Fuzzy hypergroups based on fuzzy relations

AbstractBased on fuzzy reasoning in fuzzy logic, this paper studies a fuzzy hyperoperation and a fuzzy hypergroupoid associated with a fuzzy relation. A sufficient and necessary condition for such a fuzzy hypergroupoid being a fuzzy hypergroup is given, and the properties of the fuzzy hypergroups associated with fuzzy relations are investigated. Furthermore, the definition of normal fuzzy hypergroups is put forward and it is shown that the category NFHG of normal fuzzy hypergroups satisfies all the axioms of topos except for the subobject classifier axiom

Interval Entropy of Fuzzy Sets and the Application to Fuzzy Multiple Attribute Decision Making

A series of new concepts including interval entropy, interval similarity measure, interval distance measure, and interval inclusion measure of fuzzy sets are introduced. Meanwhile, some theorems and corollaries are proposed to show how these definitions can be deduced from each other. And then, based on interval entropy, a fuzzy multiple attribute decision making (FMADM) model is set up. In this model, interval entropy is used as the weight, by which the evaluation values of all alternatives can be obtained. Then all alternatives with respect to each criterion can be ranked as the order of the evaluation values. At last, a practical example is given to illustrate an application of the developed model and a comparative analysis is made

Multifunctional antimicrobial biometallohydrogels based on amino acid coordinated self-assembly

There is a real need for new antibiotics against self‐evolving bacteria. One option is to use biofriendly broad‐spectrum and mechanically tunable antimicrobial hydrogels that can combat multidrug‐resistant microbes. Whilst appealing, there are currently limited options. Herein, broad‐spectrum antimicrobial biometallohydrogels based on the self‐assembly and local mineralization of Ag+‐coordinated Fmoc‐amino acids are reported. Such biometallohydrogels have the advantages of localized delivery and sustained release, reduced drug dosage and toxicity yet improved bioavailability, prolonged drug effect, and tunable mechanical strength. Furthermore, they can directly interact with the cell walls and membrane, resulting in the detachment of the plasma membrane and leakage of the cytoplasm. This leads to cell death, triggering a significant antibacterial effect against both Gram‐negative (Escherichia coli) and Gram‐positive (Staphylococcus aureus) bacteria in cells and mice. This study paves the way for developing a multifunctional integration platform based on simple biomolecules coordinated self‐assembly toward a broad range of biomedical applications

A New Fuzzy System Based on Rectangular Pyramid

A new fuzzy system is proposed in this paper. The novelty of the proposed system is mainly in the compound of the antecedents, which is based on the proposed rectangular pyramid membership function instead of t-norm. It is proved that the system is capable of approximating any continuous function of two variables to arbitrary degree on a compact domain. Moreover, this paper provides one sufficient condition of approximating function so that the new fuzzy system can approximate any continuous function of two variables with bounded partial derivatives. Finally, simulation examples are given to show how the proposed fuzzy system can be effectively used for function approximation

Distributed and Deep Vertical Federated Learning with Big Data

In recent years, data are typically distributed in multiple organizations while the data security is becoming increasingly important. Federated Learning (FL), which enables multiple parties to collaboratively train a model without exchanging the raw data, has attracted more and more attention. Based on the distribution of data, FL can be realized in three scenarios, i.e., horizontal, vertical, and hybrid. In this paper, we propose to combine distributed machine learning techniques with Vertical FL and propose a Distributed Vertical Federated Learning (DVFL) approach. The DVFL approach exploits a fully distributed architecture within each party in order to accelerate the training process. In addition, we exploit Homomorphic Encryption (HE) to protect the data against honest-but-curious participants. We conduct extensive experimentation in a large-scale cluster environment and a cloud environment in order to show the efficiency and scalability of our proposed approach. The experiments demonstrate the good scalability of our approach and the significant efficiency advantage (up to 6.8 times with a single server and 15.1 times with multiple servers in terms of the training time) compared with baseline frameworks.Comment: To appear in CCPE (Concurrency and Computation: Practice and Experience