanding the structure and behavior of the fuzzy rule base under consideration. It is based on the basic principles of social network analysis which have been properly adapted to the design of fuzzy systems.

Nowadays, one of the significant topics in fuzzy systems design is that of the interpretability-accuracy trade-off. We can consider that the presence of this question as a key aspect of fuzziness is quite new, as a matter of fact, only at the beginning of this century, the question has been formalized and analyzed. But, on the other hand, most of us, who have been working in fuzzy systems design for many years, have crossed the border line between interpretable and accurate fuzzy systems, several times in our career.

Looking for a good interpretability-accuracy trade-off is one of the most challenging tasks on fuzzy modelling. Indeed, interpretability is acknowledged as a distinguishing capability of linguistic fuzzy systems since the proposal of Zadeh and Mamdani's seminal ideas. Anyway, obtaining interpretable fuzzy systems is not straightforward. It becomes a matter of careful design which must cover several abstraction levels. Namely, from the design of each individual linguistic term (and its related fuzzy set) to the analysis of the cooperation among several rules, what depends on the fuzzy inference mechanism. This work gives an overview on existing tools for fuzzy system modelling. Moreover, it introduces GUAJE which is an open-source free-software java environment for building understandable and accurate fuzzy rule-based systems by means of combining several pre-existing tools.

The use of hybrid artificial intelligence systems in operations management has grown during the last years given their ability to tackle combinatorial and NP hard problems. Furthermore, operations management problems usually involve imprecision, uncertainty, vagueness, and high-dimensionality. This paper examines recent developments in the field of hybrid artificial intelligence systems for those operations management problems where hybrid approaches are more representative: design engineering, process planning, assembly line balancing, and dynamic scheduling.

The framework of this paper is robot localization inside buildings using WiFi signal strength measure. This localization is usually made up of two phases: training and estimation stages. In the former the WiFi signal strength of all visible Access Points (APs) are collected and stored in a database or Wifi map, while in the latter the signal strengths received from all APs at a certain position are compared with the WiFi map to estimate the robot location. This work proposes the use of Fuzzy Rule-based Classification in order to obtain the robot position during the estimation stage, after a short training stage where only a few significant WiFi measures are needed. As a result, the proposed method is easily adaptable to new environments where triangulation algorithms can not be applied since the AP physical location is unknown. It has been tested in a real environment using our own robotic platform. Experimental results are better than those achieved by other classical methods.

Overview.- Accuracy Improvements to Find the Balance Interpretability-Accuracy in Linguistic Fuzzy Modeling: An Overview.- Accuracy Improvements Constrained by Interpretability Criteria.- COR Methodology: A Simple Way to Obtain Linguistic Fuzzy Models with Good Interpretability and Accuracy.- Constrained optimization of genetic fuzzy systems.- Trade-off between the Number of Fuzzy Rules and Their Classification Performance.- Generating distinguishable, complete, consistent and compact fuzzy systems using evolutionary algorithms.- Fuzzy CoCo: Balancing Accuracy and Interpretability of Fuzzy Models by Means of Coevolution.- On the Achievement of Both Accurate and Interpretable Fuzzy Systems Using Data-Driven Design Processes.- Extending the Modeling Process to Improve the Accuracy.- Linguistic Hedges and Fuzzy Rule Based Systems.- Automatic Construction of Fuzzy Rule-Based Systems: A trade-off between complexity and accuracy maintaining interpretability.- Using Individually Tested Rules for the Data-based Generation of Interpretable Rule Bases with High Accuracy.- Extending the Model Structure to Improve the Accuracy.- A description of several characteristics for improving the accuracy and interpretability of inductive linguistic rule learning algorithms.- An Iterative Learning Methodology to Design Hierarchical Systems of Linguistic Rules for Linguistic Modeling.- Learning Default Fuzzy Rules with General and Punctual Exceptions.- Integration of Fuzzy Knowledge.- Tuning fuzzy partitions or assigning weights to fuzzy rules: which is better?.

In this contribution, we propose a genetic process to select an appropiate set of features in a Fuzzy Rule-Based Classification System (FRBCS) and to automatically learn the whole Data Base definition using a non linear scaling function to adapt the fuzzy partition contexts and determining an appropiate granularity for each of them. An ad-hoc data covering learning method is considered to obtain the Rule Base. The method uses a multiobjective genetic algorithm in order to obtain a good trade-off between accuracy and interpretability.

System modeling with fuzzy rule-based systems (FRBSs), i.e. fuzzy modeling (FM), usually comes with two contradictory requirements in the obtained model: the interpretability, capability to express the behavior of the real system in an understandable way, and the accuracy, capability to faithfully represent the real system. While linguistic FM (mainly developed by linguistic FRBSs) is focused on the interpretability, precise FM (mainly developed by Takagi-Sugeno-Kang FRBSs) is focused on the accuracy. Since both criteria are of vital importance in system modeling, the balance between them has started to pay attention in the fuzzy community in the last few years.

System modeling with fuzzy rule-based systems (FRBSs), i.e. fuzzy modeling (FM), usually comes with two contradictory requirements in the obtained model: the interpretability, capability to express the behavior of the real system in an understandable way, and the accuracy, capability to faithfully represent the real system. While linguistic FM (mainly developed by linguistic FRBSs) is focused on the interpretability, precise FM (mainly developed by Takagi-Sugeno-Kang FRBSs) is focused on the accuracy. Since both criteria are of vital importance in system modeling, the balance between them has started to pay attention in the fuzzy community in the last few years.

A way to improve the reliability and to reduce costs in autonomous robots is to add intelligence to on-board diagnosis and control systems to avoid expensive hardware redundancy and inopportune mission abortion. According to this, the main goal of the ADVOCATE II project is to adapt legacy piloting software around a generic SOAP (Simple Object Access Protocol) architecture on which intelligent modules could be plugged. Artificial Intelligent (AI) modules using Belief Bayesian Networks (BBN), Neuro-Symbolic Systems (NSS), and Fuzzy Logic (FL) are coordinated to help the operator or piloting system manage fault detection, risk assessment, and recovery plans. In this paper, the specification of the ADVOCATE II system is presented.