Terrain Aided Navigation(TAN)technology has become increasingly important due to its effectiveness in environments where Global Positioning System(GPS)is unavailable.In recent years,TAN systems have been extensively r...Terrain Aided Navigation(TAN)technology has become increasingly important due to its effectiveness in environments where Global Positioning System(GPS)is unavailable.In recent years,TAN systems have been extensively researched for both aerial and underwater navigation applications.However,many TAN systems that rely on recursive Unmanned Aerial Vehicle(UAV)position estimation methods,such as Extended Kalman Filters(EKF),often face challenges with divergence and instability,particularly in highly non-linear systems.To address these issues,this paper proposes and investigates a hybrid two-stage TAN positioning system for UAVs that utilizes Particle Filter.To enhance the system’s robustness against uncertainties caused by noise and to estimate additional system states,a Fuzzy Particle Filter(FPF)is employed in the first stage.This approach introduces a novel terrain composite feature that enables a fuzzy expert system to analyze terrain non-linearities and dynamically adjust the number of particles in real-time.This design allows the UAV to be efficiently localized in GPS-denied environments while also reducing the computational complexity of the particle filter in real-time applications.In the second stage,an Error State Kalman Filter(ESKF)is implemented to estimate the UAV’s altitude.The ESKF is chosen over the conventional EKF method because it is more suitable for non-linear systems.Simulation results demonstrate that the proposed fuzzy-based terrain composite method achieves high positional accuracy while reducing computational time and memory usage.展开更多
C.L. Chang’s introduction of fuzzy topology in 1981 opened up new avenues for parallel theories in topology. However, Chang’s work appears to focus more on the topology of fuzzy sets rather than fuzzy topology itsel...C.L. Chang’s introduction of fuzzy topology in 1981 opened up new avenues for parallel theories in topology. However, Chang’s work appears to focus more on the topology of fuzzy sets rather than fuzzy topology itself. In 1975, Michálek presented a functional definition of ordinary topology and later developed fuzzy topology as a distinct extension of this idea, setting it apart from Chang’s approach. While there has been significant research on Chang’s fuzzy topology, Michálek’s version has not received as much attention. This paper introduces the concept of fuzzy regularly closed filters, or FRCM filters, within Michálek’s fuzzy topological space and explores some properties of FRCM ultrafilters.展开更多
In this study, we are first examining well-known approach to improve fuzzy reasoning model (FRM) by use of the genetic-based learning mechanism [1]. Later we propose our alternative way to build FRM, which has signifi...In this study, we are first examining well-known approach to improve fuzzy reasoning model (FRM) by use of the genetic-based learning mechanism [1]. Later we propose our alternative way to build FRM, which has significant precision advantages and does not require any adjustment/learning. We put together neuro-fuzzy system (NFS) to connect the set of exemplar input feature vectors (FV) with associated output label (target), both represented by their membership functions (MF). Next unknown FV would be classified by getting upper value of current output MF. After that the fuzzy truths for all MF upper values are maximized and the label of the winner is considered as the class of the input FV. We use the knowledge in the exemplar-label pairs directly with no training. It sets up automatically and then classifies all input FV from the same population as the exemplar FVs. We show that our approach statistically is almost twice as accurate, as well-known genetic-based learning mechanism FRM.展开更多
Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Hel...Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .展开更多
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
文摘Terrain Aided Navigation(TAN)technology has become increasingly important due to its effectiveness in environments where Global Positioning System(GPS)is unavailable.In recent years,TAN systems have been extensively researched for both aerial and underwater navigation applications.However,many TAN systems that rely on recursive Unmanned Aerial Vehicle(UAV)position estimation methods,such as Extended Kalman Filters(EKF),often face challenges with divergence and instability,particularly in highly non-linear systems.To address these issues,this paper proposes and investigates a hybrid two-stage TAN positioning system for UAVs that utilizes Particle Filter.To enhance the system’s robustness against uncertainties caused by noise and to estimate additional system states,a Fuzzy Particle Filter(FPF)is employed in the first stage.This approach introduces a novel terrain composite feature that enables a fuzzy expert system to analyze terrain non-linearities and dynamically adjust the number of particles in real-time.This design allows the UAV to be efficiently localized in GPS-denied environments while also reducing the computational complexity of the particle filter in real-time applications.In the second stage,an Error State Kalman Filter(ESKF)is implemented to estimate the UAV’s altitude.The ESKF is chosen over the conventional EKF method because it is more suitable for non-linear systems.Simulation results demonstrate that the proposed fuzzy-based terrain composite method achieves high positional accuracy while reducing computational time and memory usage.
文摘C.L. Chang’s introduction of fuzzy topology in 1981 opened up new avenues for parallel theories in topology. However, Chang’s work appears to focus more on the topology of fuzzy sets rather than fuzzy topology itself. In 1975, Michálek presented a functional definition of ordinary topology and later developed fuzzy topology as a distinct extension of this idea, setting it apart from Chang’s approach. While there has been significant research on Chang’s fuzzy topology, Michálek’s version has not received as much attention. This paper introduces the concept of fuzzy regularly closed filters, or FRCM filters, within Michálek’s fuzzy topological space and explores some properties of FRCM ultrafilters.
文摘In this study, we are first examining well-known approach to improve fuzzy reasoning model (FRM) by use of the genetic-based learning mechanism [1]. Later we propose our alternative way to build FRM, which has significant precision advantages and does not require any adjustment/learning. We put together neuro-fuzzy system (NFS) to connect the set of exemplar input feature vectors (FV) with associated output label (target), both represented by their membership functions (MF). Next unknown FV would be classified by getting upper value of current output MF. After that the fuzzy truths for all MF upper values are maximized and the label of the winner is considered as the class of the input FV. We use the knowledge in the exemplar-label pairs directly with no training. It sets up automatically and then classifies all input FV from the same population as the exemplar FVs. We show that our approach statistically is almost twice as accurate, as well-known genetic-based learning mechanism FRM.
文摘Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .
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.
