Soft -ideals of soft BCI-algebras

Molodtsov [D. Molodtsov, Soft set theory–First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Jun [Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413] applied first the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. In this paper we introduce the notion of soft p-ideals and p-idealistic soft BCI-algebras, and then investigate their basic properties. Using soft sets, we give characterizations of (fuzzy) p-ideals in BCI-algebras. We provide relations between fuzzy p-ideals and p-idealistic soft BCI-algebras.     

Intuitionistic fuzzy left k-ideals of semirings

We introduce the notion of intuitionistic fuzzy left k-ideals of semirings and investigate their properties and connections with left k-ideals of the corresponding semirings. Next we give some important characterizations of intuitionistic fuzzy left k-ideals of different type and describe various methods of constructions of such intuitionistic fuzzy sets. Finally, we propose some natural classification of intuitionistic fuzzy left k-ideals. The research work was supported by PUCIT.     

一种基于K-Means局部最优性的高效聚类算法

K-Means聚类算法只能保证收敛到局部最优,从而导致聚类结果对初始代表点的选择非常敏感.许多研究工作都着力于降低这种敏感性.然而,K-Means的局部最优和结果敏感性却构成了K-MeanSCAN聚类算法的基础.K-MeanSCAN算法对数据集进行多次采样和K-Means预聚类以产生多组不同的聚类结果,来自不同聚类结果的子簇之间必然会存在交集.算法的核心思想是,利用这些交集构造出关于子簇的加权连通图,并根据连通性合并子簇.理论和实验证明,K-MeanScan算法可以在很大程度上提高聚类结果的质量和算法的效率.     

Continuous K-Nearest Neighbor Query for Moving Objects with Uncertain Velocity

One of the most important queries in spatio-temporal databases that aim at managing moving objects efficiently is the continuous K-nearest neighbor (CKNN) query. A CKNN query is to retrieve the K-nearest neighbors (KNNs) of a moving user at each time instant within a user-given time interval [t _s , t _e ]. In this paper, we investigate how to process a CKNN query efficiently. Different from the previous related works, our work relieves the past assumption, that an object moves with a fixed velocity, by allowing that the velocity of the object can vary within a known range. Due to the introduction of this uncertainty on the velocity of each object, processing a CKNN query becomes much more complicated. We will discuss the complications incurred by this uncertainty and propose a cost-effective P² KNN algorithm to find the objects that could be the KNNs at each time instant within the given query time interval. Besides, a probability-based model is designed to quantify the possibility of each object being one of the KNNs. Comprehensive experiments demonstrate the efficiency and the effectiveness of the proposed approach.

Geno-mathematical identification of the multi-layer perceptron

In this paper, we will focus on the use of the three-layer backpropagation network in vector-valued time series estimation problems. The neural network provides a framework for noncomplex calculations to solve the estimation problem, yet the search for optimal or even feasible neural networks for stochastic processes is both time consuming and uncertain. The backpropagation algorithm—written in strict ANSI C—has been implemented as a standalone support library for the genetic hybrid algorithm (GHA) running on any sequential or parallel main frame computer. In order to cope with ill-conditioned time series problems, we extended the original backpropagation algorithm to a K nearest neighbors algorithm (K-NARX), where the number K is determined genetically along with a set of key parameters. In the K-NARX algorithm, the terminal solution at instant t can be used as a starting point for the next t, which tends to stabilize the optimization process when dealing with autocorrelated time series vectors. This possibility has proved to be especially useful in difficult time series problems. Following the prevailing research directions, we use a genetic algorithm to determine optimal parameterizations for the network, including the lag structure for the nonlinear vector time series system, the net structure with one or two hidden layers and the corresponding number of nodes, type of activation function (currently the standard logistic sigmoid, a bipolar transformation, the hyperbolic tangent, an exponential function and the sine function), the type of minimization algorithm, the number K of nearest neighbors in the K-NARX procedure, the initial value of the Levenberg–Marquardt damping parameter and the value of the neural learning (stabilization) coefficient α. We have focused on a flexible structure allowing addition of, e.g., new minimization algorithms and activation functions in the future. We demonstrate the power of the genetically trimmed K-NARX algorithm on a representative data set.     

