Reduction method based on a new fuzzy rough set in fuzzy information system and its applications to scheduling problems

AbstractIn this paper, we present the concept of fuzzy information granule based on a relatively weaker fuzzy similarity relation called fuzzy TL-similarity relation for the first time. Then, according to the fuzzy information granule, we define the lower and upper approximations of fuzzy sets and a corresponding new fuzzy rough set. Furthermore, we construct a kind of new fuzzy information system based on the fuzzy TL-similarity relation and study its reduction using the fuzzy rough set. At last, we apply the reduction method based on the defined fuzzy rough set in the above fuzzy information system to the reduction of the redundant multiple fuzzy rule in the scheduling problems, and numerical computational results show that the reduction method based on the new fuzzy rough set is more suitable for the reduction of multiple fuzzy rules in the scheduling problems compared with the reduction methods based on the existing fuzzy rough set

Exploring the Boundary Region of Tolerance Rough Sets for Feature Selection

Of all of the challenges which face the effective application of computational intelli-gence technologies for pattern recognition, dataset dimensionality is undoubtedly one of the primary impediments. In order for pattern classifiers to be efficient, a dimensionality reduction stage is usually performed prior to classification. Much use has been made of Rough Set Theory for this purpose as it is completely data-driven and no other information is required; most other methods require some additional knowledge. However, traditional rough set-based methods in the literature are restricted to the requirement that all data must be discrete. It is therefore not possible to consider real-valued or noisy data. This is usually addressed by employing a discretisation method, which can result in information loss. This paper proposes a new approach based on the tolerance rough set model, which has the abil-ity to deal with real-valued data whilst simultaneously retaining dataset semantics. More significantly, this paper describes the underlying mechanism for this new approach to utilise the information contained within the boundary region or region of uncertainty. The use of this information can result in the discovery of more compact feature subsets and improved classification accuracy. These results are supported by an experimental evaluation which compares the proposed approach with a number of existing feature selection techniques. Key words: feature selection, attribute reduction, rough sets, classification

Finding Fuzzy-rough Reducts with Fuzzy Entropy

Abstract—Dataset dimensionality is undoubtedly the single most significant obstacle which exasperates any attempt to apply effective computational intelligence techniques to problem domains. In order to address this problem a technique which re-duces dimensionality is employed prior to the application of any classification learning. Such feature selection (FS) techniques attempt to select a subset of the original features of a dataset which are rich in the most useful information. The benefits can include improved data visualisation and transparency, a reduction in training and utilisation times and potentially, im-proved prediction performance. Methods based on fuzzy-rough set theory have demonstrated this with much success. Such methods have employed the dependency function which is based on the information contained in the lower approximation as an evaluation step in the FS process. This paper presents three novel feature selection techniques employing fuzzy entropy to locate fuzzy-rough reducts. This approach is compared with two other fuzzy-rough feature selection approaches which utilise other measures for the selection of subsets. I

Rough action on topological rough groups

[EN] In this paper we explore the interrelations between rough set theory and group theory. To this end, we first define a topological rough group homomorphism and its kernel. Moreover, we introduce rough action and topological rough group homeomorphisms, providing several examples. Next, we combine these two notions in order to define topological rough homogeneous spaces, discussing results concerning open subsets in topological rough groups.The authors wish to thank the Deanship for Scientific Research (DSR) at King Abdulaziz University for financially funding this project under grant no. KEP-PhD-2-130-39. Also, we would like to thank the editor and referees for their valuable suggestions which have improved the presentation of the paper.Altassan, A.; Alharbi, N.; Aydi, H.; Özel, C. (2020). Rough action on topological rough groups. Applied General Topology. 21(2):295-304. https://doi.org/10.4995/agt.2020.13156OJS295304212S. Akduman, E. Zeliha, A. Zemci and S. 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Consensus Acceleration in Multiagent Systems with the Chebyshev Semi-Iterative Method

We consider the fundamental problem of reaching consensus in multiagent systems; an operation required in many applications such as, among others, vehicle formation and coordination, shape formation in modular robotics, distributed target tracking, and environmental modeling. To date, the consensus problem (the problem where agents have to agree on their reported values) has been typically solved with iterative decentralized algorithms based on graph Laplacians. However, the convergence of these existing consensus algorithms is often too slow for many important multiagent applications, and thus they are increasingly being combined with acceleration methods. Unfortunately, state-of-the-art acceleration techniques require parameters that can be optimally selected only if complete information about the network topology is available, which is rarely the case in practice. We address this limitation by deriving two novel acceleration methods that can deliver good performance even if little information about the network is available. The first proposed algorithm is based on the Chebyshev semi-iterative method and is optimal in a well defined sense; it maximizes the worst-case convergence speed (in the mean sense) given that only rough bounds on the extremal eigenvalues of the network matrix are available. It can be applied to systems where agents use unreliable communication links, and its computational complexity is similar to those of simple Laplacian-based methods. This algorithm requires synchronization among agents, so we also propose an asynchronous version that approximates the output of the synchronous algorithm. Mathematical analysis and numerical simulations show that the convergence speed of the proposed acceleration methods decrease gracefully in scenarios where the sole use of Laplacian-based methods is known to be impractical

A Framework for Semi-automatic Fiducial Localization in Volumetric Images

Fiducial localization in volumetric images is a common task performed by image-guided navigation and augmented reality systems. These systems often rely on fiducials for image-space to physical-space registration, or as easily identifiable structures for registration validation purposes. Automated methods for fiducial localization in volumetric im- ages are available. Unfortunately, these methods are not generalizable as they explicitly utilize strong a priori knowledge such as fiducial intensity values in CT, or known spatial configurations as part of the algorithm. Thus, manual localization has remained the most general approach, read- ily applicable across fiducial types and imaging modalities. The main drawbacks of manual localization are the variability and accuracy errors associated with visual localization. We describe a semi-automatic fiducial localization approach that combines the strengths of the human opera- tor and an underlying computational system. The operator identifies the rough location of the fiducial, and the computational system accurately localizes it via intensity based registration using the mutual information similarity measure. This approach is generic, implicitly accommodating for all fiducial types and imaging modalities. The framework was evalu- ated using five fiducial types and three imaging modalities. We obtained a maximal localization accuracy error of 0.35mm, with a maximal preci- sion variability of 0.5mm