多重模糊蕴涵与生成模糊蕴涵的新方法

提出一种生成模糊蕴涵的新方法,即通过一个或多个选定的模糊蕴涵作多重迭代生成新的模糊蕴涵,称为多重模糊蕴涵.从选定的模糊蕴涵出发,根据不同的迭代次数,分别证明迭代结果仍为模糊蕴涵.进一步,分析当选定的模糊蕴涵具有某种性质时,所生成的多重模糊蕴涵是否仍保持这些性质.还对选定的模糊蕴涵分别为(S,N)-蕴涵和R-蕴涵这两种重要情形,进行更深入的分析.这些结果将为模糊蕴涵在控制及决策等领域的应用提供支持.     

A novel memetic algorithm and its application to data clustering

In this paper, a novel memetic algorithm (MA) named GS-MPSO is proposed by combining a particle swarm optimization (PSO) with a Gaussian mutation operator and a Simulated Annealing (SA)-based local search operator. In GS-MPSO, the particles are organized as a ring lattice. The Gaussian mutation operator is applied to the stagnant particles to prevent GS-MPSO trapping into local optima. The SA-based local search strategy is developed to combine with the cognition-only PSO model and perform a fine-grained local search around the promising regions. The experimental results show that GS-MPSO is superior to some other variants of PSO with better performance on optimizing the benchmark functions when the computing resource is limited. Data clustering is studied as a real case study to further demonstrate its optimization ability and usability, too.     

Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation

Numerical Algorithms - The main contribution of this article is to introduce new compact fourth-order, standard fourth-order, and standard second-order finite difference schemes for solving the...     

A posteriori accuracy estimations of solutions to ill-posed inverse problems and extra-optimal regularizing algorithms for their solution

A new scheme of a posteriori accuracy estimation for approximate solutions to ill-posed inverse problems is presented along with an algorithm of calculating this estimation. A new notion of extra-optimal regularizing algorithmis introduced as a method for solving ill-posed inverse problems having optimal in order a posteriori accuracy estimation. Sufficient conditions of extra-optimality are formulated and an example of extra-optimal regularizing algorithm is given. The developed theory is illustrated by numerical experiments.     

The minimum cost flow problem: A unifying approach to dual algorithms and a new tree-search algorithm

This paper is concerned with the minimum cost flow problem. It is shown that the class of dual algorithms which solve this problem consists of different variants of a common general algorithm. We develop a new variant which is, in fact, a new form of the ‘primal-dual algorithm’ and which has several interesting properties. It uses, explicitly only dual variables. The slope of the change in the (dual) objective is monotone. The bound on the maximum number of iterations to solve a problem with integral bounds on the flow is better than bounds for other algorithms. This paper is part of the author's doctoral dissertation submitted at Yale University.     

A continuum of solutions to variational inequality with nonlinear constraints: Existence and simplicial algorithm

In this paper, we obtain an existence theorem of a connected set of solutions to a nonlinear variational inequality with explicit nonlinear constraints. This result follows in a constructive way by designing a simplicial algorithm. The algorithm operates on a triangulation of the unbounded regions and generates a piecewise linear path of parametrized stationary points. Each point on the path is an approximate solution.     

Existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non-Lipschitzian condition

This paper makes a research into a class of fuzzy stochastic differential equations (FSDEs) driven by a continuous local martingale under the non-Lipschitzian condition. Such equations can be useful in modelling of hybrid systems, where the phenomena are subjected to two kinds of uncertainties: randomness and fuzziness, simultaneously. The solutions of FSDEs are the fuzzy stochastic processes, and their uniqueness is considered to be in a strong sense. Thus, the existence and uniqueness of solutions to FSDEs under the non-Lipschitzian condition is first proven. And the continuity of solutions to FSDEs with respect to the initial data or the coefficients of the equations is investigated.     

A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis

Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets(IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.     

A hybrid method of Pareto,TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments

Multi-periodic inventory control problems are mainly studied employing one of two assumptions. The first is the continuous review, where depending on the inventory level, orders can be placed at any time, and the other is the periodic review, where orders can be placed only at the beginning of each period. In this paper, we relax these assumptions and assume that the time-periods between two replenishments are random fuzzy variables. While in the model of the problem at hand the decision variables are of integer type and there are space and service level constraints, for the shortages we consider a combination of back-order and lost-sales. We show the model of this problem to be an integer-nonlinear-programming type and in order to solve it, a hybrid method of Pareto, TOPSIS and Genetic Algorithm approach is used. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology.