There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Theory of fuzzy integrals and its applications

Swarm robotics is an approach to collective robotics that takes inspiration from the self-organized behaviors of social animals. Through simple rules and local interactions, swarm robotics aims at designing robust, scalable, and flexible collective behaviors for the coordination of large numbers of robots. In this paper, we analyze the literature from the point of view of swarm engineering: we focus mainly on ideas and concepts that contribute to the advancement of swarm robotics as an engineering field and that could be relevant to tackle real-world applications. Swarm engineering is an emerging discipline that aims at defining systematic and well founded procedures for modeling, designing, realizing, verifying, validating, operating, and maintaining a swarm robotics system. We propose two taxonomies: in the first taxonomy, we classify works that deal with design and analysis methods; in the second taxonomy, we classify works according to the collective behavior studied. We conclude with a discussion of the current limits of swarm robotics as an engineering discipline and with suggestions for future research directions.

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Swarm robotics: a review from the swarm engineering perspective

An evolutionary recurrent network which automates the design of recurrent neural/fuzzy networks using a new evolutionary learning algorithm is proposed in this paper. This new evolutionary learning algorithm is based on a hybrid of genetic algorithm (GA) and particle swarm optimization (PSO), and is thus called HGAPSO. In HGAPSO, individuals in a new generation are created, not only by crossover and mutation operation as in GA, but also by PSO. The concept of elite strategy is adopted in HGAPSO, where the upper-half of the best-performing individuals in a population are regarded as elites. However, instead of being reproduced directly to the next generation, these elites are first enhanced. The group constituted by the elites is regarded as a swarm, and each elite corresponds to a particle within it. In this regard, the elites are enhanced by PSO, an operation which mimics the maturing phenomenon in nature. These enhanced elites constitute half of the population in the new generation, whereas the other half is generated by performing crossover and mutation operation on these enhanced elites. HGAPSO is applied to recurrent neural/fuzzy network design as follows. For recurrent neural network, a fully connected recurrent neural network is designed and applied to a temporal sequence production problem. For recurrent fuzzy network design, a Takagi-Sugeno-Kang-type recurrent fuzzy network is designed and applied to dynamic plant control. The performance of HGAPSO is compared to both GA and PSO in these recurrent networks design problems, demonstrating its superiority.

A hybrid of genetic algorithm and particle swarm optimization for recurrent network design

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

Ten years of genetic fuzzy systems: current framework and new trends

Although fuzzy systems demonstrated their ability to solve different kinds of problems in various applications, there is an increasing interest on augmenting them with learning capabilities. Two of the most successful approaches to hybridise fuzzy systems with adaptation methods have been made in the realm of soft computing: neuro-fuzzy systems and genetic fuzzy systems hybridise the approximate reasoning method of fuzzy systems with the learning capabilities of neural networks and evolutionary algorithms. The article focuses on genetic fuzzy systems, paying special attention to genetic fuzzy rule based systems, giving a brief overview of the field.

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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?.

Accuracy Improvements in Linguistic Fuzzy Modeling

This work describes a color Vision-based System intended to perform stable autonomous driving on unmarked roads. Accordingly, this implies the development of an accurate road surface detection system that ensures vehicle stability. Although this topic has already been documented in the technical literature by different research groups, the vast majority of the already existing Intelligent Transportation Systems are devoted to assisted driving of vehicles on marked extra urban roads and highways. The complete system was tested on the BABIECA prototype vehicle, which was autonomously driven for hundred of kilometers accomplishing different navigation missions on a private circuit that emulates an urban quarter. During the tests, the navigation system demonstrated its robustness with regard to shadows, road texture, and weather and changing illumination conditions.

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Luis Magdalena

Papers

Ten years of genetic fuzzy systems: current framework and new trends

Ten years of genetic fuzzy systems: current framework and new trends

Accuracy Improvements in Linguistic Fuzzy Modeling

A Color Vision-Based Lane Tracking System for Autonomous Driving on Unmarked Roads

Looking for a good fuzzy system interpretability index: An experimental approach