Fuzzy Entropy： Axiomatic Definition and Neural Networks Model

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.     

广义拟变分不等式解集的稳定性及本质连通区的存在性

在赋范线性空间下．讨论广义拟变分不等式解集的稳定性，证明了满足一定连续性和凸性条件的广义拟变分不等式问题构成的空间M中，大多数(在Baire分类意义下)广义拟变分不等式问题的解集是稳定的，并证明了M中每一个广义拟变分不等式的解集至少存在一个本质连通区。     

非终身免疫传染病模型解的适定性

本文将讨论非终生免疫性传染病模型解的适定性及正则性；同时证明了整体解的存在，以及解对初值的连续依赖。     

An Approach to Fuzzy Noncooperative Nash Games

Systems that involve more than one decision maker are often optimized using the theory of games. In the traditional game theory, it is assumed that each player has a well-defined quantitative utility function over a set of the player decision space. Each player attempts to maximize/minimize his/her own expected utility and each is assumed to know the extensive game in full. At present, it cannot be claimed that the first assumption has been shown to be true in a wide variety of situations involving complex problems in economics, engineering, social and political sciences due to the difficulty inherent in defining an adequate utility function for each player in these types of problems. On the other hand, in many of such complex problems, each player has a heuristic knowledge of the desires of the other players and a heuristic knowledge of the control choices that they will make in order to meet their ends.In this paper, we utilize fuzzy set theory in order to incorporate the players' heuristic knowledge of decision making into the framework of conventional game theory or ordinal game theory. We define a new approach to N-person static fuzzy noncooperative games and develop a solution concept such as Nash for these types of games. We show that this general formulation of fuzzy noncooperative games can be applied to solve multidecision-making problems where no objective function is specified. The computational procedure is illustrated via application to a multiagent optimization problem dealing with the design and operation of future military operations.     

Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

Classical H. Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H. Minkowski uniqueness theorem due to A.D. Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.     

广义向量均衡问题的解与解集的凸性

引进集值映射的锥真拟凹概念，讨论一类具有集值映射的广义向量衡问题解的存在性与解集的凸性。     

Monotone Mappings and Flows of Viscous Media

We establish solvability of the boundary-value problems describing stationary and periodic flows of viscoplastic media. In the case of stationary flows we study the question of convergence of the Galerkin method. For the problem of periodic flows we prove a version of the second Bogolyubov theorem.     

A new proof for Rockafellar's characterization of maximal monotone operators

We provide a new and short proof for Rockafellar's characterization of maximal monotone operators in reflexive Banach spaces based on S. Fitzpatrick's function and a technique used by R. S. Burachik and B. F. Svaiter for proving their result on the representation of a maximal monotone operator by convex functions.

     

向量优化问题广义有效点的一个存在性定理

利用集值映射不动点定理及最优化问题与变分不等式的关系给出线性G^↑ateaux可微的锥凸映射的广义有效点的一个存在性定理。     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.