New Mathematics and Natural Computation

A general and a comprehensive theory of fuzzy topological spaces on the basis of a fixed quadruple M = (L, ≤, ⊗, *), where (L, ≤), ⊗ and *, respectively, denote a complete lattice and binary operations on L satisfying some further axioms, was introduced by Höhle and Šostak. L-topological spaces, convergence structure of L-topological spaces and L-continuous functions form an important part of their work. The present paper continues the study in this area, and provides new results on the convergence structure of L-topological spaces and the continuity in L-topological spaces.

We shall extend the notion of a K-proximity relation and its properties into an intuitionistic fuzzy sense. We generate an intuitionistic fuzzy K-proximity by a given fuzzy K-proximity in different forms. Also, intuitionistic fuzzy K-proximity mappings and its properties are considered.

In this paper, we introduce the notions of fuzzy prime and fuzzy semiprime S-subacts, where S is a monoid with a zero and S-acts are representations of S. We establish their basic properties and prove some fundamental results in a fuzzy context, analogous to the results in ordinary semigroups and S-acts. It is shown, among other results, that if a fuzzy right S-subact is fuzzy irreducible, then the difference between fuzzy prime and fuzzy semiprime disappears.

The global robust asymptotic stability of bi-directional associative memory (BAM) neural networks with constant or time-varying delays is studied. An approach combining the Lyapunov-Krasovskii functional with the linear matrix inequality (LMI) is taken to study the problem. Some a criteria for the global robust asymptotic stability, which gives information on the delay-dependent property, are derived. Some illustrative examples are given to demonstrate the effectiveness of the obtained results.

In this paper, we first propose a reverse engineering solution to decode the NK Boolean dynamic network given the input and output of the system. This theory utilizes basis functions and dynamic matrices, through which the network's evolutionary behavior can be simulated in a rigorous mathematical manner. Then, a general network model, fuzzy logic network (FLN), is presented as the extension of the Boolean network. This novel network model assigns variable values in a continuous domain, and it can accommodate internal conflicts among variables. In addition, the FLN uses fuzzy logical functions instead of Boolean logical functions, which enables it to model highly non-linear relationships and periodicity. Using the approach of annealed approximations, we proved important theorems concerning the dynamic property of the FLN. Combined with the Zipf's law, the criteria of applying FLN to the modeling of gene regulatory networks were achieved.

The security of both technical and trade credit factors becomes a serious bottleneck that affects the current development of e-business. Honest behavior is one of the important aspects of trade credit safety. It is a vital step to establish and maintain a safe credit system. In this paper, we analyze the characteristic of the credit in e-business and establish a motivation model that violates honest behavior in e-business. We evaluate the credit, the mode of evaluation and the behavior of the credit in e-business by using game theory. We present the factors that affect the justness of credit evaluation in e-business.

Customer classification is one of the major tasks in customer relationship management. Customers often have both static characteristics and dynamic behavioral features. Using both kinds of data to conduct comprehensive analysis can enhance the reasonability of customer classification. In the proposed classification method, customer dynamic data is clustered using a hybrid genetic algorithm. The result is then combined with customer static data to give reasonable customer segmentation supported by neural network technique. A bank dataset-based experiment shows that applying the proposed method can obviously improve the accuracy of customer classification comparing with the traditional methods where only static data is used.

In order to help tourism organizations enhance customer satisfaction (CS) for their websites and online services, this study develops a two layer supply-demand analysis model for tourism websites CS evaluation. This model is built based on the functionalities of tourism websites, and it mainly focuses on the CS evaluations from successful tourism websites applications. A number of tourism online service websites in Beijing, China, are taken as study cases for measuring and analyzing the supply-demand difference of online services presented in the model. The model can be used in regional tourism management to identify issues regarding the activity characteristics of tourism websites and to obtain suggestions to both customer satisfaction and tourism website provider profit.

Information sharing and the conformity of information systems in China's hospitals have drawn attention due to the rapid development of the medicine industry and medical information systems. The paper proposes a game theory-based model for information sharing in hospitals by analyzing the current situation in China. Using the proposed model, a Doctor Workstation System (DWS) is developed. This DWS implements the conformity of the medical information systems by applying semantic web and web service techniques. The results show that the conformity of information systems for hospitals is a trend for the medical informalization in China.