Regular relations play in hyperquasigroups theory a role analogous to congruences in semigroup theory.The aim of this paper is to introduce the concept of regular relations on hyperquasigroups and to investigate some ...Regular relations play in hyperquasigroups theory a role analogous to congruences in semigroup theory.The aim of this paper is to introduce the concept of regular relations on hyperquasigroups and to investigate some related properties.Further,the notion of fuzzy regular relations on hyperquasigroups is introduced and some characterizations are discussed.展开更多
Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At f...Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of R n . Secondly,by introducing cut preserving fuzzy mapping,the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions.展开更多
In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characteriz...In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.展开更多
The approximation capability of regular fuzzy neural networks to fuzzy functions is studied. When σ is a nonconstant, bounded and continuous function of $\mathbb{R}$ , some equivalent conditions are obtained, with wh...The approximation capability of regular fuzzy neural networks to fuzzy functions is studied. When σ is a nonconstant, bounded and continuous function of $\mathbb{R}$ , some equivalent conditions are obtained, with which continuous fuzzy functions can be approximated to any degree of accuracy by the four-layer feedforward regular fuzzy neural networks $\sum\limits_{k = 1}^q {\tilde W_k } \cdot \left( {\sum\limits_{j = 1}^p {\tilde V_{kj} \cdot \sigma (\tilde X \cdot \tilde U_j + \tilde \Theta _j )} } \right)$ . Finally a few examples of such fuzzy functions are given.展开更多
Purpose-The purpose of this study is to develop a hybrid algorithm for segmenting tumor from ultrasound images of the liver.Design/methodology/approach-After collecting the ultrasound images,contrast-limited adaptive ...Purpose-The purpose of this study is to develop a hybrid algorithm for segmenting tumor from ultrasound images of the liver.Design/methodology/approach-After collecting the ultrasound images,contrast-limited adaptive histogram equalization approach(CLAHE)is applied as preprocessing,in order to enhance the visual quality of the images that helps in better segmentation.Then,adaptively regularized kernel-based fuzzy C means(ARKFCM)is used to segment tumor from the enhanced image along with local ternary pattern combined with selective level set approaches.Findings-The proposed segmentation algorithm precisely segments the tumor portions from the enhanced images with lower computation cost.The proposed segmentation algorithm is compared with the existing algorithms and ground truth values in terms of Jaccard coefficient,dice coefficient,precision,Matthews correlation coefficient,f-score and accuracy.The experimental analysis shows that the proposed algorithm achieved 99.18% of accuracy and 92.17% of f-score value,which is better than the existing algorithms.Practical implications-From the experimental analysis,the proposed ARKFCM with enhanced level set algorithm obtained better performance in ultrasound liver tumor segmentation related to graph-based algorithm.However,the proposed algorithm showed 3.11% improvement in dice coefficient compared to graph-based algorithm.Originality/value-The image preprocessing is carried out using CLAHE algorithm.The preprocessed image is segmented by employing selective level set model and Local Ternary Pattern in ARKFCM algorithm.In this research,the proposed algorithm has advantages such as independence of clustering parameters,robustness in preserving the image details and optimal in finding the threshold value that effectively reduces the computational cost.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.60875034)the Natural Science Foun-ation of Education Committee of Hubei Province (Grant Nos.D20092901+3 种基金Q20092907D20082903B200529001)the Natural Science Foundation of Hubei Province (Grant No.2009CDB340)
文摘Regular relations play in hyperquasigroups theory a role analogous to congruences in semigroup theory.The aim of this paper is to introduce the concept of regular relations on hyperquasigroups and to investigate some related properties.Further,the notion of fuzzy regular relations on hyperquasigroups is introduced and some characterizations are discussed.
基金This work was supported by National Natural Science Foundation(699740 4 1 699740 0 6)
文摘Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of R n . Secondly,by introducing cut preserving fuzzy mapping,the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions.
文摘In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19601012).
文摘The approximation capability of regular fuzzy neural networks to fuzzy functions is studied. When σ is a nonconstant, bounded and continuous function of $\mathbb{R}$ , some equivalent conditions are obtained, with which continuous fuzzy functions can be approximated to any degree of accuracy by the four-layer feedforward regular fuzzy neural networks $\sum\limits_{k = 1}^q {\tilde W_k } \cdot \left( {\sum\limits_{j = 1}^p {\tilde V_{kj} \cdot \sigma (\tilde X \cdot \tilde U_j + \tilde \Theta _j )} } \right)$ . Finally a few examples of such fuzzy functions are given.
文摘Purpose-The purpose of this study is to develop a hybrid algorithm for segmenting tumor from ultrasound images of the liver.Design/methodology/approach-After collecting the ultrasound images,contrast-limited adaptive histogram equalization approach(CLAHE)is applied as preprocessing,in order to enhance the visual quality of the images that helps in better segmentation.Then,adaptively regularized kernel-based fuzzy C means(ARKFCM)is used to segment tumor from the enhanced image along with local ternary pattern combined with selective level set approaches.Findings-The proposed segmentation algorithm precisely segments the tumor portions from the enhanced images with lower computation cost.The proposed segmentation algorithm is compared with the existing algorithms and ground truth values in terms of Jaccard coefficient,dice coefficient,precision,Matthews correlation coefficient,f-score and accuracy.The experimental analysis shows that the proposed algorithm achieved 99.18% of accuracy and 92.17% of f-score value,which is better than the existing algorithms.Practical implications-From the experimental analysis,the proposed ARKFCM with enhanced level set algorithm obtained better performance in ultrasound liver tumor segmentation related to graph-based algorithm.However,the proposed algorithm showed 3.11% improvement in dice coefficient compared to graph-based algorithm.Originality/value-The image preprocessing is carried out using CLAHE algorithm.The preprocessed image is segmented by employing selective level set model and Local Ternary Pattern in ARKFCM algorithm.In this research,the proposed algorithm has advantages such as independence of clustering parameters,robustness in preserving the image details and optimal in finding the threshold value that effectively reduces the computational cost.
