集合环

本文用集环来表现模糊集，得到了表现定理的新形式，并证明了这种表现可以有限化，即用有限个经典集近似刻划模糊集并且这样的刻划是同态的。最后，证明了集对方法是集环表现的特殊情形。     

Continuous Selectors of Fixed Point Sets of Multifunctions with Decomposable Values

Existence theorems of continuous selectors whose values are fixed points of multivalued contractions are proved. As an application, the existence of continuous selectors to generalized solution sets of partial differential inclusions, depending on a parameter, is obtained.     

Second Order Representations of the Least Absolute Deviation Regression Estimator

We consider exact weak and strong Bahadur-Kiefer representations of the least absolute deviation estimator for the linear regression model. The precise behavior of these representations is obtained under minimal conditions.     

CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION

By using cone-directed contingent derivatives, the unified necessary and suffi-cient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set valued optimization.     

Partition Lattice q-Analogs Related to q-Stirling Numbers

We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F _q. Another member is constructed so as to mirror the partial order in the subspace lattice.     

SOLVABILITY OF FORWARD-BACKWARD SDES AND THE NODAL SET OF HAMILTON-JACOBI-BELLMAN EQUATIONS

The solvability of a class of forward-backward stochastic differential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. The authors design a stochastic relaxed control problem, with both drift and difftusion all being controlled, so that the solvability problem is converted to a problem of finding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. This method overcomes the fatal difficulty encountered in the traditional contraction mapping approach to the existence theorem of such SDEs.     

双参数随机Sierpinski垫的相位曲线

引入双参数随机置换，考虑了具有参数ｐ，ｑ的随机Ｓｉｅｒｐｉｎｓｋｉ垫的各种形态的相位，讨论了ｐ，ｑ跨跃某些相位曲线时，其构成形态的变化情形，它包括了ｑ＝０的Ｓｉｅｒｐｉｎｓｋｉ垫和ｑ＝ｐ的Ｍａｎｄｅｌｂｒｏｔ渗流模型。     

An Interval-Parameter Fuzzy Approach for Multiobjective Linear Programming Under Uncertainty

An interval-parameter fuzzy linear programming method (IFMOLP) is proposed in this study for multiple objective decision-making under uncertainty. As a hybrid of interval-parameter and fuzzy methodologies, the IFMOLP incorporates interval-parameter linear programming and fuzzy multiobjective programming approaches to form an integrated optimization system. The method inherits advantages of interval-parameter programming, and allows uncertainties and decision-makers’ aspirations to be effectively communicated into its programming processes and resulting solutions. Membership functions for both objectives and constraints are formulated to reflect uncertainties in different system components and their interrelationships. An interactive solution procedure has been developed based on solution approaches of the interval-parameter and fuzzy programming techniques, plus necessary measures for handling the multiobjective feature. A didactic example is provided in the paper to illustrate the detailed solution process. Possibilities of further improvements by seeking Pareto optimum and incorporating flexible preference within constraints are also discussed.     

On Vector Quasi-Variational Inequality Problems in H-Space

The purpose to this paper is to study the existence problem of solutions to the vector quasi-variational inequality for vector-valued functions in H-space.     

Polynomial expansion of basis sets: Alternatives to fully optimized exponents

Alternatives based on polynomial expansions of gaussian basis set exponents are introduced and evaluated. The formulas presented here outperform methods based upon the even-tempered formula or combinations of it. They closely match the performance of other methods based upon larger polynomial expansions of the logarithm of the exponents using the same or one less parameter per orbital angular symmetry.