Da-Zeng Tian

Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making

In this paper, we develop a series of induced generalized aggregation operators for hesitant fuzzy or interval-valued hesitant fuzzy information, including induced generalized hesitant fuzzy ordered weighted averaging (IGHFOWA) operators, induced generalized hesitant fuzzy ordered weighted geometric (IGHFOWG) operators, induced generalized interval-valued hesitant fuzzy ordered weighted averaging (IGIVHFOWA) operators, and induced generalized interval-valued hesitant fuzzy ordered weighted geometric (IGIVHFOWG) operators. Next, we investigate their various properties and some of their special cases. Furthermore, some approaches based on the proposed operators are developed to solve multiple attribute group decision making (MAGDM) problems with hesitant fuzzy or interval-valued hesitant fuzzy information. Finally, some numerical examples are provided to illustrate the developed approaches.

Applications of wavelet transform in medical image processing

The wavelet transform and inverse transform algorithm are introduced. The medical image plays an important role in clinical diagnosis and therapy of doctor and teaching and researching. This paper gives reviews of some applications in medical image with wavelet, such as ECG signal processing, EEG signal processing, medical image compression, medical image reinforcing and edge detection, medical image register. With the further development of wavelet theory, wavelet transform be widely applied to the domain of medical image.

The Fuzzy- Number Based Key Theorem of Statistical Learning Theory

Recently, many scholars are becoming interested in the study of statistical learning theory based on fuzzy field. In this paper, we redefine the definitions of fuzzy expected risk functional, fuzzy empirical risk functional and fuzzy empirical risk minimization principal based on fuzzy samples, where the two type of fuzzy risk functional are still fuzzy number. Based on the above, we give the proof of the key theorem, which plays an important role in the statistical learning theory

Fuzzy support vector machine based on non-equilibrium data

Fuzzy support vector machine (FSVM), whose membership function is based on class centers, can effectively solve the problem that the traditional support vector machine (SVM) is sensitive to the noises and outliers. However, FSVM assigns smaller memberships to support vectors, which may decrease the effects of these support vectors upon the construction of classification hyperplane. At the same time, FSVM has some disadvantages in dealing with the non-equilibrium data classification. Therefore, a novel method to determine membership function is proposed, and a new FSVM based on non-equilibrium data is constructed. Experiments show that the new FSVM can effectively reduce the misclassification rates produced by the class with fewer samples in dealing with non-equilibrium data classification problem. Therefore, the proposed FSVM may make the misclassification rates upon two classes approximately equal.

Parameterized intuitionistic fuzzy trapezoidal operators and their application to multiple attribute group decision making

The aim of this paper is to develop a series of parameterized intuitionistic fuzzy trapezoidal operators for aggregating intuitionistic fuzzy trapezoidal numbers. First, the concept and some operational laws of intuitionistic fuzzy trapezoidal numbers are introduced. Then, based on these operational laws, we present some parameterized intuitionistic fuzzy trapezoidal operators for aggregating the attribute values that take the form of intuitionistic fuzzy trapezoidal numbers. We study some desired properties of these aggregation operators and investigate the relationships among these operators. Furthermore, we apply these aggregation operators to develop an approach to multiple attribute group decision making with intuitionistic fuzzy trapezoidal information. Finally, an illustrative example is provided to demonstrate the practicality and effectiveness of the developed approach.

Rough set model based on credibility measure

Probabilistic rough set model is based on probabilistic measure which satisfied additive property. But in practical applications, there exist some non-additive set functions. So combining with credibility measure with self-duality and non-additive property, the conditional credibility measure is introduced, the entire credibility formula is given, the rough set model based on credibility measure is constructed, some properties of this model is proved. This model is applied to the Bayesian decision. Finally, the difference between this model and Pawlak rough set model is discussed.

Rough set model based on Sugeno measure

Probabilistic rough set model has a wide range of applications in uncertain information system. However, the probabilistic rough set model is based on the probability measure, which satisfies countable additivity. Considering the existence of many non-additive set functions in practical applications, rough set model based on the Sugeno measure is proposed. Moreover, the properties, the definition of roughness, together with the approximation accuracy of the proposed rough set model are provided.

Optical Formula Extraction Based on Irregularity Degree

Optical formula extraction is considered as an important step of mathematical formula recognition, which can convert scientific papers into their corresponding electronic format. So far little research has been done in this area. This paper proposes an approach of extracting embedded formulas that first invokes a searching algorithm to find the connected components of the input document, calculates the layout feature of every component based on irregularity degree, and then locates the formula symbols according to the features. Finally, several measurements including linking grammar are used to locate the formula areas. The experimental results indicate that the proposed method can obtain favorable results

An exponential entropy on intuitionistic fuzzy sets

According to the axiomatic definition of fuzzy degree on intuitionistic fuzzy sets, an exponential fuzzy degree is presented. Based on this, an exponential entropy on intuitionistic fuzzy sets is given, and the effectiveness of the entropy is verified by applying it to the multiple attribute decision algorithm.

The key theorem of learning theory based on hybrid variable

The definitions of hybrid empirical risk functional, hybrid excepted risk functional and hybrid empirical risk minimization principle in chance space are proposed; The Khintchine law of large numbers based on hybrid variable in chance space is proved; And the key theorem of learning theory based on hybrid variable in chance space is proved.