Qun-Feng Zhang

Markov property of Markov chains and its test

Markov chains, with Markov property as its essence, are widely used in the fields such as information theory, automatic control, communication techniques, genetics, computer sciences, economic administration, education administration, and market forecasts. While using Markov chains to predict the future events, we must test the Markov property of random variable sequences of the past statistic data. Only when the random variable sequences satisfy the Markov property, can the prediction could be precise. This paper discusses the concept of Markov property and its features, studies its test method, and by example demonstrates the effectiveness of this prediction method.

Rough Modules and their Some Properties

The theory of rough set is of great advantages in dealing with the ambiguity in information systems. Combining it with abstract algebra is a way generalizing it. Some papers proposed the concepts of rough groups and rough rings in approximate spaces, and investigated their properties. In this paper, firstly we introduce the concepts of rough module, rough sub-module, rough quotient module in approximate spaces. Then we give some properties of them, and prove the fundamental theorem of homomorphism for rough modules

On the application of rough sets to data mining in economic practice

Mathematical models play an important role in the studies of modern economics. But in many fields of economics, it is difficult to build mathematical models for complex phenomena. So data mining is getting more and more popular in discovering the potential pattern of economic knowledge from databases. As a powerful tool for data mining, rough set theory has been widely used. In this research, we draw guidelines from several cases of rough set application in economic practice. Furthermore, to avoid the drawbacks of the existing methods, we develop a methodology for rough analysis in economic sector by combining the advantages of the fuzzy variable precision rough set model.

An Improved Authenticated (T, N) Threshold Signature Encryption Scheme Based on ECC

The improved authenticated (t, n) threshold signature encryption scheme based on ECC can not only shorten the time for data transmission, make operation accelerate and substantially reduce the load on the signer, but also have higher security not to be deceived by the third. The scheme uses a division-of-labor signature that decreases the workload on the signer and improves the performance; an idea in which the private key is concealed confines the authority of the SA, consequently, the new scheme is safer. Moreover, the scheme is based on the elliptic curve cryptosystem, supporting the practical use of the scheme, because of its highly efficient performance and comprehensiveness of security

A new hybrid intelligence algorithm for global optimization in logistics distribution system.

Modern city logistics plays an important role in developing economics, so many intelligent algorithms are employed to solve the problem locating the product distribution centers to minimize the total cost. Many factors affecting the cost must be taken into account. This paper proposes mathematical model of the problem and introduces a new hybrid intelligent algorithm by combining particle swarm optimization algorithm with gradient descent algorithm. Numerical experiments demonstrate the proposed algorithm has a better performance than those compared.

A kind of absorption probability of finite random walk on the plane

In this paper, a kind of finite-step random walks with three absorption boundaries is studied. First, the general expression of absorption probability for the random dots being absorbed by the three absorption boundaries is obtained. Second, the related mathematical proofs are provided.

Structural risk minimization principle on Sugeno space

In this paper, the idea of the structural risk minimization (SRM) on Sugeno measure space is presented; Borel-Cantelli lemma is proven on Sugeno measure space; a theorem is proven to answer the following question, is the structural risk minimization principle consistent on Sugeno measure space?

Induction of fuzzy decision tree based on fuzzy similarity relationship

A method based on fuzzy similarity relationship is proposed for learning a fuzzy decision tree from a real-valued decision system. First, fuzzy similarity relationships are utilized to fuzzy the real-valued attributes of the decision system into fuzzy-valued attributes by computing the closures of the similarity matrices. Second, a measure of importance of condition attributes is introduced using the loose lower approximation, which is based on similarity relationship. Finally, using the measure as the criteria to select the expanding attribute, an algorithm for a fuzzy decision tree is proposed, and an illustrative example is demonstrated.

Some topological and measure properties of rough sets

Since rough set theory was proposed by Pawlak in 1982, it has been investigated extensively and applied in a wide range of research fields such as machine learning and data mining. However, the pure mathematical explorations of rough sets have not been paid sufficient attention. This paper explores rough set theory from the point of view of topology and measure theory, and proves a few propositions about its properties.

An framework for generating fuzzy decision trees based on fuzzy rough techniques

Fuzzy decision tree is useful for expressing fuzzy knowledge because of its readability. There have been several induction algorithms for fuzzy decision trees from real value data sets. In this paper, we propose a framework for generating fuzzy decision trees based on fuzzy rough techniques. Firstly, the ordinary fuzzification techniques are replaced by a clustering technique based on the tolerance relation corresponding to every attribute. Secondly, a new fuzzy rough technique is introduced to reduce the dimensions. Thirdly, a new heuristics employing fuzzy rough lower approximation is constructed to generate a fuzzy decision tree. A small data is used for demonstrating the practicability of the proposed method.