Special types of intuitionistic fuzzy left <Emphasis Type="Italic">h</Emphasis>-ideals of hemirings

Characteristic, normal and completely normal intuitionistic fuzzy left h-ideals of hemirings are described.     

Partial match queries in relaxed multidimensional search trees

Partial match queries arise frequently in the context of large databases, where each record contains a distinct multidimensional key, that is, the key of each record is aK-tuple of values. The components of a key are called thecoordinates orattributes of the key. In a partial match query we specify the value ofs attributes, 0<s<K, and leave the remainingK —s attributes unspecified. The goal is to retrieve all the records in the database that match the specified attributes. In this paper we present several results about the average performance and variance of partial matches in relaxedK-dimensional trees (search trees and digital tries). These data structures are variants of the well knownK d-trees andK d-tries. In relaxed trees the sequence of attributes used to guide a query is explicitly stored at the nodes of the tree and randomly generated and, in general, will be different for different search paths. In the standard variants, the sequence of attributes that guides a query examines the attributes in a cyclic fashion, fixed and identical for all search paths. We show that the probabilistic analysis of the relaxed multidimensional trees is very similar to that of standardK d-trees andK d-tries, and also to the analysis of quadtrees. In fact, besides the average cost and variance of partial match in relaxedK d-trees andK d-tries, we also obtain the variance of partial matches in two-dimensional quadtrees. We also compute the average cost of partial matches in other relaxed multidimensional digital tries, namely, relaxedK d-Patricia and relaxedK d-digital search trees. This research was supported by Acciones Integradas Hispano-Austríacas HU1997-0016 (Austrian-Spanish Scientific Exchange Program). The first author was also supported by ESPRIT LTR 20244 (ALCOM IT), CICYT TIC97-1475-CE, DGES PB95-0787 (KOALA), and CIRIT 1997SGR-00366 (SGR). The second author was also supported by the Austrian Research Society (FWF) under Project P12599-MAT. Online publication October 13, 2000.     

Semirings and pseudo MV algebras

In this paper, we describe the relationships between pseudo MV algebras and semirings. We also give definitions of automata on lattice ordered semirings, prove that the family of K-Languages is closed under union, and discuss the conditions for the closedness of families of K-languages under intersection, generalized intersection and reversal operations.     

On the strict logic foundation of fuzzy reasoning

This paper focuses on the logic foundation of fuzzy reasoning. At first, a new complete first-order fuzzy predicate calculus system K^* corresponding to the formal system L^* is built. Based on the many-sort system K_ms^* corresponding to K^*, the triple I methods of FMP and FMT for fuzzy reasoning and their consistency are formalized, thus fuzzy reasoning is put completely and rigorously into the logic framework of fuzzy logic.The author is indebted to anonymous referee for his useful comments which have helped to improve the paper.     

States on <Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript> algebras

The aim of this paper is to introduce the notion of states on R ₀ algebras and investigate some of their properties. We prove that every R ₀ algebra possesses at least one state. Moreover, we investigate states on weak R ₀ algebras and give some examples to show that, in contrast to R ₀ algebras, there exist weak R ₀ algebras which have no states. We also derive the condition under which finite linearly ordered weak R ₀ algebras have a state. This work is supported by NSFC (No.60605017).     

一种基于彩色编码技术的基序发现算法

从DNA序列中发现基序是生物计算中的一个重要问题,序列条数K=20包含基序用例的序列条数k=16的(l,d)-(K-k)问题(记作(l,d)-(20-16)问题)是目前生物学家十分关注的基序发现问题.针对该问题提出了一种基于彩色编码技术的SDA(sample-driven algorithm)搜索算法--彩色编码基序搜索算法(color coding motif finding algorithm,简称CCMF算法).它利用彩色编码技术将该问题转化为(l,d)-(16-16)问题,再采用分治算法和分支定界法来求解.在解决将(l,d)-(20-16)问题转化为(l,d)-(16-16)问题时,CCMF算法利用彩色编码技术将4 845个组合降低到403个着色,这将极大地提高算法的整体运行效率.使用模拟数据和生物数据进行测试的结果表明,CCMF算法能够快速发现所有(l,d)-(20-16)问题的基序模型和基序用例,具有优于其他算法的综合性能评价,能够用于真实的基序发现问题.同时,通过修改着色方案,CCMF算法可以用于求解一般的(l,d)-(K-k)问题,其中,k＜K.     

Duality for nondifferentiable static multiobjective variational problems involving generalized (F, ?)-Convex functions

Using the generalized Schwarz inequality, we establish some weak duality theorems for nondifferentiable static multiobjective variational problems involving generalized (F, )-convex functions. Later in the sequel, we introduce three dual models for the nondifferentiable static multiobjective fractional variational problems and derive weak duality results for such programs.     

An Efficient Parallel Strategy for ComputingK-Terminal Reliability and Finding Most Vital Edges in 2-Trees and Partial 2-Trees

In this paper, we first develop a parallel algorithm for computingK-terminal reliability, denoted byR(G_K), in 2-trees. Based on this result, we can also computeR(G_K) in partial 2-trees using a method that transforms, in parallel, a given partial 2-tree into a 2-tree. Finally, we solve the problem of finding most vital edges with respect toK-terminal reliability in partial 2-trees. Our algorithms takeO(log n) time withC(m, n) processors on a CRCW PRAM, whereC(m, n) is the number of processors required to find the connected components of a graph withmedges andnvertices in logarithmic time.     

Harmony K-means algorithm for document clustering

Fast and high quality document clustering is a crucial task in organizing information, search engine results, enhancing web crawling, and information retrieval or filtering. Recent studies have shown that the most commonly used partition-based clustering algorithm, the K-means algorithm, is more suitable for large datasets. However, the K-means algorithm can generate a local optimal solution. In this paper we propose a novel Harmony K-means Algorithm (HKA) that deals with document clustering based on Harmony Search (HS) optimization method. It is proved by means of finite Markov chain theory that the HKA converges to the global optimum. To demonstrate the effectiveness and speed of HKA, we have applied HKA algorithms on some standard datasets. We also compare the HKA with other meta-heuristic and model-based document clustering approaches. Experimental results reveal that the HKA algorithm converges to the best known optimum faster than other methods and the quality of clusters are comparable.     

Relationship between the attenuation of downwelling irradiance at 490 nm with the attenuation of PAR (400 nm-700 nm) in the Baltic Sea

The vertical attenuation coefficient of diffuse downwelling irradiance at 490 nm (K_d 490) is a parameter that we routinely derive from SeaWiFS images of the Baltic Sea. Here, through model simulations, we examine the relationship between K_d(490), and the vertical attenuation coefficient of PAR (K_d PAR), as this later coefficient determines the light available for aquatic photosynthesis. A simple semi-analytical model is used to predict K_d(490) and K_d(PAR), as a function of the concentrations of chlorophyll, colored dissolved organic material (CDOM), suspended inorganic, and suspended organic particulate material. A series of model simulations based on variations in these optically significant constituents over a range realistic for the Baltic Sea, are used to define the relationship between the two attenuation coefficients.

Kd(PAR)=0.6677Kd^0.6763(490).     

A discrete-time dynamic K-winners-take-all neural circuit

A discrete-time mathematical model of K-winners-take-all (KWTA) neural circuit that can quickly identify the K-winning from N neurons, where 1K<N, whose input signals are larger than that of remaining N−K neurons, is given and analyzed. A functional block scheme of the circuit is presented. For N competitors, such circuit is composed of N feedforward and one feedback hard-limiting neurons that are used to determine the dynamic shift of input signals. The circuit has low computational and hardware implementation complexity, high speed of signal processing, can process signals of any finite range, possesses signal order preserving property and does not require resetting and corresponding supervisory circuit that additionally increases a speed of signal processing.     

基于熵加权K-means全局信息聚类的高光谱图像分类

目的 高光谱图像波段数目巨大，导致在解译及分类过程中出现“维数灾难”的现象。针对该问题，在K-means聚类算法基础上，考虑各个波段对不同聚类的重要程度，同时顾及类间信息，提出一种基于熵加权K-means全局信息聚类的高光谱图像分类算法。方法 首先，引入波段权重，用来刻画各个波段对不同聚类的重要程度，并定义熵信息测度表达该权重。其次，为避免局部最优聚类，引入类间距离测度实现全局最优聚类。最后，将上述两类测度引入K-means聚类目标函数，通过最小化目标函数得到最优分类结果。结果 为了验证提出的高光谱图像分类方法的有效性，对Salinas高光谱图像和Pavia University高光谱图像标准图中的地物类别根据其光谱反射率差异程度进行合并，将合并后的标准图作为新的标准分类图。分别采用本文算法和传统K-means算法对Salinas高光谱图像和Pavia University高光谱图像进行实验，并定性、定量地评价和分析了实验结果。对于图像中合并后的地物类别，光谱反射率差异程度大，从视觉上看，本文算法较传统K-means算法有更好的分类结果；从分类精度看，本文算法的总精度分别为92.20%和82.96%， K-means算法的总精度分别为83.39%和67.06%，较K-means算法增长8.81%和15.9%。结论 提出一种基于熵加权K-means全局信息聚类的高光谱图像分类算法，实验结果表明，本文算法对高光谱图像中具有不同光谱反射率差异程度的各类地物目标均能取得很好的分类结果。     

Maximum <Emphasis Type="Italic">k</Emphasis>-Splittable <Emphasis Type="Italic">s</Emphasis>,<Emphasis Type="Italic">t</Emphasis>-Flows

Given a graph with a source and a sink node, the NP-hard maximum k-splittable s,t-flow (M k SF) problem is to find a flow of maximum value from s to t with a flow decomposition using at most k paths. The multicommodity variant of this problem is a natural generalization of disjoint paths and unsplittable flow problems. Constructing a k-splittable flow requires two interdepending decisions. One has to decide on k paths (routing) and on the flow values for the paths (packing). We give efficient algorithms for computing exact and approximate solutions by decoupling the two decisions into a first packing step and a second routing step. Usually the routing is considered before the packing. Our main contributions are as follows: (i) We show that for constant k a polynomial number of packing alternatives containing at least one packing used by an optimal M k SF solution can be constructed in polynomial time. If k is part of the input, we obtain a slightly weaker result. In this case we can guarantee that, for any fixed ε>0, the computed set of alternatives contains a packing used by a (1−ε)-approximate solution. The latter result is based on the observation that (1−ε)-approximate flows only require constantly many different flow values. We believe that this observation is of interest in its own right. (ii) Based on (i), we prove that, for constant k, the M k SF problem can be solved in polynomial time on graphs of bounded treewidth. If k is part of the input, this problem is still NP-hard and we present a polynomial time approximation scheme for it.     

Extensions of fuzzy hyperideals in <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">V</Emphasis></Subscript>-semigroups

The object of the present paper is the investigation and study of (fuzzy) hyperideals in H _v - semigroups. Regular equivalence relations play in H _v - semigroup theory a role analogous to congruences in semigroup theory, so we introduce fuzzy regular equivalence relations on H _v -semigroups and then we study fuzzy Rees regular relations on H _v -semigroups. Using this ideas, we establish a relation between fuzzy hyperideal of an H _v -semigroup H and fuzzy hyperideal of a quotient H _v -semigroup of H. Some characterizations of them are then shown.      

Detecting Communities in <Emphasis Type="Italic">K</Emphasis>-Partite <Emphasis Type="Italic">K</Emphasis>-Uniform (Hyper)Networks

In social tagging systems such as Delicious and Flickr,users collaboratively manage tags to annotate resources.Naturally,a social tagging system can be modeled as a (user,tag,resource) hypernetwork,where there are three different types of nodes,namely users,resources and tags,and each hyperedge has three end nodes,connecting a user,a resource and a tag that the user employs to annotate the resource.Then how can we automatically cluster related users,resources and tags,respectively? This is a problem of community detection in a 3-partite,3-uniform hypernetwork.More generally,given a K-partite K-uniform (hyper)network,where each (hyper)edge is a K-tuple composed of nodes of K different types,how can we automatically detect communities for nodes of different types? In this paper,by turning this problem into a problem of finding an efficient compression of the (hyper)network’s structure,we propose a quality function for measuring the goodness of partitions of a K-partite K-uniform (hyper)network into communities,and develop a fast community detection method based on optimization.Our method overcomes the limitations of state of the art techniques and has several desired properties such as comprehensive,parameter-free,and scalable.We compare our method with existing methods in both synthetic and real-world datasets.