Multisets排序的最优并行算法

排序是一个既有十分重要的理论意义又有广泛的实际应用价值的问题 ,其中 ,Multisets排序问题是指对只有k个不同关键字值的n个数据 (记录 )进行排序 ,0 <k <n 基于“中值的中值”思想和“筛选”原理 ,通过在递归过程中不断地“筛选”掉某些具有相同关键字值的数据 ,以及自适应地动态分配处理器以平衡计算负载的方法 ,设计一种确定的稳定的Multisets排序并行算法 在具有 p =n1-ε(0 <ε<1)个处理器的共享存储并行机器上 ,对于CREWPRAM模型 ,算法的时间复杂度为O((n/ p +pε)logk) ,获得最优执行代价O(nlogk) ;对于EREWPRAM模型 ,算法所需时间为O((n/ p+pε+logp)logk) ,当 plogp≤n时 ,其执行代价也是最优的

一种基于PVM的Multisets并行归并算法

Multisets排序是指对具有k个不同关键字的n个数据进行排序(0<k<n)。本文提出一种在分布存储计算机系统、基于消息传递环境下,以加法运算为基础的稳定的归并并行算法,该算法实现对Multisets的排序,其时间复杂度为O(n/p log P+k log p+4p+n/2)。

Weighted Parameterized Correlation Coefficients of Indeterminacy Fuzzy Multisets and Their Multicriteria Group Decision Making Method with Different Decision Risks

Real-life data introduce noise,uncertainty,and imprecision to statistical projects;it is advantageous to consider strategies to overcome these information expressions and processing problems.Neutrosophic(indeterminate)numbers can flexibly and conveniently represent the hybrid information of the partial determinacy and partial indeterminacy in an indeterminate setting,while a fuzzy multiset is a vital mathematical tool in the expression and processing of multi-valued fuzzy information with different and/or same fuzzy values.If neutrosophic numbers are introduced into fuzzy sequences in a fuzzy multiset,the introduced neutrosophic number sequences can be constructed as the neutrosophic number multiset or indeterminate fuzzy multiset.Motivated based on the idea,this study first proposes an indeterminate fuzzy multiset,where each element in a universe set can be repeated more than once with the different and/or identical indeterminate membership values.Then,we propose the parameterized correlation coefficients of indeterminate fuzzy multisets based on the de-neutrosophication of transforming indeterminate fuzzy multisets into the parameterized fuzzy multisets by a parameter(the parameterized de-neutrosophication method).Since indeterminate decision-making issues need to be handled by an indeterminate decision-making method,a group decision-making method using the weighted parameterized correlation coefficients of indeterminate fuzzy multisets is developed along with decision makers’different decision risks(small,moderate,and large risks)so as to handle multicriteria group decision-making problems in indeterminate fuzzy multiset setting.Finally,the developed group decision-making approach is used in an example on a selection problem of slope design schemes for an open-pit mine to demonstrate its usability and flexibility in the indeterminate group decision-making problem with indeterminate fuzzy multisets.

Multiple moving sources passive location based on multiset canonical correlation analysis

To solve the problem of multiple moving sources passive location, a novel blind source separa- tion （BSS） algorithm based on the muhiset canonical correlation analysis （MCCA） is presented by exploiting the different temporal structure of uncorrelated source signals first, and then on the basis of this algorithm, a novel multiple moving sources passive location method is proposed using time difference of arrival （TDOA） and frequency difference of arrival （FDOA） measurements. The key technique of this location method is TDOA and FDOA joint estimation, which is based on BSS. By blindly separating mixed signals from multiple moving sources, the multiple sources location problem can be translated to each source location in turn, and the effect of interference and noise can also he removed. The simulation results illustrate that the performance of the MCCA algorithm is very good with relatively light computation burden, and the location algorithm is relatively simple and effective.

On Addition of Sets in Boolean Space

In many problems of combinatory analysis, operations of addition of sets are used (sum, direct sum, direct product etc.). In the present paper, as well as in the preceding one [1], some properties of addition operation of sets (namely, Minkowski addition) in Boolean space Bn are presented. Also, sums and multisums of various “classical figures” as: sphere, layer, interval etc. are considered. The obtained results make possible to describe multisums by such characteristics of summands as: the sphere radius, weight of layer, dimension of interval etc. using the methods presented in [2], as well as possible solutions of the equation X+Y=A, where , are considered. In spite of simplicity of the statement of the problem, complexity of its solutions is obvious at once, when the connection of solutions with constructions of equidistant codes or existence the Hadamard matrices is apparent. The present paper submits certain results (statements) which are to be the ground for next investigations dealing with Minkowski summation operations of sets in Boolean space.

MULTIPLE CRITERIA DECISION MAKING： DISCORDANT PREFERENCES AND PROBLEM DESCRIPTION

There are many practical decision problems where decision makers＇ preferences may be inconsistent and contradictory. In this paper, new methods for ordering and classifying multi-attribute objects by discordant collective preferences are suggested. These methods are based on the theory of multiset metric spaces. The proposed techniques are applied to ranking companies and a competitive selection of projects, which are estimated by several experts upon multiple qualitative criteria.

Algorithms for enumeration problem of linear congruence modulo m as sum of restricted partition numbers

We consider the congruence x1＋ x2 ＋… ＋ xr - c （mod m）, wherem and r are positive integers and c ∈Zm ：= {0, 1, ..., m- 1} （m ≥ 2）. Recently,W.-S. thou, T. X. He,and Peter J.-S. Shiue considered the enumerationproblems of this congruence, namely, the number of solutions with the restriction x1≤~ x2≤ ... ≤ xr, and got some properties and a neat formula ofthe solutions. Due to the lack of a simple computational method for calculating the number of the solution of the congruence, we provide an algebraic and a recursive algorithms for those numbers. The former one can also give a new and simple approach to derive some properties of solution numbers.