Rough communication of crisp concept in fuzzy approximation spaces

To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy approximation spaces, the problem of uncertainty exists, for each agent has a different language and cannot provide precise communication to each other. By means of some concepts, such as CF rough communication cut, which is a bridge between fuzzy concept and crisp concept, cut analysis of CF rough communication is made, and the relation theorem between CF rough communication and rough communication of crisp concept is obtained. Finally, in order to give an intuitive analysis of the relation between CF rough communication and rough communication of crisp concept, an example is given.

APPROXIMATION CAPABILITIES OF MULTILAYER FEEDFORWARD REGULAR FUZZY NEURAL NETWORKS

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.

Transformation and entropy for fuzzy rough sets

A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.

Fuzzy rough sets in Sostak sense

In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.

Numerical Solution of Second-Orders Fuzzy Linear Differential Equation

In this paper, the numerical solution of the boundary value problem that is two-order fuzzy linear differential equations is discussed. Based on the generalized Hukuhara difference, the fuzzy differential equation is converted into a fuzzy difference equation by means of decentralization. The numerical solution of the boundary value problem is obtained by calculating the fuzzy differential equation. Finally, an example is given to verify the effectiveness of the proposed method.

Attribute reduction based on fuzziness of approximation set in multi-granulation spaces

Rough set theory is an important tool to solve uncertain problems. Attribute reduction, as one of the core issues of rough set theory, has been proven to be an effective method for knowledge acquisition. Most of heuristic attribute reduction algorithms usually keep the positive region of a target set unchanged and ignore boundary region information. So, how to acquire knowledge from the boundary region of a target set in a multi-granulation space is an interesting issue. In this paper, a new concept, fuzziness of an approximation set of rough set is put forward firstly. Then the change rules of fuzziness in changing granularity spaces are analyzed. Finally, a new algorithm for attribute reduction based on the fuzziness of 0.5-approximation set is presented. Several experimental results show that the attribute reduction by the proposed method has relative better classification characteristics compared with various classification algorithms.

A stall diagnosis method based on entropy feature identification in axial compressors

A stall diagnosis method based on the entropy feature extraction algorithm is developed in axial compressors.The reliability of the proposed method is determined and a parametric sensitivity analysis is experimentally conducted for two different types of compressor stall diagnoses.A collection of time‐resolved pressure sensors is mounted circumferentially and along the chord direction to measure the dynamic pressure on the casing.Results show that the stall and prestall precursor embedded in the dynamic pressures are identified through nonlinear feature perturbation extraction using the entropy feature extraction algorithm.Further analysis demonstrates that the prestall precursor with the peak entropy value is related to the unsteady tip leakage flow for the spike‐type stall diagnosis.The modal wave inception with increasing amplitude is identified by the considerable increase of the entropy value.The flow field in the tip region indicates that the modal wave corresponds to the flow separation in the suction side of the rotor blade.The warning time is 100–300 rotor revolutions for both types of stall diagnoses,which is beneficial for stall control in different axial compressors.Moreover,a parametric study of the embedding dimension m,similar tolerance n,similar radius r,and data length N in the fuzzy entropy method is conducted to determine the optimal parameter setting for stall diagnosis.The stall warning based on the entropy feature extraction algorithm provides a new stall diagnosis approach in the axial compressor with different stall types.This stall warning can also be adopted as an online stability monitoring index when using the concept of active stall control.