Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, ...Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, the θ-intuitionistic fuzzy mapping is defined, and the θ-intuitionistic fuzzy homomorphism of groups is obtained. The properties of intuitionistic fuzzy subgroups and intuitionistic fuzzy normal subgroups are studied under the θ-intuitionistic fuzzy homomorphism of groups, and the fundamental theorem of θ-intuitionistic fuzzy homomorphism is proved.展开更多
Blockchain technology has garnered significant attention from global organizations and researchers due to its potential as a solution for centralized system challenges.Concurrently,the Internet of Things(IoT)has revol...Blockchain technology has garnered significant attention from global organizations and researchers due to its potential as a solution for centralized system challenges.Concurrently,the Internet of Things(IoT)has revolutionized the Fourth Industrial Revolution by enabling interconnected devices to offer innovative services,ultimately enhancing human lives.This paper presents a new approach utilizing lightweight blockchain technology,effectively reducing the computational burden typically associated with conventional blockchain systems.By integrating this lightweight blockchain with IoT systems,substantial reductions in implementation time and computational complexity can be achieved.Moreover,the paper proposes the utilization of the Okamoto Uchiyama encryption algorithm,renowned for its homomorphic characteristics,to reinforce the privacy and security of IoT-generated data.The integration of homomorphic encryption and blockchain technology establishes a secure and decentralized platformfor storing and analyzing sensitive data of the supply chain data.This platformfacilitates the development of some business models and empowers decentralized applications to perform computations on encrypted data while maintaining data privacy.The results validate the robust security of the proposed system,comparable to standard blockchain implementations,leveraging the distinctive homomorphic attributes of the Okamoto Uchiyama algorithm and the lightweight blockchain paradigm.展开更多
Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homo...Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.展开更多
文摘Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, the θ-intuitionistic fuzzy mapping is defined, and the θ-intuitionistic fuzzy homomorphism of groups is obtained. The properties of intuitionistic fuzzy subgroups and intuitionistic fuzzy normal subgroups are studied under the θ-intuitionistic fuzzy homomorphism of groups, and the fundamental theorem of θ-intuitionistic fuzzy homomorphism is proved.
文摘Blockchain technology has garnered significant attention from global organizations and researchers due to its potential as a solution for centralized system challenges.Concurrently,the Internet of Things(IoT)has revolutionized the Fourth Industrial Revolution by enabling interconnected devices to offer innovative services,ultimately enhancing human lives.This paper presents a new approach utilizing lightweight blockchain technology,effectively reducing the computational burden typically associated with conventional blockchain systems.By integrating this lightweight blockchain with IoT systems,substantial reductions in implementation time and computational complexity can be achieved.Moreover,the paper proposes the utilization of the Okamoto Uchiyama encryption algorithm,renowned for its homomorphic characteristics,to reinforce the privacy and security of IoT-generated data.The integration of homomorphic encryption and blockchain technology establishes a secure and decentralized platformfor storing and analyzing sensitive data of the supply chain data.This platformfacilitates the development of some business models and empowers decentralized applications to perform computations on encrypted data while maintaining data privacy.The results validate the robust security of the proposed system,comparable to standard blockchain implementations,leveraging the distinctive homomorphic attributes of the Okamoto Uchiyama algorithm and the lightweight blockchain paradigm.
文摘Several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when G is given and H is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case.
