Improved filtering H∞ finite frequency of Takagi-Sugeno fuzzy systems

The work treats the filter H∞ finite frequency (FF) in Takagi-Sugeno (T-S) two dimensional (2-D) systems described by Fornasini-Marchesini local state-space (FM LSS)models. The goal of this work is to find an FF H∞ T-S fuzzy filter model design in such a way that the error system is stable and has a reduced FF H∞ performance over FF area swith noise is established as aprerequisite. Via the use of the generalized Kalman Yakubovich Popov (gKYP) lemma, Lyapunov functions approach, Finsler’s lemma, and parameterize slack matrices, new design conditions guaranteeing the FF H∞ T-S fuzzy filter method of FM LSS models are developed by solving linear matrix inequalities (LMIs). At last, the simulation results are provided to show the effectiveness and the validity of the proposed FF T-S fuzzy of FM LSS models strategy by a practical application has been made.

Improvement in CNN-Based Multifocus Image Fusion Algorithm with Triangulated Fuzzy Filter

Multifocus image fusion is a demanding research field due to the utilization of modern imaging devices. Generally, the scene to be captured contains objects at different distances from these devices and so a set of multifocus images of the scene is captured with different objects in-focus. However, to improve the situational awareness of the captured scene, these sets of images are required to be fused together. Therefore, a multifocus image fusion algorithm based on Convolutional Neural Network (CNN) and triangulated fuzzy filter is proposed. A CNN is used to extract information regarding focused pixels of input images and the same is used as fusion rule for fusing the input images. The focused information so extracted may still need to be refined near the boundaries. Therefore, asymmetrical triangular fuzzy filter with the median center (ATMED) is employed to correctly classify the pixels near the boundary. The advantage of using this filter is to rely on precise detection results since any misdetection may considerably degrade the fusion quality. The performance of the proposed algorithm is compared with the state-of-art image fusion algorithms, both subjectively and objectively. Various parameters such as edge strength ([Formula: see text]), fusion loss (FL), fusion artifacts (FA), entropy ([Formula: see text]), standard deviation (SD), spatial frequency (SF), structural similarity index measure (SSIM) and feature similarity index measure (FSIM) are used to evaluate the performance of the proposed algorithm. Experimental results proved that the proposed fusion algorithm produces a fused image that contains all-in-one focused pixels and is better than those obtained using other popular and latest image fusion works.

Falling shadow theory with applications in hoops

The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filer are displayed.

Fuzzy filters of Sheffer stroke Hilbert algebras

The aim of this study is to introduce fuzzy filters of Sheffer stroke Hilbert algebra. After defining fuzzy filters of Sheffer stroke Hilbert algebra, it is shown that a quotient structure of this algebra is described by its fuzzy filter. In addition to this, the level filter of a Sheffer stroke Hilbert algebra is determined by its fuzzy filter. Some fuzzy filters of a Sheffer stroke Hilbert algebra are defined by a homomorphism. Normal and maximal fuzzy filters of a Sheffer stroke Hilbert algebra and the relation between them are presented. By giving the Cartesian product of fuzzy filters of a Sheffer stroke Hilbert algebra, various properties are examined.

μ -Fuzzy Filters in Distributive Lattices

In this paper, we introduce the concept of μ -fuzzy filters in distributive lattices. We study the special class of fuzzy filters called μ -fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of coannihilators. We observe that every μ -fuzzy filter is the intersection of all prime μ -fuzzy filters containing it. We also topologize the set of all prime μ -fuzzy filters of a distributive lattice. Properties of the space are also studied. We show that there is a one-to-one correspondence between the class of μ -fuzzy filters and the lattice of all open sets in X μ . It is proved that the space X μ is a T 0 space.

Filtering a Signal in a Fuzzy Filter Based on the Area Ratio Method

Purpose of reseach. Digital signal filtering allows real-time noise reduction in electronic devices. Currently, there are many different digital filters, differing in speed, computing power, algorithms and restrictions on the conditions of use. One of these filters is the Kalman filter, but adjusting the gains of this filter is very complicated by the process of additional experiments and collection of statistical information. Therefore, in this paper, the authors consider a simplified algorithm for finding the control coefficients of a fuzzy digital filter with defuzzifier based on the area ratio method and investigate the influence of the area ratio method parameters on signal filtering, thereby achieving the goal of improving the accuracy of the fuzzy digital filter. Methods. For the algorithm for finding the control coefficients of the digital filter, a fuzzy logic apparatus was used. The control factors are determined using a defuzzifier based on the area ratio method. Results. In the course of experimental studies, the mean square error RMSE was calculated for a fuzzy digital filter using the area ratio method, the center of gravity method and the Kalman filter. Based on the results obtained, it was concluded that the fuzzy filter based on the area ratio RMSE method is 5.43 times less than for the Kalman filter and 2.77 times less than for the defuzzifier based on the center of gravity method. The results obtained prove the effectiveness of using a fuzzy digital filter with the area ratio method. Conclusion: This article considers an algorithm for the operation of a fuzzy digital filter, simulates a fuzzy digital filter and a Kalman filter in the Simulink system and calculates the RMSE values for a fuzzy digital filter with the area ratio method and the center of gravity method, as well as the Kalman filter.